Celebrating 19 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “Truth is ever to be found in simplicity, and not in the multiplicity and confusion of things.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index A > Category: Analysis

Analysis Quotes (166 quotes)
Analysing Quotes, Analyzing Quotes, Analysed Quotes, Analyzed Quotes, Analytical Quotes

An diesen Apparate ist nichts neu als seine Einfachkeit und die vollkommene zu Verlaessigkeit, welche er gewaehst.
In this apparatus is nothing new but its simplicity and thorough trustworthiness.
On his revolutionary method of organic analysis.
Poggendorf's Annalen, (1831), 21, 4. Trans. W. H. Brock.
Science quotes on:  |  Apparatus (37)  |  Organic Chemistry (33)  |  Reliability (15)  |  Simplicity (147)

Bei solchen chemischen Untersuchungen, die man zersetzende oder zergliedernde nennt, kommt es zunächst darauf an, zu ermitteln, mit welchen Stoffen man es zu thun hat, oder um chemisch zu reden, welche Stoffe in einem bestimmten Gemenge oder Gemisch enthalten sind. Hierzu bedient man sich sogenannter gegenwirkender Mittel, d. h. Stoffe, die bestimmte Eigenschaften und Eigenthümlichkeiten besitzen und die man aus Ueberlieferung oder eigner Erfahrung genau kennt, so daß die Veränderungen, welche sie bewirken oder erleiden, gleichsam die Sprache sind, mit der sie reden und dadurch dem Forscher anzeigen, daß der und der bestimmte Stoff in der fraglichen Mischung enthalten sei.
In the case of chemical investigations known as decompositions or analyses, it is first important to determine exactly what ingredients you are dealing with, or chemically speaking, what substances are contained in a given mixture or composite. For this purpose we use reagents, i.e., substances that possess certain properties and characteristics, which we well know from references or personal experience, such that the changes which they bring about or undergo, so to say the language that they speak thereby inform the researcher that this or that specific substance is present in the mixture in question.
From Zur Farben-Chemie Musterbilder für Freunde des Schönen und zum Gebrauch für Zeichner, Maler, Verzierer und Zeugdrucker [On Colour Chemistry...] (1850), Introduction. Translation tweaked by Webmaster from version in Herbert and W. Roesky and Klaud Möckel, translated from the original German by T.N. Mitchell and W.E. Russey, Chemical Curiosities: Spectacular Experiments and Inspired Quotes (1996), 1.
Science quotes on:  |  Change (364)  |  Characteristic (96)  |  Chemical (79)  |  Composite (4)  |  Contain (67)  |  Decomposition (12)  |  Determination (57)  |  Exactly (13)  |  Experience (342)  |  Inform (16)  |  Ingredient (14)  |  Investigation (176)  |  Know (556)  |  Language (228)  |  Mixture (26)  |  Personal (66)  |  Present (176)  |  Property (126)  |  Question (404)  |  Reagent (5)  |  Reference (33)  |  Researcher (17)  |  Speak (92)  |  Specific (37)  |  Substance (87)  |  Undergo (14)

[Recalling Professor Ira Remsen's remarks (1895) to a group of his graduate students about to go out with their degrees into the world beyond the university:]
He talked to us for an hour on what was ahead of us; cautioned us against giving up the desire to push ahead by continued study and work. He warned us against allowing our present accomplishments to be the high spot in our lives. He urged us not to wait for a brilliant idea before beginning independent research, and emphasized the fact the Lavoisier's first contribution to chemistry was the analysis of a sample of gypsum. He told us that the fields in which the great masters had worked were still fruitful; the ground had only been scratched and the gleaner could be sure of ample reward.
Quoted in Frederick Hutton Getman, The Life of Ira Remsen (1980), 73.
Science quotes on:  |  Accomplishment (80)  |  Ample (4)  |  Brilliance (10)  |  Chemist (89)  |  Chemistry (252)  |  Contribution (60)  |  Desire (142)  |  Field (171)  |  Fruitful (43)  |  Graduation (4)  |  Ground (90)  |  Gypsum (2)  |  Idea (580)  |  Independent (67)  |  Antoine-Laurent Lavoisier (40)  |  Master (98)  |  Ira Remsen (6)  |  Research (590)  |  Reward (49)  |  Scratch (7)  |  Study (476)  |  Work (635)

A careful analysis of the process of observation in atomic physics has shown that the subatomic particles have no meaning as isolated entities, but can only be understood as interconnections between the preparation of an experiment and the subsequent measurement.
The Tao of Physics: An Exploration of the Parallels Between Modern Physics (1975), 68.
Science quotes on:  |  Atomic Physics (7)  |  Care (95)  |  Entity (31)  |  Experiment (602)  |  Interconnection (7)  |  Isolation (26)  |  Meaning (113)  |  Measurement (161)  |  Observation (450)  |  Particle (99)  |  Preparation (43)  |  Process (267)  |  Subatomic (7)  |  Subsequent (19)  |  Understanding (325)

A discovery in science, or a new theory, even when it appears most unitary and most all-embracing, deals with some immediate element of novelty or paradox within the framework of far vaster, unanalysed, unarticulated reserves of knowledge, experience, faith, and presupposition. Our progress is narrow; it takes a vast world unchallenged and for granted. This is one reason why, however great the novelty or scope of new discovery, we neither can, nor need, rebuild the house of the mind very rapidly. This is one reason why science, for all its revolutions, is conservative. This is why we will have to accept the fact that no one of us really will ever know very much. This is why we shall have to find comfort in the fact that, taken together, we know more and more.
Science and the Common Understanding (1954), 53-4.
Science quotes on:  |  Acceptance (45)  |  Articulation (2)  |  Challenge (61)  |  Comfort (49)  |  Conservative (11)  |  Discovery (680)  |  Element (162)  |  Experience (342)  |  Fact (733)  |  Faith (157)  |  Framework (20)  |  Granted (5)  |  House (43)  |  Immediate (43)  |  Knowledge (1306)  |  Mind (760)  |  Narrow (48)  |  Need (287)  |  Novelty (23)  |  Paradox (43)  |  Progress (368)  |  Rapidly (13)  |  Reason (471)  |  Rebuild (4)  |  Reserve (15)  |  Revolution (69)  |  Scope (23)  |  Theory (696)  |  Unitary (2)  |  Vastness (11)

A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
In Time Enough for Love: The Lives of Lazarus Long (1973), 265.
Science quotes on:  |  Account (68)  |  Act (117)  |  Alone (106)  |  Balance (55)  |  Bone (63)  |  Building (52)  |  Butcher (8)  |  Change (364)  |  Comfort (49)  |  Computer (105)  |  Cooking (7)  |  Cooperation (30)  |  Death (302)  |  Design (115)  |  Diaper (2)  |  Efficiency (30)  |  Equation (96)  |  Fight (44)  |  Gallant (2)  |  Hog (4)  |  Human (550)  |  Insect (64)  |  Invasion (8)  |  Manure (8)  |  Meal (16)  |  New (496)  |  Order (242)  |  Pitch (7)  |  Plan (87)  |  Problem (497)  |  Program (52)  |  Set (99)  |  Ship (44)  |  Solution (216)  |  Sonnet (4)  |  Specialization (17)  |  Wall (28)  |  Writing (81)

A statistical analysis, properly conducted, is a delicate dissection of uncertainties, a surgery of suppositions.
In Facts from Figures (1951), 3.
Science quotes on:  |  Conduct (31)  |  Delicate (21)  |  Dissection (29)  |  Proper (38)  |  Statistics (147)  |  Supposition (37)  |  Surgery (43)  |  Uncertainty (42)

A student who wishes now-a-days to study geometry by dividing it sharply from analysis, without taking account of the progress which the latter has made and is making, that student no matter how great his genius, will never be a whole geometer. He will not possess those powerful instruments of research which modern analysis puts into the hands of modern geometry. He will remain ignorant of many geometrical results which are to be found, perhaps implicitly, in the writings of the analyst. And not only will he be unable to use them in his own researches, but he will probably toil to discover them himself, and, as happens very often, he will publish them as new, when really he has only rediscovered them.
From 'On Some Recent Tendencies in Geometrical Investigations', Rivista di Matematica (1891), 43. In Bulletin American Mathematical Society (1904), 443.
Science quotes on:  |  Discover (199)  |  Divide (40)  |  Genius (249)  |  Geometer (24)  |  Geometry (232)  |  Ignorant (40)  |  Implicit (7)  |  Instrument (95)  |  Modern (162)  |  New (496)  |  Possess (56)  |  Powerful (68)  |  Progress (368)  |  Publish (34)  |  Research (590)  |  Result (389)  |  Student (203)  |  Study (476)  |  Study And Research In Mathematics (61)  |  Toil (18)  |  Whole (192)  |  Writing (81)

Accordingly, we find Euler and D'Alembert devoting their talent and their patience to the establishment of the laws of rotation of the solid bodies. Lagrange has incorporated his own analysis of the problem with his general treatment of mechanics, and since his time M. Poinsôt has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligent propositions supersede equations.
J. C. Maxwell on Louis Poinsôt (1777-1859) in 'On a Dynamical Top' (1857). In W. D. Niven (ed.), The Scientific Papers of James Clerk Maxwell (1890), Vol. 1, 248.
Science quotes on:  |  Calculus (51)  |  Jean le Rond D’Alembert (11)  |  Equation (96)  |  Establishment (35)  |  Leonhard Euler (35)  |  Idea (580)  |  Count Joseph-Louis de Lagrange (26)  |  Law (515)  |  Mechanics (57)  |  Patience (39)  |  Louis Poinsot (3)  |  Problem (497)  |  Proposition (83)  |  Rotation (7)  |  Symbol (73)  |  Talent (63)

Again and again in reading even his [William Thomson] most abstract writings one is struck by the tenacity with which physical ideas control in him the mathematical form in which he expressed them. An instance of this is afforded by … an example of a mathematical result that is, in his own words, “not instantly obvious from the analytical form of my solution, but which we immediately see must be the case by thinking of the physical meaning of the result.”
As given in Life of Lord Kelvin (1910), Vol. 2, 1136. The ellipsis gives the reference to the quoted footnote, to a passage in his Mathematical and Physical Papers, Vol. 1, 457. [Note: William Thomson, later became Lord Kelvin. —Webmaster]
Science quotes on:  |  Abstract (86)  |  Afford (17)  |  Control (114)  |  Idea (580)  |  Immediately (23)  |  Instantly (6)  |  Baron William Thomson Kelvin (70)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1205)  |  Meaning (113)  |  Obvious (83)  |  Physical (134)  |  Result (389)  |  Solution (216)  |  Tenacity (7)  |  Think (347)  |  Understand (340)  |  Writing (81)

All that can be said upon the number and nature of elements is, in my opinion, confined to discussions entirely of a metaphysical nature. The subject only furnishes us with indefinite problems, which may be solved in a thousand different ways, not one of which, in all probability, is consistent with nature. I shall therefore only add upon this subject, that if, by the term elements, we mean to express those simple and indivisible atoms of which matter is composed, it is extremely probable we know nothing at all about them; but, if we apply the term elements, or principles of bodies, to express our idea of the last point which analysis is capable of reaching, we must admit, as elements, all the substances into which we are capable, by any means, to reduce bodies by decomposition.
Elements of Chemistry (1790), trans. R. Kerr, Preface, xxiv.
Science quotes on:  |  Atom (280)  |  Composition (60)  |  Decomposition (12)  |  Element (162)  |  Idea (580)  |  Indivisible (12)  |  Knowledge (1306)  |  Matter (343)  |  Metaphysics (36)  |  Principle (292)  |  Problem (497)  |  Reduction (41)  |  Solution (216)  |  Substance (87)

Although we often hear that data speak for themselves, their voices can be soft and sly.
In Frederick Mosteller, Stephen E. Fienberg and Robert E. K. Rourke, Beginning Statistics with Data Analysis (1983), 234.
Science quotes on:  |  Data (120)  |  Voice (51)

Analysis and natural philosophy owe their most important discoveries to this fruitful means, which is called induction. Newton was indebted to it for his theorem of the binomial and the principle of universal gravity.
In Frederick Wilson Truscott (trans.) and Frederick Lincoln Emory (trans.), A Philosophical Essay on Probabilities (1902), 176.
Science quotes on:  |  Binomial Theorem (3)  |  Discovery (680)  |  Fruitful (43)  |  Important (205)  |  Indebted (7)  |  Induction (60)  |  Law Of Gravitation (19)  |  Means (176)  |  Natural Philosophy (31)  |  Nature Of Mathematics (80)  |  Sir Isaac Newton (333)

And indeed I am not humming,
Thus to sing of Cl-ke and C-ming,
Who all the universe surpasses
in cutting up and making gases;
With anatomy and chemics,
Metaphysics and polemics,
Analyzing and chirugery,
And scientific surgery …
H-slow's lectures on the cabbage
Useful are as roots of Babbage;
Fluxions and beet-root botany,
Some would call pure monotony.
Magazine
Punch in Cambridge (28 Jan 1834). In Mark Weatherall, Gentlemen, Scientists, and Medicine at Cambridge 1800-1940 (2000), Vol. 3,77. The professors named were William Clark (anatomy), James Cumming (chemistry) and Johns Stephens Henslow (botany).
Science quotes on:  |  Anatomy (63)  |  Charles Babbage (54)  |  Botany (51)  |  Cabbage (5)  |  Chemistry (252)  |  Cutting (6)  |  Fluxion (4)  |  Gas (50)  |  John Stevens Henslow (2)  |  Humming (3)  |  Lecture (68)  |  Metaphysics (36)  |  Monotony (3)  |  Poem (92)  |  Root (61)  |  Surgery (43)  |  Surpassing (7)  |  Universe (686)  |  Usefulness (77)

As in Mathematicks, so in Natural Philosophy, the Investigation of difficult Things by the Method of Analysis, ought ever to precede the Method of Composition. This Analysis consists in making Experiments and Observations, and in drawing general Conclusions from them by Induction, and admitting of no Objections against the Conclusions, but such as are taken from Experiments, or other certain Truths. For Hypotheses are not to be regarded in experimental Philosophy.
From Opticks, (1704, 2nd ed. 1718), Book 3, Query 31, 380.
Science quotes on:  |  Conclusion (160)  |  Experiment (602)  |  Hypothesis (252)  |  Induction (60)  |  Investigation (176)  |  Mathematics (1205)  |  Natural Philosophy (31)  |  Observation (450)  |  Truth (928)

As soon as we touch the complex processes that go on in a living thing, be it plant or animal, we are at once forced to use the methods of this science [chemistry]. No longer will the microscope, the kymograph, the scalpel avail for the complete solution of the problem. For the further analysis of these phenomena which are in flux and flow, the investigator must associate himself with those who have labored in fields where molecules and atoms, rather than multicellular tissues or even unicellular organisms, are the units of study.
'Experimental and Chemical Studies of the Blood with an Appeal for More Extended Chemical Training for the Biological and Medical Investigator', Science (6 Aug 1915), 42, 176.
Science quotes on:  |  Animal (359)  |  Atom (280)  |  Biochemistry (46)  |  Biology (168)  |  Cell (137)  |  Chemistry (252)  |  Complexity (91)  |  Flow (42)  |  Flux (13)  |  Investigator (35)  |  Life (1131)  |  Method (239)  |  Microscope (74)  |  Molecule (133)  |  Organism (150)  |  Phenomenon (278)  |  Plant (200)  |  Problem (497)  |  Process (267)  |  Scalpel (2)  |  Solution (216)  |  Study (476)  |  Tissue (27)

Behind and permeating all our scientific activity, whether in critical analysis or in discovery, there is an elementary and overwhelming faith in the possibility of grasping the real world with out concepts, and, above all, faith in the truth over which we have no control but in the service of which our rationality stands or falls. Faith and intrinsic rationality are interlocked with one another
Christian Theology of Scientific Culture (1981), 63. In Vinoth Ramachandra, Subverting Global Myths: Theology and the Public Issues Shaping our World (2008), 187.
Science quotes on:  |  Activity (135)  |  Behind (38)  |  Concept (146)  |  Control (114)  |  Critical (41)  |  Discovery (680)  |  Elementary (45)  |  Faith (157)  |  Fall (120)  |  Grasp (60)  |  Interlock (3)  |  Intrinsic (12)  |  Overwhelming (21)  |  Permeate (2)  |  Possibility (116)  |  Rationality (16)  |  Real World (14)  |  Scientific (236)  |  Service (64)  |  Stand (108)  |  Truth (928)

Bertrand, Darboux, and Glaisher have compared Cayley to Euler, alike for his range, his analytical power, and, not least, for his prolific production of new views and fertile theories. There is hardly a subject in the whole of pure mathematics at which he has not worked.
In Proceedings of London Royal Society (1895), 58, 21.
Science quotes on:  |  Joseph Bertrand (6)  |  Arthur Cayley (17)  |  Compare (38)  |  Leonhard Euler (35)  |  Fertile (16)  |  James Whitbread Lee Glaisher (3)  |  Mathematicians and Anecdotes (141)  |  New (496)  |  Power (366)  |  Production (117)  |  Prolific (5)  |  Pure Mathematics (65)  |  Range (57)  |  Subject (240)  |  Theory (696)  |  View (171)  |  Work (635)

Built up of carbon, hydrogen, oxygen, nitrogen, together with traces of a few other elements, yet of a complexity of structure that has hitherto resisted all attempts at complete analysis, protoplasm is at once the most enduring and the most easily destroyed of substances; its molecules are constantly breaking down to furnish the power for the manifestations of vital phenomena, and yet, through its remarkable property of assimilation, a power possessed by nothing else upon earth, it constantly builds up its substance anew from the surrounding medium.
In History of the Human Body (1919), 1.
Science quotes on:  |  Assimilation (11)  |  Attempt (126)  |  Carbon (49)  |  Complexity (91)  |  Destruction (85)  |  Enduring (6)  |  Furnish (42)  |  Hydrogen (44)  |  Manifestation (35)  |  Medium (12)  |  Molecule (133)  |  Nitrogen (19)  |  Oxygen (55)  |  Phenomenon (278)  |  Power (366)  |  Protoplasm (12)  |  Resistance (26)  |  Structure (225)  |  Substance (87)  |  Vital (39)

Cayley was singularly learned in the work of other men, and catholic in his range of knowledge. Yet he did not read a memoir completely through: his custom was to read only so much as would enable him to grasp the meaning of the symbols and understand its scope. The main result would then become to him a subject of investigation: he would establish it (or test it) by algebraic analysis and, not infrequently, develop it so to obtain other results. This faculty of grasping and testing rapidly the work of others, together with his great knowledge, made him an invaluable referee; his services in this capacity were used through a long series of years by a number of societies to which he was almost in the position of standing mathematical advisor.
In Proceedings of London Royal Society (1895), 58, 11-12.
Science quotes on:  |  Advisor (3)  |  Algebraic (5)  |  Capacity (64)  |  Catholic (8)  |  Arthur Cayley (17)  |  Completely (32)  |  Custom (30)  |  Develop (107)  |  Enable (46)  |  Establish (56)  |  Faculty (70)  |  Grasp (60)  |  Great (534)  |  Infrequent (2)  |  Invaluable (7)  |  Investigation (176)  |  Knowledge (1306)  |  Learned (24)  |  Main (28)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1205)  |  Mean (101)  |  Memoir (13)  |  Obtain (45)  |  Position (76)  |  Range (57)  |  Rapid (32)  |  Read (145)  |  Referee (6)  |  Result (389)  |  Scope (23)  |  Service (64)  |  Society (228)  |  Stand (108)  |  Subject (240)  |  Symbol (73)  |  Test (125)  |  Together (79)  |  Understand (340)  |  Work (635)

Chemistry affords two general methods of determining the constituent principles of bodies, the method of analysis, and that of synthesis. When, for instance, by combining water with alkohol, we form the species of liquor called, in commercial language, brandy or spirit of wine, we certainly have a right to conclude, that brandy, or spirit of wine, is composed of alkohol combined with water. We can produce the same result by the analytical method; and in general it ought to be considered as a principle in chemical science, never to rest satisfied without both these species of proofs. We have this advantage in the analysis of atmospherical air, being able both to decompound it, and to form it a new in the most satisfactory manner.
Elements of Chemistry (1790), trans. R. Kerr, 33.
Science quotes on:  |  Air (190)  |  Alcohol (18)  |  Atmosphere (79)  |  Brandy (2)  |  Chemistry (252)  |  Conclusion (160)  |  Decomposition (12)  |  Language (228)  |  Proof (245)  |  Synthesis (44)  |  Wine (28)

Chemistry works with an enormous number of substances, but cares only for some few of their properties; it is an extensive science. Physics on the other hand works with rather few substances, such as mercury, water, alcohol, glass, air, but analyses the experimental results very thoroughly; it is an intensive science. Physical chemistry is the child of these two sciences; it has inherited the extensive character from chemistry. Upon this depends its all-embracing feature, which has attracted so great admiration. But on the other hand it has its profound quantitative character from the science of physics.
In Theories of Solutions (1912), xix.
Science quotes on:  |  Admiration (44)  |  Air (190)  |  Alcohol (18)  |  Care (95)  |  Character (118)  |  Chemistry (252)  |  Child (252)  |  Enormous (41)  |  Experiment (602)  |  Extensive (18)  |  Feature (44)  |  Few (13)  |  Glass (44)  |  Inheritance (19)  |  Intensive (8)  |  Mercury (44)  |  Number (282)  |  Physical Chemistry (5)  |  Physics (348)  |  Property (126)  |  Quantitative (19)  |  Result (389)  |  Substance (87)  |  Through (3)  |  Water (293)

During a conversation with the writer in the last weeks of his life, Sylvester remarked as curious that notwithstanding he had always considered the bent of his mind to be rather analytical than geometrical, he found in nearly every case that the solution of an analytical problem turned upon some quite simple geometrical notion, and that he was never satisfied until he could present the argument in geometrical language.
In Proceedings London Royal Society, 63, 17.
Science quotes on:  |  Argument (82)  |  Conversation (26)  |  Curious (43)  |  Geometry (232)  |  Language (228)  |  Life (1131)  |  Mind (760)  |  Notion (59)  |  Present (176)  |  Problem (497)  |  Remark (27)  |  Satisfied (23)  |  Simple (178)  |  Solution (216)  |  Study And Research In Mathematics (61)  |  James Joseph Sylvester (58)  |  Turn (118)  |  Writer (46)

Either one or the other [analysis or synthesis] may be direct or indirect. The direct procedure is when the point of departure is known-direct synthesis in the elements of geometry. By combining at random simple truths with each other, more complicated ones are deduced from them. This is the method of discovery, the special method of inventions, contrary to popular opinion.
Ampère gives this example drawn from geometry to illustrate his meaning for “direct synthesis” when deductions following from more simple, already-known theorems leads to a new discovery. In James R. Hofmann, André-Marie Ampère (1996), 159. Cites Académie des Sciences Ampère Archives, box 261.
Science quotes on:  |  Combination (91)  |  Complication (24)  |  Contrary (34)  |  Deduction (69)  |  Departure (9)  |  Direct (84)  |  Discovery (680)  |  Element (162)  |  Geometry (232)  |  Indirect (10)  |  Invention (324)  |  Knowledge (1306)  |  Method (239)  |  Opinion (176)  |  Point (123)  |  Popular (29)  |  Procedure (25)  |  Random (25)  |  Simple (178)  |  Special (77)  |  Synthesis (44)  |  Truth (928)

Engineering is not merely knowing and being knowledgeable, like a walking encyclopedia; engineering is not merely analysis; engineering is not merely the possession of the capacity to get elegant solutions to non-existent engineering problems; engineering is practicing the art of the organizing forces of technological change ... Engineers operate at the interface between science and society.
In Bert Scalzo, et al., Database Benchmarking: Practical Methods for Oracle & SQL Server (2007), 37.
Science quotes on:  |  Engineering (141)  |  Knowledge (1306)  |  Progress (368)  |  Society (228)  |  Solution (216)  |  Technology (222)

Euclidean mathematics assumes the completeness and invariability of mathematical forms; these forms it describes with appropriate accuracy and enumerates their inherent and related properties with perfect clearness, order, and completeness, that is, Euclidean mathematics operates on forms after the manner that anatomy operates on the dead body and its members. On the other hand, the mathematics of variable magnitudes—function theory or analysis—considers mathematical forms in their genesis. By writing the equation of the parabola, we express its law of generation, the law according to which the variable point moves. The path, produced before the eyes of the student by a point moving in accordance to this law, is the parabola.
If, then, Euclidean mathematics treats space and number forms after the manner in which anatomy treats the dead body, modern mathematics deals, as it were, with the living body, with growing and changing forms, and thus furnishes an insight, not only into nature as she is and appears, but also into nature as she generates and creates,—reveals her transition steps and in so doing creates a mind for and understanding of the laws of becoming. Thus modern mathematics bears the same relation to Euclidean mathematics that physiology or biology … bears to anatomy.
In Die Mathematik die Fackelträgerin einer neuen Zeit (1889), 38. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 112-113.
Science quotes on:  |  Accord (36)  |  Accordance (10)  |  Accuracy (60)  |  Anatomy (63)  |  Appear (118)  |  Appropriate (28)  |  Bear (67)  |  Become (172)  |  Biology (168)  |  Body (247)  |  Change (364)  |  Clearness (11)  |  Completeness (15)  |  Consider (81)  |  Create (153)  |  Dead (57)  |  Deal (49)  |  Describe (57)  |  Enumerate (3)  |  Equation (96)  |  Euclid (54)  |  Express (65)  |  Eye (222)  |  Form (314)  |  Furnish (42)  |  Generate (14)  |  Generation (141)  |  Genesis (17)  |  Grow (99)  |  Inherent (30)  |  Invariability (5)  |  Living Body (3)  |  Magnitude (45)  |  Manner (57)  |  Member (40)  |  Mind (760)  |  Move (94)  |  Number (282)  |  On The Other Hand (34)  |  Operate (17)  |  Order (242)  |  Parabola (2)  |  Path (84)  |  Perfect (89)  |  Physiology (83)  |  Point (123)  |  Produce (102)  |  Property (126)  |  Relate (20)  |  Relation (154)  |  Reveal (52)  |  Same (156)  |  Space (257)  |  Step (110)  |  Student (203)  |  Transition (18)  |  Treat (34)  |  Understand (340)  |  Variable (16)  |  Write (154)

Euler who could have been called almost without metaphor, and certainly without hyperbole, analysis incarnate.
In Oeuvres, t. 2 (1854), 443.
Science quotes on:  |  Call (128)  |  Certainly (31)  |  Leonhard Euler (35)  |  Mathematicians and Anecdotes (141)  |  Metaphor (25)

Familiar things happen, and mankind does not bother about them. It requires a very unusual mind to undertake the analysis of the obvious.
In Science and the Modern World: Lowell Lectures, 1925 (1925), 6.
Science quotes on:  |  Mind (760)  |  Obvious (83)  |  Requirement (47)  |  Undertake (20)  |  Unusual (16)

Fortunately analysis is not the only way to resolve inner conflicts. Life itself still remains a very effective therapist.
Our Inner Conflicts: A Constructive Theory of Neurosis (1945, 1999), 240.
Science quotes on:  |  Conflict (55)  |  Life (1131)  |  Resolve (19)  |  Therapist (2)

Fourier’s Theorem … is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics. To mention only sonorous vibrations, the propagation of electric signals along a telegraph wire, and the conduction of heat by the earth’s crust, as subjects in their generality intractable without it, is to give but a feeble idea of its importance.
In William Thomson and Peter Guthrie Tait, Treatise on Natural Philosophy (1867), Vol. 1, 28.
Science quotes on:  |  Beautiful (144)  |  Conduction (4)  |  Crust (18)  |  Earth (638)  |  Electric (15)  |  Feeble (27)  |  Baron Jean-Baptiste-Joseph Fourier (17)  |  Generality (34)  |  Heat (100)  |  Idea (580)  |  Importance (218)  |  Indispensable (28)  |  Instrument (95)  |  Intractable (2)  |  Mention (23)  |  Modern (162)  |  Modern Physics (14)  |  Propagation (10)  |  Question (404)  |  Recondite (5)  |  Result (389)  |  Signal (18)  |  Sound (90)  |  Subject (240)  |  Telegraph (32)  |  Theorem (90)  |  Treatment (100)  |  Vibration (16)  |  Wire (20)

Furious activity is no substitute for analytical thought.
Quoted in New Scientist (1972), 55, 429.
Science quotes on:  |  Activity (135)  |  Furious (2)  |  Substitute (28)  |  Thinking (231)

Games are among the most interesting creations of the human mind, and the analysis of their structure is full of adventure and surprises. Unfortunately there is never a lack of mathematicians for the job of transforming delectable ingredients into a dish that tastes like a damp blanket.
In J.R. Newman (ed.), 'Commentary on Games and Puzzles', The World of Mathematics (1956), Vol. 4, 2414.
Science quotes on:  |  Adventure (47)  |  Blanket (9)  |  Creation (242)  |  Delectable (2)  |  Dish (3)  |  Game (61)  |  Human Mind (82)  |  Ingredient (14)  |  Interesting (48)  |  Job (43)  |  Lack (77)  |  Mathematician (384)  |  Structure (225)  |  Surprise (71)  |  Taste (48)  |  Transform (35)  |  Unfortunately (18)

Geometry may sometimes appear to take the lead of analysis, but in fact precedes it only as a servant goes before his master to clear the path and light him on his way. The interval between the two is as wide as between empiricism and science, as between the understanding and the reason, or as between the finite and the infinite.
From 'Astronomical Prolusions', Philosophical Magazine (Jan 1866), 31, No. 206, 54, collected in Collected Mathematical Papers of James Joseph Sylvester (1908), Vol. 2, 521.
Science quotes on:  |  Empiricism (19)  |  Finite (32)  |  Geometry (232)  |  Infinite (130)  |  Interval (13)  |  Master (98)  |  Precede (23)  |  Reason (471)  |  Science (2067)  |  Servant (18)  |  Understand (340)  |  Wide (28)

Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine is too complicated for all the elements to be able to enter into the analytical comparison which we wish to make, we separate the more inconvenient [elements], we substitute others for them, less troublesome, but also less real, and we are surprised to arrive, notwithstanding a painful labour, only at a result contradicted by nature; as if after having disguised it, cut it short or altered it, a purely mechanical combination could give it back to us.
From Essai d’une nouvelle théorie de la résistance des fluides (1752), translated as an epigram in Ivor Grattan-Guinness, Convolutions in French Mathematics, 1800-1840: From the Calculus and Mechanics to Mathematical Analysis and Mathematical Physics (1990), Vol. 1, 33.
Science quotes on:  |  Alter (23)  |  Arrive (35)  |  Combination (91)  |  Command (28)  |  Comparison (64)  |  Complicated (62)  |  Contradict (12)  |  Cut (39)  |  Disguise (10)  |  Element (162)  |  Enter (32)  |  Examine (44)  |  Geometry (232)  |  Inconvenient (4)  |  Labour (47)  |  Less (102)  |  Mechanical (50)  |  Nature (1223)  |  Obey (16)  |  Painful (10)  |  Physics (348)  |  Question (404)  |  Real (149)  |  Result (389)  |  Separate (74)  |  Short (51)  |  Sometimes (43)  |  Substitute (28)  |  Surprise (71)  |  Troublesome (7)  |  United (14)

Half of analysis is anal.
Quoted in: 1,911 Best Things Anybody Ever Said, R. Byrne.
Science quotes on:  |  Half (56)  |  Medicine (344)

Here I shall present, without using Analysis [mathematics], the principles and general results of the Théorie, applying them to the most important questions of life, which are indeed, for the most part, only problems in probability. One may even say, strictly speaking, that almost all our knowledge is only probable; and in the small number of things that we are able to know with certainty, in the mathematical sciences themselves, the principal means of arriving at the truth—induction and analogy—are based on probabilities, so that the whole system of human knowledge is tied up with the theory set out in this essay.
Philosophical Essay on Probabilities (1814), 5th edition (1825), trans. Andrew I. Dale (1995), 1.
Science quotes on:  |  Analogy (60)  |  Certainty (131)  |  Importance (218)  |  Induction (60)  |  Knowledge (1306)  |  Life (1131)  |  Mathematics (1205)  |  Principle (292)  |  Probability (106)  |  Problem (497)  |  Question (404)  |  Result (389)  |  Theory (696)  |  Truth (928)

How have people come to be taken in by The Phenomenon of Man? Just as compulsory primary education created a market catered for by cheap dailies and weeklies, so the spread of secondary and latterly of tertiary education has created a large population of people, often with well-developed literary and scholarly tastes who have been educated far beyond their capacity to undertake analytical thought … [The Phenomenon of Man] is written in an all but totally unintelligible style, and this is construed as prima-facie evidence of profundity.
Medawar’s book review of The Phenomenon of Man by Teilhard de Chardin first appeared as 'Critical Notice' in the journal Mind (1961), 70, No. 277, 105. The book review was reprinted in The Art of the Soluble: Creativity and Originality in Science (1967).
Science quotes on:  |  Capacity (64)  |  Cheap (11)  |  Compulsory (7)  |  Construed (2)  |  Created (6)  |  Daily (29)  |  Developed (11)  |  Educated (11)  |  Education (347)  |  Evidence (183)  |  Large (130)  |  Literary (12)  |  Market (11)  |  Person (154)  |  Phenomenon (278)  |  Population (79)  |  Primary (41)  |  Profundity (6)  |  Secondary (14)  |  Spread (34)  |  Style (22)  |  Taste (48)  |  Tertiary (3)  |  Thought (546)  |  Undertake (20)  |  Unintelligible (10)  |  Written (6)

Hubris is the greatest danger that accompanies formal data analysis, including formalized statistical analysis. The feeling of “Give me (or more likely even, give my assistant) the data, and I will tell you what the real answer is!” is one we must all fight against again and again, and yet again.
In 'Sunset Salvo', The American Statistician (Feb 1986), 40, No. 1, 75.
Science quotes on:  |  Accompany (22)  |  Answer (249)  |  Assistant (5)  |  Danger (78)  |  Data (120)  |  Feeling (91)  |  Fight (44)  |  Formal (33)  |  Greatest (63)  |  Hubris (2)  |  Real (149)  |  Statistics (147)  |  Tell (110)

Humor can be dissected, as a frog can, but the thing dies in the process and the innards are discouraging to any but the purely scientific mind.
In Elwyn Brooks White, Katharine Sergeant Angell White, first paragraph, 'The Preaching Humorist', The Saturday Review (18 Oct 1941), 16. Also collected in the same authors’ book, A Subtreasury of American Humor (1941), xvii. Seen in later books, in a number of variants, for example, “Analyzing humor is like dissecting a frog. Few people are interested and the frog dies of it”, in Bob Phillips, Phillips’ Treasury of Humorous Quotations (2004), 130.
Science quotes on:  |  Death (302)  |  Dissection (29)  |  Frog (33)  |  Humour (103)  |  Interest (237)  |  People (390)

I am particularly concerned to determine the probability of causes and results, as exhibited in events that occur in large numbers, and to investigate the laws according to which that probability approaches a limit in proportion to the repetition of events. That investigation deserves the attention of mathematicians because of the analysis required. It is primarily there that the approximation of formulas that are functions of large numbers has its most important applications. The investigation will benefit observers in identifying the mean to be chosen among the results of their observations and the probability of the errors still to be apprehended. Lastly, the investigation is one that deserves the attention of philosophers in showing how in the final analysis there is a regularity underlying the very things that seem to us to pertain entirely to chance, and in unveiling the hidden but constant causes on which that regularity depends. It is on the regularity of the main outcomes of events taken in large numbers that various institutions depend, such as annuities, tontines, and insurance policies. Questions about those subjects, as well as about inoculation with vaccine and decisions of electoral assemblies, present no further difficulty in the light of my theory. I limit myself here to resolving the most general of them, but the importance of these concerns in civil life, the moral considerations that complicate them, and the voluminous data that they presuppose require a separate work.
Philosophical Essay on Probabilities (1825), trans. Andrew I. Dale (1995), Introduction.
Science quotes on:  |  Application (170)  |  Approximation (22)  |  Cause (285)  |  Chance (160)  |  Complication (24)  |  Concern (110)  |  Data (120)  |  Determine (76)  |  Difficulty (146)  |  Error (277)  |  Event (116)  |  Formula (80)  |  Function (131)  |  Government (93)  |  Inoculation (8)  |  Institution (39)  |  Insurance (9)  |  Investigation (176)  |  Law (515)  |  Limit (126)  |  Mathematician (384)  |  Mean (101)  |  Morality (42)  |  Outcome (13)  |  Philosopher (166)  |  Probability (106)  |  Proportion (72)  |  Regularity (29)  |  Result (389)  |  Theory (696)  |  Vaccine (9)

I have no fault to find with those who teach geometry. That science is the only one which has not produced sects; it is founded on analysis and on synthesis and on the calculus; it does not occupy itself with the probable truth; moreover it has the same method in every country.
In Oeuvres de Frederic Le Grand edited by J.D.E. Preuss (1849), Vol. 7, 100. In Robert Édouard Moritz, Memorabilia Mathematica (1917), 310.
Science quotes on:  |  Calculus (51)  |  Geometry (232)  |  International (23)  |  Method (239)  |  Synthesis (44)  |  Truth (928)

I have no patience with attempts to identify science with measurement, which is but one of its tools, or with any definition of the scientist which would exclude a Darwin, a Pasteur or a Kekulé. The scientist is a practical man and his are practical aims. He does not seek the ultimate but the proximate. He does not speak of the last analysis but rather of the next approximation. His are not those beautiful structures so delicately designed that a single flaw may cause the collapse of the whole. The scientist builds slowly and with a gross but solid kind of masonry. If dissatisfied with any of his work, even if it be near the very foundations, he can replace that part without damage to the remainder. On the whole, he is satisfied with his work, for while science may never be wholly right it certainly is never wholly wrong; and it seems to be improving from decade to decade.
The Anatomy of Science (1926), 6-7.
Science quotes on:  |  Approximation (22)  |  Collapse (17)  |  Damage (28)  |  Definition (192)  |  Dissatisfaction (6)  |  Flaw (10)  |  Foundation (108)  |  Improvement (74)  |  August Kekulé (13)  |  Masonry (3)  |  Measurement (161)  |  Sir Isaac Newton (333)  |  Louis Pasteur (81)  |  Practical (133)  |  Progress (368)  |  Right (197)  |  Satisfaction (56)  |  Structure (225)  |  Ultimate (84)  |  Wrong (139)

I presume that few who have paid any attention to the history of the Mathematical Analysis, will doubt that it has been developed in a certain order, or that that order has been, to a great extent, necessary—being determined, either by steps of logical deduction, or by the successive introduction of new ideas and conceptions, when the time for their evolution had arrived. And these are the causes that operate in perfect harmony. Each new scientific conception gives occasion to new applications of deductive reasoning; but those applications may be only possible through the methods and the processes which belong to an earlier stage.
Explaining his choice for the exposition in historical order of the topics in A Treatise on Differential Equations (1859), Preface, v-vi.
Science quotes on:  |  Application (170)  |  Cause (285)  |  Conception (92)  |  Deduction (69)  |  Development (289)  |  Earlier (9)  |  Evolution (535)  |  Harmony (72)  |  History (369)  |  Idea (580)  |  Introduction (35)  |  Logic (260)  |  Mathematics (1205)  |  Necessity (143)  |  New (496)  |  Occasion (23)  |  Order (242)  |  Process (267)  |  Reasoning (100)  |  Scientific (236)  |  Successive (23)

I regarded as quite useless the reading of large treatises of pure analysis: too large a number of methods pass at once before the eyes. It is in the works of application that one must study them; one judges their utility there and appraises the manner of making use of them.
As reported by J. F. Maurice in Moniteur Universel (1814), 228.
Science quotes on:  |  Utility (33)

I shall devote all my efforts to bring light into the immense obscurity that today reigns in Analysis. It so lacks any plan or system, that one is really astonished that so many people devote themselves to it—and, still worse, it is absolutely devoid of any rigour.
In Oeuvres (1826), Vol. 2, 263. As translated and cited in Ernst Hairer and Gerhard Wanner Analysis by Its History (2008), 188. From the original French, “Je consacrerai toutes mes forces à répandre de la lumière sur l’immense obscurité qui règne aujourd’hui dans l’Analyse. Elle est tellement dépourvue de tout plan et de tout système, qu’on s’étonne seulement qu’il y ait tant de gens qui s’y livrent—et ce qui pis est, elle manque absolument de rigueur.”
Science quotes on:  |  Absolutely (39)  |  Astonished (9)  |  Badly (15)  |  Bring (90)  |  Devoid (11)  |  Devote (35)  |  Effort (144)  |  Immense (42)  |  Lack (77)  |  Light (347)  |  Obscurity (27)  |  People (390)  |  Plan (87)  |  Really (78)  |  Reign (12)  |  Rigour (16)  |  System (191)  |  Today (117)

I should not like to leave an impression that all structural problems can be settled by X-ray analysis or that all crystal structures are easy to solve. I seem to have spent much more of my life not solving structures than solving them.
In 'X-ray Analysis of Complicated Molecules', Nobel Lecture (11 Dec 1964). In Nobel Lectures: Chemistry 1942-1962 (1964), 88.
Science quotes on:  |  Easy (102)  |  Impression (72)  |  Problem (497)  |  Settle (18)  |  Solve (78)  |  Structure (225)  |  X-ray Crystallography (11)

I think chemistry is being frittered away by the hairsplitting of the organic chemists; we have new compounds discovered, which scarcely differ from the known ones and when discovered are valueless—very illustrations perhaps of their refinements in analysis, but very little aiding the progress of true science.
Letter to William Grove (5 Jan 1845), The Letters of Faraday and Schoenbein, 1836-1862 (1899), Footnote, 209.
Science quotes on:  |  Chemistry (252)  |  Compound (58)  |  Difference (246)  |  Discovery (680)  |  Frittering (2)  |  Illustration (29)  |  Knowledge (1306)  |  Organic Chemistry (33)  |  Progress (368)  |  Refinement (13)  |  Science (2067)  |  True Science (22)  |  Valueless (3)

I think we are beginning to suspect that man is not a tiny cog that doesn’t really make much difference to the running of the huge machine but rather that there is a much more intimate tie between man and the universe than we heretofore suspected. … [Consider if] the particles and their properties are not somehow related to making man possible. Man, the start of the analysis, man, the end of the analysis—because the physical world is, in some deep sense, tied to the human being.
In The Intellectual Digest (Jun 1973), as quoted and cited in Mark Chandos, 'Philosophical Essay: Story Theory", Kosmoautikon: Exodus From Sapiens (2015).
Science quotes on:  |  Cog (3)  |  Difference (246)  |  Human Being (73)  |  Intimate (15)  |  Machine (157)  |  Man (373)  |  Particle (99)  |  Physical (134)  |  Property (126)  |  Tie (24)  |  Universe (686)  |  World (898)

I thought that the wisdom of our City had certainly designed the laudable practice of taking and distributing these accompts [parish records of christenings and deaths] for other and greater uses than [merely casual comments], or, at least, that some other uses might be made of them; and thereupon I ... could, and (to be short) to furnish myself with as much matter of that kind ... the which when I had reduced into tables ... so as to have a view of the whole together, in order to the more ready comparing of one Year, Season, Parish, or other Division of the City, with another, in respect of all Burials and Christnings, and of all the Diseases and Casualties happening in each of them respectively...
Moreover, finding some Truths and not-commonly-believed opinions to arise from my meditations upon these neglected Papers, I proceeded further to consider what benefit the knowledge of the same would bring to the world, ... with some real fruit from those ayrie blossoms.
From Natural and Political Observations Mentioned in a Following Index and Made upon Bills of Mortality (1662), Preface. Reproduced in Cornelius Walford, The Insurance Cyclopaedia (1871), Vol. 1, 286-287.
Science quotes on:  |  Benefit (73)  |  Burial (7)  |  Casualty (3)  |  Comparison (64)  |  Data (120)  |  Disease (275)  |  Knowledge (1306)  |  Meditation (12)  |  Opinion (176)  |  Season (26)  |  Statistics (147)  |  Table (36)  |  Together (79)  |  Truth (928)  |  Use (76)  |  Whole (192)  |  Wisdom (182)  |  Year (299)

I was depressed at that time. I was in analysis. I was suicidal as a matter of fact and would have killed myself, but I was in analysis with a strict Freudian, and, if you kill yourself, they make you pay for the sessions you miss.
As character Alvy Singer doing a stand-up comedy act to a college audience, in movie Annie Hall (1977). Screenplay by Woody Allen with Marshall Brickman, transcript printed in Four films of Woody Allen (1982), 53.
Science quotes on:  |  Depression (19)  |  Freudian (4)  |  Killed (2)  |  Missing (7)  |  Pay (43)  |  Session (3)  |  Strict (17)  |  Suicide (18)

If we view mathematical speculations with reference to their use, it appears that they should be divided into two classes. To the first belong those which furnish some marked advantage either to common life or to some art, and the value of such is usually determined by the magnitude of this advantage. The other class embraces those speculations which, though offering no direct advantage, are nevertheless valuable in that they extend the boundaries of analysis and increase our resources and skill. Now since many investigations, from which great advantage may be expected, must be abandoned solely because of the imperfection of analysis, no small value should be assigned to those speculations which promise to enlarge the field of anaylsis.
In Novi Comm. Petr., Vol. 4, Preface.
Science quotes on:  |  Abandon (48)  |  Advantage (77)  |  Appear (118)  |  Art (294)  |  Assign (13)  |  Belong (53)  |  Boundary (38)  |  Class (84)  |  Common (122)  |  Determine (76)  |  Direct (84)  |  Divide (40)  |  Embrace (33)  |  Enlarge (27)  |  Expect (44)  |  Extend (44)  |  Field (171)  |  First (314)  |  Furnish (42)  |  Great (534)  |  Imperfection (24)  |  Increase (146)  |  Investigation (176)  |  Life (1131)  |  Magnitude (45)  |  Mark (42)  |  Mathematics (1205)  |  Offer (43)  |  Promise (38)  |  Reference (33)  |  Resource (62)  |  Skill (66)  |  Small (163)  |  Solely (9)  |  Speculation (104)  |  Study And Research In Mathematics (61)  |  Usually (31)  |  Value (242)  |  View (171)

If, unwarned by my example, any man shall undertake and shall succeed in really constructing an engine embodying in itself the whole of the executive department of mathematical analysis upon different principles or by simpler mechanical means, I have no fear of leaving my reputation in his charge, for he alone will be fully able to appreciate the nature of my efforts and the value of their results.
In Passages from the Life of a Philosopher (1864), 450.
Science quotes on:  |  Appreciate (30)  |  Charge (35)  |  Construct (41)  |  Department (47)  |  Different (186)  |  Effort (144)  |  Embody (16)  |  Engine (29)  |  Example (94)  |  Executive (3)  |  Mathematics (1205)  |  Means (176)  |  Mechanical (50)  |  Nature (1223)  |  Principle (292)  |  Reputation (28)  |  Result (389)  |  Simpler (8)  |  Succeed (27)  |  Undertake (20)  |  Value (242)  |  Warning (10)  |  Whole (192)

In a certain sense I made a living for five or six years out of that one star [υ Sagittarii] and it is still a fascinating, not understood, star. It’s the first star in which you could clearly demonstrate an enormous difference in chemical composition from the sun. It had almost no hydrogen. It was made largely of helium, and had much too much nitrogen and neon. It’s still a mystery in many ways … But it was the first star ever analysed that had a different composition, and I started that area of spectroscopy in the late thirties.
Oral History Transcript of interview with Dr. Jesse Greenstein by Paul Wright (31 Jul 1974), on website of American Institute of Physics, about his research on strange shell stars. As quoted in J. B. Hearnshaw, The Analysis of Starlight: One Hundred and Fifty Years of Astronomical Spectroscopy (1986, 1990), 362. Hearnshaw footnoted that Berman earlier analysed the peculiar star R CrB (1935).
Science quotes on:  |  Chemical (79)  |  Composition (60)  |  Difference (246)  |  Fascinating (22)  |  Helium (9)  |  Hydrogen (44)  |  Living (56)  |  Mystery (153)  |  Neon (4)  |  Nitrogen (19)  |  Spectroscopy (11)  |  Star (336)  |  Sun (276)  |  Understanding (325)

In a sense, of course, probability theory in the form of the simple laws of chance is the key to the analysis of warfare;… My own experience of actual operational research work, has however, shown that its is generally possible to avoid using anything more sophisticated. … In fact the wise operational research worker attempts to concentrate his efforts in finding results which are so obvious as not to need elaborate statistical methods to demonstrate their truth. In this sense advanced probability theory is something one has to know about in order to avoid having to use it.
In 'Operations Research', Physics Today (Nov 1951), 19. As cited by Maurice W. Kirby and Jonathan Rosenhead, 'Patrick Blackett (1897)' in Arjang A. Assad (ed.) and Saul I. Gass (ed.),Profiles in Operations Research: Pioneers and Innovators (2011), 25.
Science quotes on:  |  Advanced (11)  |  Chance (160)  |  Concentrate (18)  |  Demonstrate (53)  |  Effort (144)  |  Elaborate (21)  |  Experience (342)  |  Finding (30)  |  Key (50)  |  Law (515)  |  Method (239)  |  Obvious (83)  |  Probability (106)  |  Result (389)  |  Simple (178)  |  Sophisticated (15)  |  Statistics (147)  |  Theory (696)  |  Truth (928)  |  Warfare (6)  |  Wise (61)

In a word, I consider hospitals only as the entrance to scientific medicine; they are the first field of observation which a physician enters; but the true sanctuary of medical science is a laboratory; only there can he seek explanations of life in the normal and pathological states by means of experimental analysis.
From An Introduction to the Study of Experimental Medicine (1865), as translated by Henry Copley Greene (1957), 146.
Science quotes on:  |  Hospital (33)  |  Laboratory (132)  |  Life (1131)  |  Pathology (14)  |  Physician (243)

In future times Tait will be best known for his work in the quaternion analysis. Had it not been for his expositions, developments and applications, Hamilton’s invention would be today, in all probability, a mathematical curiosity.
In Bibliotheca Mathematica (1903), 3, 189. As cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 178. [Note: Tait is Peter Guthrie Tait; Hamilton is Sir William Rowan Hamilton. —Webmaster]
Science quotes on:  |  Application (170)  |  Curiosity (106)  |  Development (289)  |  Exposition (15)  |  Future (287)  |  Sir William Rowan Hamilton (10)  |  Invention (324)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1205)  |  Quaternion (9)  |  Peter Guthrie Tait (10)

In order that the facts obtained by observation and experiment may be capable of being used in furtherance of our exact and solid knowledge, they must be apprehended and analysed according to some Conceptions which, applied for this purpose, give distinct and definite results, such as can be steadily taken hold of and reasoned from.
Philosophy of the Inductive Sciences (1840), Vol. 2, 205.
Science quotes on:  |  Capability (37)  |  Conception (92)  |  Definite (43)  |  Distinct (46)  |  Exact (68)  |  Experiment (602)  |  Fact (733)  |  Furtherance (2)  |  Knowledge (1306)  |  Observation (450)  |  Purpose (194)  |  Reason (471)  |  Result (389)

In the 1940s when I did my natural sciences degree in zoology it was very much laboratory-based. … I was not keen on the idea of spending the rest of my life in the lab. I also don’t think I would have been particularly good at it. I don't think I have as analytical a mind or the degree of application that one would need to become a first-rate research scientist.
From interview with Michael Bond, 'It’s a Wonderful Life', New Scientist (14 Dec 2002), 176, No. 2373, 48.
Science quotes on:  |  Application (170)  |  Degree (82)  |  Idea (580)  |  Keen (10)  |  Laboratory (132)  |  Mind (760)  |  Natural Science (90)  |  Research (590)  |  Scientist (522)  |  Zoology (31)

In the final analysis, our most basic common link is that we all inhabit this small planet. We all breathe the same air. We all cherish our children's future. And we are all mortal.
Commencement Address at American University, Washington, D.C. (Jun 1963). In Steven Cohen, Understanding Environmental Policy (2006), Preface, xi. Also on web site of John F. Kennedy Presidential Library and Museum.
Science quotes on:  |  Air (190)  |  All (8)  |  Basic (66)  |  Breathe (36)  |  Cherish (11)  |  Children (20)  |  Common (122)  |  Future (287)  |  Inhabit (16)  |  Link (42)  |  Mortal (28)  |  Planet (263)  |  Small (163)

In the higher walks of politics the same sort of thing occurs. The statesman who has gradually concentrated all power within himself … may have had anything but a public motive… The phrases which are customary on the platform and in the Party Press have gradually come to him to seem to express truths, and he mistakes the rhetoric of partisanship for a genuine analysis of motives… He retires from the world after the world has retired from him.
In The Conquest of Happiness (1930, 2006), 79.
Science quotes on:  |  Genuine (26)  |  Mistake (132)  |  Motive (33)  |  Party (18)  |  Phrase (29)  |  Platform (3)  |  Politics (96)  |  Power (366)  |  Press (21)  |  Public (94)  |  Retire (3)  |  Rhetoric (8)  |  Statesman (18)  |  Truth (928)  |  World (898)

In the last analysis the best guarantee that a thing should happen is that it appears to us as vitally necessary.
In Teilhard de Chardin and Sara Appleton-Weber (trans.), The Human Phenomenon (1999, 2003), 163. Originally published in French as Le Phénomene Humain (1955).
Science quotes on:  |  Appearance (85)  |  Best (173)  |  Guarantee (21)  |  Happening (32)  |  Last (19)  |  Necessity (143)  |  Vital (39)

In this great society wide lying around us, a critical analysis would find very few spontaneous actions. It is almost all custom and gross sense.
Science quotes on:  |  Action (185)  |  Critical (41)  |  Custom (30)  |  Gross (7)  |  Sense (321)  |  Society (228)  |  Sociology (43)  |  Spontaneous (14)

It is easy without any very profound logical analysis to perceive the difference between a succession of favorable deviations from the laws of chance, and on the other hand, the continuous and cumulative action of these laws. It is on the latter that the principle of Natural Selection relies.
In The Genetical Theory of Natural Selection (1930), 37. Reprinted as A Complete Variorum Edition (2003), 37.
Science quotes on:  |  Action (185)  |  Continuous (38)  |  Cumulative (9)  |  Deviation (11)  |  Difference (246)  |  Favorable (12)  |  Natural Selection (90)  |  On The Other Hand (34)  |  Principle (292)  |  Probability (106)  |  Succession (45)

It is going to be necessary that everything that happens in a finite volume of space and time would have to be analyzable with a finite number of logical operations. The present theory of physics is not that way, apparently. It allows space to go down into infinitesimal distances, wavelengths to get infinitely great, terms to be summed in infinite order, and so forth; and therefore, if this proposition [that physics is computer-simulatable] is right, physical law is wrong.
International Journal of Theoretical Physics (1982), 21 Nos. 6-7, 468. Quoted in Brian Rotman, Mathematics as Sign (2000), 82.
Science quotes on:  |  Computer (105)  |  Finite (32)  |  Infinite (130)  |  Infinitesimal (15)  |  Physical Law (8)  |  Physics (348)  |  Proposition (83)  |  Simulation (6)  |  Space (257)  |  Theory (696)  |  Time (595)  |  Wavelength (6)

It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
Science quotes on:  |  A Priori (22)  |  Achievement (150)  |  Administrator (10)  |  Admit (45)  |  Affair (29)  |  Aid (42)  |  Alike (22)  |  Alone (106)  |  Analogous (5)  |  Anatomist (17)  |  Application (170)  |  François Arago (14)  |  Army (25)  |  Attain (45)  |  Author (62)  |  Balance (55)  |  Behold (18)  |  Bernhard Bolzano (2)  |  Calculation (100)  |  Calculus (51)  |  Call (128)  |  Lazare-Nicolas-Marguerite Carnot (4)  |  Celebrated (2)  |  Central (34)  |  Certainty (131)  |  Chair (11)  |  Civil (6)  |  Classic (10)  |  William Kingdon Clifford (21)  |  Commercial (26)  |  Comparative (13)  |  Compare (38)  |  Constantly (27)  |  Constitution (31)  |  Contemplate (17)  |  Creation (242)  |  Creator (55)  |  Current (54)  |  Baron Georges Cuvier (30)  |  Charles Darwin (301)  |  Deal (49)  |  Degree (82)  |  René Descartes (81)  |  Descriptive Geometry (3)  |  Devotee (5)  |  Devotion (25)  |  Direct (84)  |  Dissimilar (6)  |  Distinction (46)  |  Diverse (17)  |  Division (34)  |  Doctrine (75)  |  Due (20)  |  Eminent (17)  |  Empire (14)  |  Endless (28)  |  Engage (25)  |  Exercise (69)  |  Eye (222)  |  Fact (733)  |  False (99)  |  Fauna (13)  |  Field (171)  |  Finally (26)  |  Find (408)  |  Flora (9)  |  Flourish (16)  |  Baron Jean-Baptiste-Joseph Fourier (17)  |  Function (131)  |  Carl Friedrich Gauss (77)  |  General (160)  |  Genuinely (4)  |  Geometry (232)  |  Great (534)  |  Ground (90)  |  Group (72)  |  Hero (35)  |  Hide (53)  |  High (153)  |  Histology (2)  |  Host (16)  |  Idea (580)  |  Illuminate (24)  |  Immortal (19)  |  Industry (109)  |  Infinitesimal (15)  |  Inheritor (2)  |  Interest (237)  |  Intimate (15)  |  Invoke (6)  |  Judgment (101)  |  Kingdom (38)  |  Felix Klein (15)  |  Know (556)  |  Land (115)  |  Large (130)  |  Gottfried Wilhelm Leibniz (49)  |  Letter (51)  |  Logical (55)  |  Major (32)  |  Master (98)  |  Mathematician (384)  |  Mathematics (1205)  |  Matter (343)  |  Microscopic (11)  |  Mind (760)  |  Minute (44)  |  Monarch (4)  |  Gaspard Monge (2)  |  Sir Isaac Newton (333)  |  Office (22)  |  Operation (121)  |  Opinion (176)  |  Organize (20)  |  Part (222)  |  Blaise Pascal (80)  |  Peace (84)  |  Peer (11)  |  Philosophy (259)  |  Henri Poincaré (96)  |  Jean-Victor Poncelet (2)  |  Position (76)  |  Practical (133)  |  Prepare (35)  |  Probability (106)  |  Projective Geometry (2)  |  Public Service (5)  |  Pure (103)  |  Range (57)  |  Reality (190)  |  Recess (7)  |  Reduce (53)  |  Reducible (2)  |  Reflect (31)  |  Relate (20)  |  Render (33)  |  Require (85)  |  Bernhard Riemann (7)  |  Rightful (3)  |  Sagacious (4)  |  Say (228)  |  Scatter (6)  |  Science (2067)  |  Seldom (30)  |  Similarity (21)  |  Single (120)  |  Statesman (18)  |  Structure (225)  |  Surprise (71)  |  Survey (20)  |  Theory (696)  |  Tune (14)  |  Unfit (12)  |  Variety (71)  |  View (171)  |  Vision (94)  |  War (161)  |  Karl Weierstrass (9)  |  Wield (10)  |  Work (635)  |  World (898)

It is profitable nevertheless to permit ourselves to talk about 'meaningless' terms in the narrow sense if the preconditions to which all profitable operations are subject are so intuitive and so universally accepted as to form an almost unconscious part of the background of the public using the term. Physicists of the present day do constitute a homogenous public of this character; it is in the air that certain sorts of operation are valueless for achieving certain sorts of result. If one wants to know how many planets there are one counts them but does not ask a philosopher what is the perfect number.
Reflections of a Physicist (1950), 6.
Science quotes on:  |  Philosophy (259)

It is the invaluable merit of the great Basle mathematician Leonhard Euler, to have freed the analytical calculus from all geometric bounds, and thus to have established analysis as an independent science, which from his time on has maintained an unchallenged leadership in the field of mathematics.
In Die Entwickelung der Mathematik in den letzten Jahrhunderten (1884), 12. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 153. Seen incorrectly attributed to Thomas Reid in N. Rose, Mathematical and Maxims and Minims (1988).
Science quotes on:  |  Bounds (7)  |  Calculus (51)  |  Establish (56)  |  Leonhard Euler (35)  |  Field (171)  |  Free (92)  |  Geometry (232)  |  Great (534)  |  Independent (67)  |  Invaluable (7)  |  Leadership (8)  |  Maintain (33)  |  Mathematician (384)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1205)  |  Merit (32)  |  Science (2067)  |  Time (595)

It is the very strangeness of nature that makes science engrossing. That ought to be at the center of science teaching. There are more than seven-times-seven types of ambiguity in science, awaiting analysis. The poetry of Wallace Stevens is crystal-clear alongside the genetic code.
In Late Night Thoughts on Listening to Mahler's Ninth Symphony(1984), 209.
Science quotes on:  |  Ambiguity (14)  |  Center (34)  |  Code (15)  |  Genetics (101)  |  Making (27)  |  Nature (1223)  |  Ought (3)  |  Poetry (124)  |  Science (2067)  |  Seven (5)  |  Wallace Stevens (3)  |  Strangeness (10)  |  Teaching (108)  |  Wait (58)

It is to geometry that we owe in some sort the source of this discovery [of beryllium]; it is that [science] that furnished the first idea of it, and we may say that without it the knowledge of this new earth would not have been acquired for a long time, since according to the analysis of the emerald by M. Klaproth and that of the beryl by M. Bindheim one would not have thought it possible to recommence this work without the strong analogies or even almost perfect identity that Citizen Haüy found for the geometrical properties between these two stony fossils.
Haüy used the geometry of cleavage to reveal the underlying crystal structure, and thus found the emeral and beryl were geometrically identical. In May Elvira Weeks, The Discovery of the Elements (1934), 153, citing Mellor, Comprehensive Treatise on Inorganic and Theoretical Chemistry (1923), 204-7.
Science quotes on:  |  Analogy (60)  |  Beryllium (2)  |  Discovery (680)  |  Furnishing (4)  |  Geometry (232)  |  Idea (580)  |  Identity (11)  |  Martin Heinrich Klaproth (3)  |  Knowledge (1306)  |  Mineral (41)  |  Owing (3)  |  Possibility (116)  |  Property (126)  |  Source (91)  |  Stone (76)  |  Work (635)

It seems that the rivers know the theory. It only remains to convince the engineers of the validity of this analysis.
Epigraph, without citation, in Péter Érdi, Complexity Explained (2007), 339. In French, “Il semble que les rivières connaissent déjà la théorie Il ne reste qu'à convaincre les ingénieurs de la validité de cette analyse.”
Science quotes on:  |  Convince (23)  |  Engineer (97)  |  Know (556)  |  River (79)  |  Seem (143)  |  Theory (696)  |  Validity (31)

It would be difficult and perhaps foolhardy to analyze the chances of further progress in almost every part of mathematics one is stopped by unsurmountable difficulties, improvements in the details seem to be the only possibilities which are left… All these difficulties seem to announce that the power of our analysis is almost exhausted, even as the power of ordinary algebra with regard to transcendental geometry in the time of Leibniz and Newton, and that there is a need of combinations opening a new field to the calculation of transcendental quantities and to the solution of the equations including them.
From Rapport historique sur les progrès des sciences mathématiques depuis 1789, et sur leur état actuel (1810), 131. As translated in George Sarton, The Study of the History of Mathematics (1936), 13. In the original French: “Il seroit difficile et peut-être téméraire d’analyser les chances que l’avenir offre à l’avancement des mathématiques: dans presque toutes les parties, on est arrêté par des difficultés insurmontables; des perfectionnements de détail semblent la seule chose qui reste à faire… Toutes ces difficultés semblent annoncer que la puissance de notre analyse est à-peu-près épuisée, comme celle de l’algèbre ordinaire l’étoit par rapport à la géométrie transcendante au temps de Leibnitz et de Newton, et qu’il faut des combinaisons qui ouvrent un nouveau champ au calcul des transcendantes et à la résolution des équations qui les contiennent.” Sarton states this comes from “the report on mathematical progress prepared for the French Academy of Sciences at Napoleon’s request”.
Science quotes on:  |  Algebra (104)  |  Analyze (10)  |  Announce (9)  |  Calculation (100)  |  Combination (91)  |  Detail (87)  |  Difficult (121)  |  Difficulty (146)  |  Equation (96)  |  Exhaust (22)  |  Field (171)  |  Geometry (232)  |  Improvement (74)  |  Gottfried Wilhelm Leibniz (49)  |  Mathematics (1205)  |  Need (287)  |  New (496)  |  Sir Isaac Newton (333)  |  Ordinary (73)  |  Power (366)  |  Progress (368)  |  Quantity (65)  |  Solution (216)  |  Stop (76)  |  Time (595)  |  Transcendental (5)

It [analysis] lacks at this point such plan and unity that it is really amazing that it can be studied by so many people. The worst is that it has not at all been treated with rigor. There are only a few propositions in higher analysis that have been demonstrated with complete rigor. Everywhere one finds the unfortunate manner of reasoning from the particular to the general, and it is very unusual that with such a method one finds, in spite of everything, only a few of what many be called paradoxes. It is really very interesting to seek the reason.
In my opinion that arises from the fact that the functions with which analysis has until now been occupied can, for the most part, be expressed by means of powers. As soon as others appear, something that, it is true, does not often happen, this no longer works and from false conclusions there flow a mass of incorrect propositions.
From a letter to his professor Hansteen in Christiania, Oslo in Correspondence (1902), 23 . In Umberto Bottazzini and Warren Van Egmond, The Higher Calculus (1986), 87-88.
Science quotes on:  |  Conclusion (160)  |  False (99)  |  Function (131)  |  Paradox (43)  |  Plan (87)  |  Proposition (83)  |  Reason (471)  |  Reasoning (100)  |  Rigour (Rigor) (2)

Just as the arts of tanning and dyeing were practiced long before the scientific principles upon which they depend were known, so also the practice of Chemical Engineering preceded any analysis or exposition of the principles upon which such practice is based.
In William H. Walker, Warren K. Lewis and William H. MacAdams, The Principles of Chemical Engineering (1923), Preface to 1st. edition, v.
Science quotes on:  |  Art (294)  |  Base (71)  |  Chemical Engineering (4)  |  Depend (90)  |  Dyeing (2)  |  Exposition (15)  |  Knowledge (1306)  |  Practice (94)  |  Precede (23)  |  Principle (292)  |  Scientific (236)  |  Tanning (3)

Knowing how hard it is to collect a fact, you understand why most people want to have some fun analyzing it.
Quoted in Fortune (May 1960), as cited in Maxine Block, Anna Herthe Rothe and Marjorie Dent Candee, Current Biography Yearbook 1963 (1964), 161.
Science quotes on:  |  Collection (44)  |  Fact (733)  |  Fun (34)  |  Knowledge (1306)  |  Understanding (325)

Knowledge and ability must be combined with ambition as well as with a sense of honesty and a severe conscience. Every analyst occasionally has doubts about the accuracy of his results, and also there are times when he knows his results to be incorrect. Sometimes a few drops of the solution were spilt, or some other slight mistake made. In these cases it requires a strong conscience to repeat the analysis and to make a rough estimate of the loss or apply a correction. Anyone not having sufficient will-power to do this is unsuited to analysis no matter how great his technical ability or knowledge. A chemist who would not take an oath guaranteeing the authenticity, as well as the accuracy of his work, should never publish his results, for if he were to do so, then the result would be detrimental not only to himself, but to the whole of science.
Anleitung zur Quantitativen Analyse (1847), preface. F. Szabadvary, History of Analytical Chemistry (1966), trans. Gyula Svehla, 176.
Science quotes on:  |  Authenticity (4)  |  Experiment (602)  |  Knowledge (1306)  |  Publication (91)

Knowledge comes by taking things apart, analysis. But wisdom comes by putting things together.
From The Role of Religion in Education. As cited in Braude's Handbook of Stories for Toastmasters and Speakers (1975), 194.
Science quotes on:  |  Knowledge (1306)  |  Together (79)  |  Wisdom (182)

Like Molière’s M. Jourdain, who spoke prose all his life without knowing it, mathematicians have been reasoning for at least two millennia without being aware of all the principles underlying what they were doing. The real nature of the tools of their craft has become evident only within recent times A renaissance of logical studies in modern times begins with the publication in 1847 of George Boole’s The Mathematical Analysis of Logic.
Co-authored with James R. Newman in Gödel's Proof (1986, 2005), 30.
Science quotes on:  |  Aware (31)  |  Begin (108)  |  George Boole (10)  |  Craft (10)  |  Evident (29)  |  Logic (260)  |  Mathematician (384)  |  Mathematics (1205)  |  Millennia (4)  |  Modern (162)  |  Nature (1223)  |  Principle (292)  |  Prose (11)  |  Publication (91)  |  Real (149)  |  Reasoning (100)  |  Recent (30)  |  Renaissance (11)  |  Study (476)  |  Time (595)  |  Tool (87)

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.
As co-author with Herbert Robbins, in What Is Mathematics?: An Elementary Approach to Ideas and Methods (1941, 1996), x.
Science quotes on:  |  Activity (135)  |  Aesthetics (4)  |  Antithesis (7)  |  Aspect (58)  |  Basic (66)  |  Constitution (31)  |  Construction (83)  |  Contemplation (52)  |  Desire (142)  |  Difference (246)  |  Element (162)  |  Emphasis (17)  |  Expression (110)  |  Force (249)  |  Generality (34)  |  Human Mind (82)  |  Individuality (13)  |  Interplay (7)  |  Intuition (57)  |  Logic (260)  |  Mathematics (1205)  |  Perfection (89)  |  Reason (471)  |  Reflection (60)  |  Struggle (78)  |  Supreme (37)  |  Synthesis (44)  |  Tradition (49)  |  Usefulness (77)  |  Value (242)  |  Will (31)

Mathematics is often considered a difficult and mysterious science, because of the numerous symbols which it employs. Of course, nothing is more incomprehensible than a symbolism which we do not understand. … But this is not because they are difficult in themselves. On the contrary they have invariably been introduced to make things easy. … [T]he symbolism is invariably an immense simplification. It … represents an analysis of the ideas of the subject and an almost pictorial representation of their relations to each other.
In Introduction to Mathematics (1911), 59-60.
Science quotes on:  |  Difficult (121)  |  Easy (102)  |  Idea (580)  |  Immense (42)  |  Incomprehensible (17)  |  Introduced (3)  |  Mathematics (1205)  |  Mathematics As A Language (20)  |  Mysterious (33)  |  Pictorial (2)  |  Relation (154)  |  Representation (36)  |  Simplification (15)  |  Symbol (73)  |  Understand (340)

Melvin Calvin was a fearless scientist, totally unafraid to venture into new fields such as hot atom chemistry, carcinogenesis, chemical evolution and the origin of life, organic geochemistry, immunochemistry, petroleum production from plants, farming, Moon rock analysis, and development of novel synthetic biomembrane models for plant photosystems.
Co-author with Andrew A. Benson, 'Melvin Calvin', Biographical Memoirs of the US National Academy of Science.
Science quotes on:  |  Atom (280)  |  Melvin Calvin (11)  |  Carcinogenesis (2)  |  Chemistry (252)  |  Development (289)  |  Evolution (535)  |  Farm (19)  |  Fearless (6)  |  Field (171)  |  Hot (20)  |  Immunochemistry (2)  |  Model (81)  |  Moon (199)  |  New (496)  |  Novel (19)  |  Organic (55)  |  Origin Of Life (35)  |  Petroleum (7)  |  Plant (200)  |  Production (117)  |  Rock (125)  |  Scientist (522)  |  Synthetic (16)  |  Venture (18)

Modern Science, as training the mind to an exact and impartial analysis of facts is an education specially fitted to promote sound citizenship.
From The Grammar of Science (1892), 11.
Science quotes on:  |  Citizenship (6)  |  Education (347)  |  Exact (68)  |  Fact (733)  |  Impartial (4)  |  Mind (760)  |  Modern Science (17)  |  Training (66)

Most, if not all, of the great ideas of modern mathematics have had their origin in observation. Take, for instance, the arithmetical theory of forms, of which the foundation was laid in the diophantine theorems of Fermat, left without proof by their author, which resisted all efforts of the myriad-minded Euler to reduce to demonstration, and only yielded up their cause of being when turned over in the blow-pipe flame of Gauss’s transcendent genius; or the doctrine of double periodicity, which resulted from the observation of Jacobi of a purely analytical fact of transformation; or Legendre’s law of reciprocity; or Sturm’s theorem about the roots of equations, which, as he informed me with his own lips, stared him in the face in the midst of some mechanical investigations connected (if my memory serves me right) with the motion of compound pendulums; or Huyghen’s method of continued fractions, characterized by Lagrange as one of the principal discoveries of that great mathematician, and to which he appears to have been led by the construction of his Planetary Automaton; or the new algebra, speaking of which one of my predecessors (Mr. Spottiswoode) has said, not without just reason and authority, from this chair, “that it reaches out and indissolubly connects itself each year with fresh branches of mathematics, that the theory of equations has become almost new through it, algebraic geometry transfigured in its light, that the calculus of variations, molecular physics, and mechanics” (he might, if speaking at the present moment, go on to add the theory of elasticity and the development of the integral calculus) “have all felt its influence”.
In 'A Plea for the Mathematician', Nature, 1, 238 in Collected Mathematical Papers, Vol. 2, 655-56.
Science quotes on:  |  Add (40)  |  Algebra (104)  |  Appear (118)  |  Arithmetical (11)  |  Author (62)  |  Authority (66)  |  Automaton (10)  |  Become (172)  |  Branch (107)  |  Calculus (51)  |  Cause (285)  |  Chair (11)  |  Characterize (20)  |  Compound (58)  |  Connect (33)  |  Construction (83)  |  Continue (65)  |  Demonstration (86)  |  Development (289)  |  Discovery (680)  |  Doctrine (75)  |  Double (15)  |  Effort (144)  |  Elasticity (5)  |  Equation (96)  |  Leonhard Euler (35)  |  Face (108)  |  Fact (733)  |  Feel (167)  |  Pierre de Fermat (15)  |  Flame (26)  |  Form (314)  |  Foundation (108)  |  Fraction (13)  |  Fresh (30)  |  Carl Friedrich Gauss (77)  |  Genius (249)  |  Geometry (232)  |  Great (534)  |  Christiaan Huygens (10)  |  Idea (580)  |  Influence (140)  |  Inform (16)  |  Instance (32)  |  Integral Calculus (5)  |  Investigation (176)  |  Karl Jacobi (10)  |  Count Joseph-Louis de Lagrange (26)  |  Laid (7)  |  Law (515)  |  Lead (160)  |  Leave (128)  |  Adrien-Marie Legendre (3)  |  Light (347)  |  Lip (4)  |  Mathematician (384)  |  Mathematics (1205)  |  Mechanic (23)  |  Mechanical (50)  |  Memory (106)  |  Method (239)  |  Midst (7)  |  Modern (162)  |  Molecular (7)  |  Moment (107)  |  Motion (160)  |  Nature Of Mathematics (80)  |  New (496)  |  Observation (450)  |  Origin (88)  |  Pendulum (15)  |  Periodicity (5)  |  Physics (348)  |  Planetary (10)  |  Predecessor (21)  |  Present (176)  |  Principal (28)  |  Proof (245)  |  Purely (28)  |  Reach (121)  |  Reason (471)  |  Reciprocity (2)  |  Reduce (53)  |  Resist (15)  |  Result (389)  |  Right (197)  |  Root (61)  |  Say (228)  |  Serve (58)  |  Speak (92)  |  William Spottiswoode (3)  |  Stare (9)  |  Theorem (90)  |  Theory (696)  |  Transcendent (2)  |  Transfigure (2)  |  Transformation (54)  |  Turn (118)  |  Variation (63)  |  Year (299)  |  Yield (38)

Non-standard analysis frequently simplifies substantially the proofs, not only of elementary theorems, but also of deep results. This is true, e.g., also for the proof of the existence of invariant subspaces for compact operators, disregarding the improvement of the result; and it is true in an even higher degree in other cases. This state of affairs should prevent a rather common misinterpretation of non-standard analysis, namely the idea that it is some kind of extravagance or fad of mathematical logicians. Nothing could be farther from the truth. Rather, there are good reasons to believe that non-standard analysis, in some version or other, will be the analysis of the future.
In 'Remark on Non-standard Analysis' (1974), in S. Feferman (ed.), Kurt Gödel Collected Works: Publications 1938-1974 (1990), Vol. 2, 311.
Science quotes on:  |  Mathematics (1205)  |  Proof (245)

Now, in the development of our knowledge of the workings of Nature out of the tremendously complex assemblage of phenomena presented to the scientific inquirer, mathematics plays in some respects a very limited, in others a very important part. As regards the limitations, it is merely necessary to refer to the sciences connected with living matter, and to the ologies generally, to see that the facts and their connections are too indistinctly known to render mathematical analysis practicable, to say nothing of the complexity.
From article 'Electro-magnetic Theory II', in The Electrician (16 Jan 1891), 26, No. 661, 331.
Science quotes on:  |  Complexity (91)  |  Development (289)  |  Enquiry (76)  |  Fact (733)  |  Knowledge (1306)  |  Limitation (30)  |  Mathematics (1205)  |  Nature (1223)  |  Phenomenon (278)  |  Theory (696)

Of the 10,000 or so meteorites that have been collected and analyzed, eight are particularly unusual. They are so unusual, in fact, that since 1979 some investigators have thought they might have originated not in asteroids, as most meteorites did, but on the surface of Mars.
In Scientific American, (Dec 1986), 255, 80.
Science quotes on:  |  Asteroid (13)  |  Collected (2)  |  Investigator (35)  |  Mars (34)  |  Meteorite (8)  |  Originate (21)  |  Surface (101)  |  Unusual (16)

One feature which will probably most impress the mathematician accustomed to the rapidity and directness secured by the generality of modern methods is the deliberation with which Archimedes approaches the solution of any one of his main problems. Yet this very characteristic, with its incidental effects, is calculated to excite the more admiration because the method suggests the tactics of some great strategist who foresees everything, eliminates everything not immediately conducive to the execution of his plan, masters every position in its order, and then suddenly (when the very elaboration of the scheme has almost obscured, in the mind of the spectator, its ultimate object) strikes the final blow. Thus we read in Archimedes proposition after proposition the bearing of which is not immediately obvious but which we find infallibly used later on; and we are led by such easy stages that the difficulties of the original problem, as presented at the outset, are scarcely appreciated. As Plutarch says: “It is not possible to find in geometry more difficult and troublesome questions, or more simple and lucid explanations.” But it is decidedly a rhetorical exaggeration when Plutarch goes on to say that we are deceived by the easiness of the successive steps into the belief that anyone could have discovered them for himself. On the contrary, the studied simplicity and the perfect finish of the treatises involve at the same time an element of mystery. Though each step depends on the preceding ones, we are left in the dark as to how they were suggested to Archimedes. There is, in fact, much truth in a remark by Wallis to the effect that he seems “as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results.” Wallis adds with equal reason that not only Archimedes but nearly all the ancients so hid away from posterity their method of Analysis (though it is certain that they had one) that more modern mathematicians found it easier to invent a new Analysis than to seek out the old.
In The Works of Archimedes (1897), Preface, vi.
Science quotes on:  |  Accustomed (16)  |  Add (40)  |  Admiration (44)  |  Ancient (106)  |  Anyone (35)  |  Appreciate (30)  |  Approach (54)  |  Archimedes (55)  |  Assent (6)  |  Bear (67)  |  Belief (504)  |  Blow (22)  |  Calculate (33)  |  Certain (126)  |  Characteristic (96)  |  Conducive (3)  |  Contrary (34)  |  Cover (37)  |  Dark (77)  |  Deceive (16)  |  Decidedly (2)  |  Deliberation (3)  |  Depend (90)  |  Difficult (121)  |  Difficulty (146)  |  Discover (199)  |  Easiness (3)  |  Easy (102)  |  Effect (166)  |  Elaboration (7)  |  Element (162)  |  Eliminate (21)  |  Equal (83)  |  Everything (181)  |  Exaggeration (11)  |  Excite (15)  |  Execution (19)  |  Explanation (177)  |  Extort (2)  |  Fact (733)  |  Feature (44)  |  Final (50)  |  Find (408)  |  Finish (25)  |  Foresee (13)  |  Generality (34)  |  Geometry (232)  |  Great (534)  |  Grudge (2)  |  Hide (53)  |  Immediately (23)  |  Impress (16)  |  Incidental (12)  |  Inquiry (45)  |  Invent (51)  |  Investigation (176)  |  Involve (48)  |  Late (52)  |  Lead (160)  |  Leave (128)  |  Lucid (5)  |  Main (28)  |  Master (98)  |  Mathematician (384)  |  Mathematicians and Anecdotes (141)  |  Method (239)  |  Mind (760)  |  Modern (162)  |  Mystery (153)  |  Nearly (26)  |  New (496)  |  Object (175)  |  Obscure (32)  |  Obvious (83)  |  Old (147)  |  Order (242)  |  Original (57)  |  Outset (7)  |  Perfect (89)  |  Plan (87)  |  Plutarch (15)  |  Position (76)  |  Possible (158)  |  Posterity (19)  |  Precede (23)  |  Present (176)  |  Probably (48)  |  Problem (497)  |  Proposition (83)  |  Purpose (194)  |  Question (404)  |  Rapidity (16)  |  Read (145)  |  Reason (471)  |  Remark (27)  |  Result (389)  |  Same (156)  |  Say (228)  |  Scarcely (13)  |  Scheme (25)  |  Secret (131)  |  Secure (21)  |  Seek (107)  |  Set (99)  |  Simple (178)  |  Simplicity (147)  |  Solution (216)  |  Spectator (10)  |  Stage (55)  |  Step (110)  |  Strike (40)  |  Study (476)  |  Successive (23)  |  Suddenly (17)  |  Suggest (33)  |  Tactic (7)  |  Time (595)  |  Trace (53)  |  Treatise (34)  |  Troublesome (7)  |  Truth (928)  |  Ultimate (84)  |  John Wallis (3)  |  Wish (92)

One of the most conspicuous and distinctive features of mathematical thought in the nineteenth century is its critical spirit. Beginning with the calculus, it soon permeates all analysis, and toward the close of the century it overhauls and recasts the foundations of geometry and aspires to further conquests in mechanics and in the immense domains of mathematical physics. … A searching examination of the foundations of arithmetic and the calculus has brought to light the insufficiency of much of the reasoning formerly considered as conclusive.
In History of Mathematics in the Nineteenth Century', Congress of Arts and Sciences (1906), Vol. 1, 482. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 113-114.
Science quotes on:  |  19th Century (27)  |  Arithmetic (121)  |  Aspire (8)  |  Calculus (51)  |  Conclusive (7)  |  Conquest (19)  |  Conspicuous (7)  |  Critical (41)  |  Distinctive (14)  |  Examination (65)  |  Foundation (108)  |  Geometry (232)  |  Insufficient (8)  |  Mathematical Physics (9)  |  Mathematics (1205)  |  Mechanics (57)  |  Modern Mathematics (38)  |  Reason (471)  |  Spirit (154)  |  Thought (546)

Our ultimate task is to find interpretative procedures that will uncover each bias and discredit its claims to universality. When this is done the eighteenth century can be formally closed and a new era that has been here a long time can be officially recognised. The individual human being, stripped of his humanity, is of no use as a conceptual base from which to make a picture of human society. No human exists except steeped in the culture of his time and place. The falsely abstracted individual has been sadly misleading to Western political thought. But now we can start again at a point where major streams of thought converge, at the other end, at the making of culture. Cultural analysis sees the whole tapestry as a whole, the picture and the weaving process, before attending to the individual threads.
As co-author with Baron Isherwood, The World of Goods: Towards an Anthropology of Consumption (1979, 2002), 41-42.
Science quotes on:  |  18th Century (19)  |  Base (71)  |  Bias (16)  |  Century (131)  |  Conceptual (10)  |  Culture (104)  |  Discredit (8)  |  Human Being (73)  |  Humanity (125)  |  Individual (221)  |  Interpretation (70)  |  Misleading (15)  |  Recognise (9)  |  Society (228)  |  Strip (6)  |  Tapestry (5)  |  Thread (18)  |  Universality (12)

Perhaps the least inadequate description of the general scope of modern Pure Mathematics—I will not call it a definition—would be to say that it deals with form, in a very general sense of the term; this would include algebraic form, functional relationship, the relations of order in any ordered set of entities such as numbers, and the analysis of the peculiarities of form of groups of operations.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 287.
Science quotes on:  |  Algebra (104)  |  Definition (192)  |  Definitions and Objects of Mathematics (33)  |  Entity (31)  |  Group (72)  |  Modern (162)  |  Number (282)  |  Operation (121)  |  Order (242)  |  Peculiar (45)  |  Pure Mathematics (65)  |  Relation (154)  |  Scope (23)  |  Set (99)

Science cannot solve the ultimate mystery of nature. And that is because, in the last analysis, we ourselves are part of nature and therefore part of the mystery that we are trying to solve. Music and art are, to an extent, also attempts to solve or at least express the mystery. But to my mind the more we progress with either the more we are brought into harmony with all nature itself. And that is one of the great services of science to the individual.
In Max Planck and James Vincent Murphy (trans.), Where is Science Going?, (1932), Epilogue, 217.
Science quotes on:  |  Mystery (153)  |  Nature (1223)  |  Part (222)  |  Science (2067)  |  Solution (216)  |  Ultimate (84)

Science is a method of logical analysis of nature’s operations. It has lessened human anxiety about the cosmos by demonstrating the materiality of nature’s forces, and their frequent predictability.
In Sexual Personae: Art and Decadence from Nefertiti to Emily Dickinson (1990), 5.
Science quotes on:  |  Anxiety (20)  |  Cosmos (52)  |  Force (249)  |  Frequent (22)  |  Human (550)  |  Lessen (4)  |  Logic (260)  |  Materiality (2)  |  Method (239)  |  Nature (1223)  |  Operation (121)  |  Predictability (6)  |  Science (2067)

Science is spectral analysis. Art is light synthesis.
Pro domo et Mundo, (1912), 83. Translated by Harry Zohn (ed.), in 'Riddles and Solutions', Half-Truths and One-And-A-Half-Truths: Selected Aphorisms (1976), 47. From the original German, “Wissenschaft ist Spektralanalyse. Kunst ist Lichtsynthese.”
Science quotes on:  |  Light (347)  |  Science And Art (181)  |  Spectrum (24)  |  Synthesis (44)

Science progresses by a series of combinations in which chance plays not the least role. Its life is rough and resembles that of minerals which grow by juxtaposition [accretion]. This applies not only to science such as it emerges [results] from the work of a series of scientists, but also to the particular research of each one of them. In vain would analysts dissimulate: (however abstract it may be, analysis is no more our power than that of others); they do not deduce, they combine, they compare: (it must be sought out, sounded out, solicited.) When they arrive at the truth it is by cannoning from one side to another that they come across it.
English translation from manuscript, in Évariste Galois and Peter M. Neumann, 'Dossier 12: On the progress of pure analysis', The Mathematical Writings of Évariste Galois (2011), 263. A transcription of the original French is on page 262. In the following quote from that page, indicated deletions are omitted, and Webmaster uses parentheses to enclose indications of insertions above the original written line. “La science progresse par une série de combinaisons où le hazard ne joue pas le moindre rôle; sa vie est brute et ressemble à celle des minéraux qui croissent par juxtà position. Cela s’applique non seulement à la science telle qu’elle résulte des travaux d’une série de savants, mais aussi aux recherches particulières à chacun d’eux. En vain les analystes voudraient-ils se le dissimuler: (toute immatérielle qu’elle wst analyse n’est pas pas plus en notre pouvoir que des autres); ils ne déduisent pas, ils combinent, ils comparent: (il faut l’epier, la sonder, la solliciter) quand ils arrivent à la vérité, c’est en heurtant de côté et d’autre qu’il y sont tombés.” Webmaster corrected from typo “put” to “but” in the English text.
Science quotes on:  |  Abstract (86)  |  Accretion (5)  |  Across (32)  |  Analyst (8)  |  Apply (77)  |  Arrive (35)  |  Chance (160)  |  Combination (91)  |  Combine (35)  |  Compare (38)  |  Deduce (25)  |  Emerge (21)  |  Grow (99)  |  In Vain (9)  |  Juxtaposition (3)  |  Least (74)  |  Life (1131)  |  Mineral (41)  |  Particular (76)  |  Play (112)  |  Power (366)  |  Progress (368)  |  Research (590)  |  Resemble (29)  |  Result (389)  |  Role (49)  |  Rough (6)  |  Science (2067)  |  Scientist (522)  |  Seek (107)  |  Series (51)  |  Side (51)  |  Sound (90)  |  Truth (928)  |  Work (635)

Sign language is the equal of speech, lending itself equally to the rigorous and the poetic, to philosophical analysis or to making love.
In The Times (16 Jun 1994).
Science quotes on:  |  Equal (83)  |  Love (224)  |  Philosophical (23)  |  Poetic (7)  |  Rigorous (23)  |  Speech (47)

Statistical analysis in cases involving small numbers can be particularly helpful because on many occasions intuition can be highly misleading.
In essay 'Statistical Proof of Employment Discrimination', collected in Judith M. Tanur et al. (eds.), Statistics, a Guide to the Unknown (3rd ed., 1989), 83.
Science quotes on:  |  Helpful (15)  |  Intuition (57)  |  Misleading (15)  |  Number (282)  |  Occasion (23)  |  Particularly (21)  |  Small (163)  |  Statistics (147)

Statistician: A man who believes figures don't lie but admits that, under analysis some of them won't stand up either.
Evan Esar
The Dictionary of Humorous Quotations (1949). In Robert Harris Shutler, Mathematics 436 - Finely Explained (2004), 3.
Science quotes on:  |  Definition (192)  |  Lie (115)  |  Number (282)  |  Quip (80)  |  Statistician (19)

Statistician: A man who believes figures don’t lie, but admits that under analysis some of them won’t stand up either.
Anonymous
From Evan Esar, Esar’s Comic Dictionary (1943), as cited in Raymond Rowe and Joseph Chamberlain, A Spoonful of Sugar: 1,001 Quotations (2007), 56.
Science quotes on:  |  Admit (45)  |  Belief (504)  |  Figure (69)  |  Lie (115)  |  Statistician (19)  |  Verify (17)

Sylvester was incapable of reading mathematics in a purely receptive way. Apparently a subject either fired in his brain a train of active and restless thought, or it would not retain his attention at all. To a man of such a temperament, it would have been peculiarly helpful to live in an atmosphere in which his human associations would have supplied the stimulus which he could not find in mere reading. The great modern work in the theory of functions and in allied disciplines, he never became acquainted with …
What would have been the effect if, in the prime of his powers, he had been surrounded by the influences which prevail in Berlin or in Gottingen? It may be confidently taken for granted that he would have done splendid work in those domains of analysis, which have furnished the laurels of the great mathematicians of Germany and France in the second half of the present century.
In Address delivered at a memorial meeting at the Johns Hopkins University (2 May 1897), published in Bulletin of the American Mathematical Society (Jun 1897), 303. Also in Johns Hopkins University Circulars, 16 (1897), 54.
Science quotes on:  |  Acquaint (9)  |  Active (25)  |  Ally (6)  |  Apparently (19)  |  Association (21)  |  Atmosphere (79)  |  Attention (121)  |  Become (172)  |  Berlin (10)  |  Brain (213)  |  Century (131)  |  Confidently (2)  |  Discipline (53)  |  Domain (42)  |  Effect (166)  |  Find (408)  |  Fire (133)  |  France (27)  |  Function (131)  |  Furnish (42)  |  Germany (13)  |  Grant (32)  |  Great (534)  |  Half (56)  |  Helpful (15)  |  Human (550)  |  Incapable (17)  |  Influence (140)  |  Laurel (2)  |  Live (272)  |  Mathematician (384)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1205)  |  Mere (82)  |  Modern (162)  |  Peculiarly (4)  |  Power (366)  |  Present (176)  |  Prevail (17)  |  Prime (11)  |  Purely (28)  |  Read (145)  |  Receptive (4)  |  Restless (11)  |  Retain (19)  |  Second (59)  |  Splendid (12)  |  Stimulus (20)  |  Subject (240)  |  Supply (47)  |  Surround (29)  |  James Joseph Sylvester (58)  |  Temperament (11)  |  Theory (696)  |  Thought (546)  |  Train (45)  |  Work (635)

Talent deals with the actual, with discovered and realized truths, any analyzing, arranging, combining, applying positive knowledge, and, in action, looking to precedents. Genius deals with the possible, creates new combinations, discovers new laws, and acts from an insight into new principles.
In 'Genius', Wellman’s Miscellany (Dec 1871), 4, No. 6, 203.
Science quotes on:  |  Act (117)  |  Action (185)  |  Actual (48)  |  Applying (3)  |  Arranging (3)  |  Combination (91)  |  Create (153)  |  Deal (49)  |  Discovery (680)  |  Genius (249)  |  Insight (73)  |  Knowledge (1306)  |  Law (515)  |  Looking (26)  |  New (496)  |  Positive (44)  |  Possibility (116)  |  Precedent (4)  |  Principle (292)  |  Realize (90)  |  Talent (63)  |  Truth (928)

The action of the mind in the acquisition of knowledge of any sort is synthetic-analytic; that is, uniting and separating. These are the two sides, or aspects, of the one process. … There is no such thing as a synthetic activity that is not accompanied by the analytic; and there is no analytic activity that is not accompanied by the synthetic. Children cannot be taught to perform these knowing acts. It is the nature of the mind to so act when it acts at all.
In The Public-School Journal (Jan 1895), Vol. 14, 281-282.
Science quotes on:  |  Accompany (22)  |  Acquisition (42)  |  Action (185)  |  Activity (135)  |  Child (252)  |  Education (347)  |  Knowledge (1306)  |  Mind (760)  |  Nature (1223)  |  Perform (38)  |  Process (267)  |  Separate (74)  |  Synthesis (44)  |  Teach (188)  |  Unite (23)

The activity characteristic of professional engineering is the design of structures, machines, circuits, or processes, or of combinations of these elements into systems or plants and the analysis and prediction of their performance and costs under specified working conditions.
1954
Science quotes on:  |  Activity (135)  |  Characteristic (96)  |  Circuit (15)  |  Combination (91)  |  Condition (163)  |  Cost (44)  |  Design (115)  |  Element (162)  |  Engineering (141)  |  Machine (157)  |  Performance (33)  |  Plant (200)  |  Prediction (71)  |  Process (267)  |  Professional (37)  |  Specify (6)  |  Structure (225)  |  System (191)  |  Work (635)

The analysis of man discloses three chemical elements - a job, a meal and a woman.
Science quotes on:  |  Element (162)  |  Food (154)  |  Job (43)  |  Man (373)  |  Woman (111)

The analysis of variance is not a mathematical theorem, but rather a convenient method of arranging the arithmetic.
Remarking on the paper, ‘Statistics in Agricultural Research’ by J. Wishart, Journal of the Royal Statistical Society, Supplement (1934), 1, 52. As cited in Michael Cowle, Statistics in Psychology: An Historical Perspective (2005), 210.
Science quotes on:  |  Arithmetic (121)  |  Arranging (3)  |  Convenience (34)  |  Mathematics (1205)  |  Method (239)  |  Theorem (90)  |  Variance (5)

The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform. It can follow analysis; but it has no power of anticipating any analytical relations or truths. Its province is to assist us to making available what we are already acquainted with.
[Describing Charles Babbage's machine.]
In her notes as translator, following her translation of I. F. Menabrea, 'Sketch of the Analytical Engine Invented by Charles Babbage, Esq.', (from Bibliothègue Universelle de Génève (Oct 1842), No. 82) in Richard Taylor (ed.), Scientific Memoirs (1843), 3, 722.
Science quotes on:  |  Analytical Engine (5)  |  Anticipate (10)  |  Charles Babbage (54)  |  Computer (105)  |  Originate (21)  |  Pretension (6)  |  Truth (928)

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method—more daring than anything that the history of philosophy records—of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.
In 'What Knowledge is of Most Worth?', Presidential address to the National Education Association, Denver, Colorado (9 Jul 1895). In Educational Review (Sep 1895), 10, 109.
Science quotes on:  |  Calculus (51)  |  René Descartes (81)  |  Estimates of Mathematics (30)  |  Carl Friedrich Gauss (77)  |  Geometry (232)  |  Gottfried Wilhelm Leibniz (49)  |  Nikolay Ivanovich Lobachevsky (2)  |  Sir Isaac Newton (333)  |  Reason (471)  |  Bernhard Riemann (7)  |  Science And Mathematics (10)  |  Sense (321)  |  Supremacy (3)  |  James Joseph Sylvester (58)  |  Tool (87)

The artist does not illustrate science; … [but] he frequently responds to the same interests that a scientist does, and expresses by a visual synthesis what the scientist converts into analytical formulae or experimental demonstrations.
'The Arts', in Charles Austin Beard, Whither Mankind: a Panorama of Modern Civilization (1928, 1971), 296.
Science quotes on:  |  Artist (69)  |  Conversion (14)  |  Demonstration (86)  |  Experiment (602)  |  Expression (110)  |  Formula (80)  |  Frequently (21)  |  Illustration (29)  |  Interest (237)  |  Response (29)  |  Scientist (522)  |  Synthesis (44)

The combination in time and space of all these thoughtful conceptions [of Nature] exhibits not only thought, it shows also premeditation, power, wisdom, greatness, prescience, omniscience, providence. In one word, all these facts in their natural connection proclaim aloud the One God, whom man may know, adore, and love; and Natural History must in good time become the analysis of the thoughts of the Creator of the Universe….
In Essay on Classification (1851), 205.
Science quotes on:  |  Adore (3)  |  Combination (91)  |  Conception (92)  |  Connection (111)  |  Creator (55)  |  Exhibit (20)  |  Fact (733)  |  God (535)  |  Greatness (42)  |  Know (556)  |  Love (224)  |  Natural (173)  |  Natural History (50)  |  Nature (1223)  |  Omniscience (3)  |  Power (366)  |  Prescience (2)  |  Proclaim (15)  |  Providence (6)  |  Science And Religion (302)  |  Show (93)  |  Thought (546)  |  Time And Space (31)  |  Universe (686)  |  Wisdom (182)

The contents of this section will furnish a very striking illustration of the truth of a remark, which I have more than once made in my philosophical writings, and which can hardly be too often repeated, as it tends greatly to encourage philosophical investigations viz. That more is owing to what we call chance, that is, philosophically speaking, to the observation of events arising from unknown causes, than to any proper design, or pre-conceived theory in this business. This does not appear in the works of those who write synthetically upon these subjects; but would, I doubt not, appear very strikingly in those who are the most celebrated for their philosophical acumen, did they write analytically and ingenuously.
'On Dephlogisticated Air, and the Constitution of the Atmosphere', in The Discovery of Oxygen, Part I, Experiments by Joseph Priestley 1775 (Alembic Club Reprint, 1894), 5.
Science quotes on:  |  Cause (285)  |  Chance (160)  |  Design (115)  |  Investigation (176)  |  Observation (450)  |  Theory (696)  |  Unknown (107)

The domain, over which the language of analysis extends its sway, is, indeed, relatively limited, but within this domain it so infinitely excels ordinary language that its attempt to follow the former must be given up after a few steps. The mathematician, who knows how to think in this marvelously condensed language, is as different from the mechanical computer as heaven from earth.
In Jahresberichte der Deutschen Mathematiker Vereinigung, 13, 367. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 197.
Science quotes on:  |  Attempt (126)  |  Computer (105)  |  Condense (12)  |  Different (186)  |  Domain (42)  |  Earth (638)  |  Excel (4)  |  Extend (44)  |  Heaven (153)  |  Infinite (130)  |  Language (228)  |  Limit (126)  |  Marvelous (19)  |  Mathematician (384)  |  Mathematics As A Language (20)  |  Mechanical (50)  |  Ordinary (73)  |  Relatively (7)  |  Sway (4)  |  Think (347)

The essence of engineering consists not so much in the mere construction of the spectacular layouts or developments, but in the invention required—the analysis of the problem, the design, the solution by the mind which directs it all.
As quoted, “he said to the writer in effect,” Robert Fletcher, 'William Hood '67, Chief Engineer of the Southern Pacific Railroad Lines, Dartmouth Alumni Magazine (1919), Vol. 11, 223.
Science quotes on:  |  Bridge (30)  |  Construction (83)  |  Design (115)  |  Engineering (141)  |  Essence (55)  |  Invention (324)  |  Layout (2)  |  Mind (760)  |  Problem (497)  |  Solution (216)  |  Spectacular (10)  |  Tunnel (8)

The faculty of resolution is possibly much invigorated by mathematical study, and especially by that highest branch of it which, unjustly, merely on account of its retrograde operations, has been called, as if par excellence, analysis.
In The Murders in Rue Morgue.
Science quotes on:  |  Account (68)  |  Branch (107)  |  Call (128)  |  Especially (31)  |  Faculty (70)  |  High (153)  |  Invigorate (3)  |  Mathematics (1205)  |  Merely (82)  |  Operation (121)  |  Par Excellence (2)  |  Possibly (19)  |  Resolution (18)  |  Retrograde (5)  |  Study (476)  |  Unjustly (2)  |  Value Of Mathematics (60)

The feeling of understanding is as private as the feeling of pain. The act of understanding is at the heart of all scientific activity; without it any ostensibly scientific activity is as sterile as that of a high school student substituting numbers into a formula. For this reason, science, when I push the analysis back as far as I can, must be private.
Reflections of a Physicist (1950), 72.
Science quotes on:  |  Understanding (325)

The great masters of modern analysis are Lagrange, Laplace, and Gauss, who were contemporaries. It is interesting to note the marked contrast in their styles. Lagrange is perfect both in form and matter, he is careful to explain his procedure, and though his arguments are general they are easy to follow. Laplace on the other hand explains nothing, is indifferent to style, and, if satisfied that his results are correct, is content to leave them either with no proof or with a faulty one. Gauss is as exact and elegant as Lagrange, but even more difficult to follow than Laplace, for he removes every trace of the analysis by which he reached his results, and studies to give a proof which while rigorous shall be as concise and synthetical as possible.
In History of Mathematics (3rd Ed., 1901), 468.
Science quotes on:  |  Anecdote (20)  |  Concise (8)  |  Contemporary (30)  |  Content (69)  |  Contrast (29)  |  Correct (85)  |  Difficult (121)  |  Easy (102)  |  Elegant (16)  |  Exact (68)  |  Explanation (177)  |  Faulty (3)  |  Carl Friedrich Gauss (77)  |  Count Joseph-Louis de Lagrange (26)  |  Pierre-Simon Laplace (62)  |  Leave (128)  |  Mathematicians and Anecdotes (141)  |  Perfection (89)  |  Procedure (25)  |  Proof (245)  |  Reasoning (100)  |  Remove (26)  |  Result (389)  |  Rigor (23)  |  Satisfy (27)  |  Style (22)  |  Synthetic (16)

The history of thought should warn us against concluding that because the scientific theory of the world is the best that has yet been formulated, it is necessarily complete and final. We must remember that at bottom the generalizations of science or, in common parlance, the laws of nature are merely hypotheses devised to explain that ever-shifting phantasmagoria of thought which we dignify with the high-sounding names of the world and the universe. In the last analysis magic, religion, and science are nothing but theories of thought.
In The Golden Bough: A Study in Magic and Religion (1890, 1900), Vol. 3, 460.
Science quotes on:  |  Best (173)  |  Common (122)  |  Complete (87)  |  Conclude (16)  |  Devise (14)  |  Dignify (2)  |  Explain (107)  |  Final (50)  |  Formulate (15)  |  Generalization (41)  |  History (369)  |  Hypothesis (252)  |  Law Of Nature (64)  |  Magic (78)  |  Mere (82)  |  Name (170)  |  Necessarily (30)  |  Nothing (395)  |  Parlance (2)  |  Phantasmagoria (3)  |  Religion (239)  |  Remember (82)  |  Science (2067)  |  Scientific Theory (24)  |  Shifting (5)  |  Theory (696)  |  Thought (546)  |  Universe (686)  |  Warn (5)  |  World (898)

The hypothesis that man is not free is essential to the application of scientific method to the study of human behavior. The free inner man who is held responsible for the behavior of the external biological organism is only a prescientific substitute for the kinds of causes which are discovered in the course of a scientific analysis.
In Science and Human Behavior (1953), 447.
Science quotes on:  |  Behavior (60)  |  Biology (168)  |  Cause (285)  |  Discovery (680)  |  External (57)  |  Freedom (102)  |  Hypothesis (252)  |  Kind (140)  |  Man (373)  |  Organism (150)  |  Responsible (17)  |  Substitute (28)

The indescribable pleasure—which pales the rest of life's joys—is abundant compensation for the investigator who endures the painful and persevering analytical work that precedes the appearance of the new truth, like the pain of childbirth. It is true to say that nothing for the scientific scholar is comparable to the things that he has discovered. Indeed, it would be difficult to find an investigator willing to exchange the paternity of a scientific conquest for all the gold on earth. And if there are some who look to science as a way of acquiring gold instead of applause from the learned, and the personal satisfaction associated with the very act of discovery, they have chosen the wrong profession.
From Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad. (1897), as translated by Neely and Larry W. Swanson, in Advice for a Young Investigator (1999), 50.
Science quotes on:  |  Abundance (21)  |  Acquisition (42)  |  Appearance (85)  |  Applause (9)  |  Childbirth (2)  |  Choice (79)  |  Comparable (6)  |  Compensation (7)  |  Conquest (19)  |  Difficulty (146)  |  Discovery (680)  |  Earth (638)  |  Endurance (4)  |  Exchange (12)  |  Find (408)  |  Gold (68)  |  Indescribable (2)  |  Investigator (35)  |  Joy (88)  |  Learned (24)  |  Life (1131)  |  New (496)  |  Nothing (395)  |  Pain (101)  |  Pale (9)  |  Paternity (2)  |  Perseverance (20)  |  Pleasure (133)  |  Preceding (8)  |  Profession (60)  |  Rest (93)  |  Satisfaction (56)  |  Scholar (38)  |  Scientist (522)  |  Truth (928)  |  Willingness (9)  |  Work (635)

The language of analysis, most perfect of all, being in itself a powerful instrument of discoveries, its notations, especially when they are necessary and happily conceived, are so many germs of new calculi.
From Theorie Analytique des Probabilités (1812), 7. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 200. From the original French, “La langue de l’Analyse, la plus parfaite de toutes, étant par elle-même un puissant instrument de découvertes, ses notations, lorsqu’elles sont nécessaires et heureusement imaginées, sont autant de germes de nouveaux calculs.”
Science quotes on:  |  Calculation (100)  |  Conceive (39)  |  Discovery (680)  |  Germ (32)  |  Instrument (95)  |  Language (228)  |  Mathematics As A Language (20)  |  Necessary (154)  |  New (496)  |  Notation (23)  |  Perfect (89)  |  Powerful (68)

The mathematical talent of Cayley was characterized by clearness and extreme elegance of analytical form; it was re-enforced by an incomparable capacity for work which has caused the distinguished scholar to be compared with Cauchy.
In Comptes Rendus (1895), 120, 234.
Science quotes on:  |  Capacity (64)  |  Baron Augustin-Louis Cauchy (10)  |  Cause (285)  |  Arthur Cayley (17)  |  Characterize (20)  |  Clearness (11)  |  Compare (38)  |  Distinguish (64)  |  Elegance (30)  |  Extreme (56)  |  Form (314)  |  Incomparable (12)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1205)  |  Scholar (38)  |  Talent (63)  |  Work (635)

The methods of science aren’t foolproof, but they are indefinitely perfectible. Just as important: there is a tradition of criticism that enforces improvement whenever and wherever flaws are discovered. The methods of science, like everything else under the sun, are themselves objects of scientific scrutiny, as method becomes methodology, the analysis of methods. Methodology in turn falls under the gaze of epistemology, the investigation of investigation itself—nothing is off limits to scientific questioning. The irony is that these fruits of scientific reflection, showing us the ineliminable smudges of imperfection, are sometimes used by those who are suspicious of science as their grounds for denying it a privileged status in the truth-seeking department—as if the institutions and practices they see competing with it were no worse off in these regards. But where are the examples of religious orthodoxy being simply abandoned in the face of irresistible evidence? Again and again in science, yesterday’s heresies have become today’s new orthodoxies. No religion exhibits that pattern in its history.
…...
Science quotes on:  |  Abandon (48)  |  Arent (5)  |  Badly (15)  |  Become (172)  |  Compete (6)  |  Criticism (60)  |  Deny (42)  |  Department (47)  |  Discover (199)  |  Enforce (8)  |  Epistemology (7)  |  Everything (181)  |  Evidence (183)  |  Example (94)  |  Exhibit (20)  |  Face (108)  |  Fall (120)  |  Flaw (10)  |  Foolproof (3)  |  Fruit (71)  |  Gaze (16)  |  Ground (90)  |  Heresy (8)  |  History (369)  |  Imperfection (24)  |  Important (205)  |  Improvement (74)  |  Indefinitely (10)  |  Institution (39)  |  Investigation (176)  |  Irony (8)  |  Irresistible (10)  |  Limit (126)  |  Method (239)  |  Methodology (8)  |  New (496)  |  Nothing (395)  |  Object (175)  |  Orthodoxy (7)  |  Pattern (79)  |  Practice (94)  |  Privilege (26)  |  Question (404)  |  Reflection (60)  |  Regard (95)  |  Religion (239)  |  Religious (49)  |  Science (2067)  |  Scientific (236)  |  Scrutiny (14)  |  See (369)  |  Show (93)  |  Simply (53)  |  Smudge (2)  |  Sometimes (43)  |  Status (20)  |  Sun (276)  |  Suspicious (3)  |  Themselves (44)  |  Today (117)  |  Tradition (49)  |  Turn (118)  |  Whenever (9)  |  Yesterday (18)

The most striking characteristic of the written language of algebra and of the higher forms of the calculus is the sharpness of definition, by which we are enabled to reason upon the symbols by the mere laws of verbal logic, discharging our minds entirely of the meaning of the symbols, until we have reached a stage of the process where we desire to interpret our results. The ability to attend to the symbols, and to perform the verbal, visible changes in the position of them permitted by the logical rules of the science, without allowing the mind to be perplexed with the meaning of the symbols until the result is reached which you wish to interpret, is a fundamental part of what is called analytical power. Many students find themselves perplexed by a perpetual attempt to interpret not only the result, but each step of the process. They thus lose much of the benefit of the labor-saving machinery of the calculus and are, indeed, frequently incapacitated for using it.
In 'Uses of Mathesis', Bibliotheca Sacra (Jul 1875), 32, 505.
Science quotes on:  |  Ability (108)  |  Algebra (104)  |  Attempt (126)  |  Benefit (73)  |  Calculus (51)  |  Characteristic (96)  |  Definition (192)  |  Fundamental (164)  |  Incapacitate (2)  |  Interpret (19)  |  Labor (73)  |  Language (228)  |  Logic (260)  |  Lose (94)  |  Machinery (33)  |  Mathematics As A Language (20)  |  Meaning (113)  |  Mind (760)  |  Perpetual (21)  |  Perplex (6)  |  Reason (471)  |  Result (389)  |  Sharp (14)  |  Step (110)  |  Student (203)  |  Symbol (73)

The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression, more exact, compact, and ready than ordinary language. The great body of physical science, a great deal of the essential facts of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of the great complex world-wide States that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write.
Mankind in the Making (1903), 204.
Science quotes on:  |  Accessible (16)  |  Average (42)  |  Citizen (31)  |  Compact (5)  |  Essential (117)  |  Expression (110)  |  Fact (733)  |  Form (314)  |  Language (228)  |  Mathematics (1205)  |  Maximum (12)  |  Minimum (12)  |  Necessity (143)  |  Physical Science (66)  |  Politics (96)  |  Quality (95)  |  Read (145)  |  Society (228)  |  Supplement (6)  |  Thought (546)  |  Training (66)  |  World (898)  |  Write (154)

The notion, which is really the fundamental one (and I cannot too strongly emphasise the assertion), underlying and pervading the whole of modern analysis and geometry, is that of imaginary magnitude in analysis and of imaginary space in geometry.
In Presidential Address, in Collected Works, Vol. 11, 434.
Science quotes on:  |  Assertion (32)  |  Emphasize (12)  |  Fundamental (164)  |  Geometry (232)  |  Imaginary (16)  |  Magnitude (45)  |  Modern (162)  |  Modern Mathematics (38)  |  Notion (59)  |  Pervade (10)  |  Space (257)  |  Strongly (9)  |  Underlying (18)  |  Whole (192)

The observer is not he who merely sees the thing which is before his eyes, but he who sees what parts the thing is composed of. To do this well is a rare talent. One person, from inattention, or attending only in the wrong place, overlooks half of what he sees; another sets down much more than he sees, confounding it with what he imagines, or with what he infers; another takes note of the kind of all the circumstances, but being inexpert in estimating their degree, leaves the quantity of each vague and uncertain; another sees indeed the whole, but makes such an awkward division of it into parts, throwing into one mass things which require to be separated, and separating others which might more conveniently be considered as one, that the result is much the same, sometimes even worse than if no analysis had been attempted at all.
In A System of Logic Ratiocinative and Inductive (1858), 216.
Science quotes on:  |  Attempt (126)  |  Attend (11)  |  Awkward (7)  |  Circumstance (66)  |  Composed (3)  |  Confound (14)  |  Consider (81)  |  Convenience (34)  |  Degree (82)  |  Division (34)  |  Estimate (28)  |  Eye (222)  |  Half (56)  |  Imagine (76)  |  Inattention (5)  |  Inexpert (2)  |  Infer (12)  |  Kind (140)  |  Mass (78)  |  Merely (82)  |  Note (34)  |  Observation (450)  |  Observer (42)  |  Overlook (12)  |  Part (222)  |  Person (154)  |  Place (175)  |  Quantity (65)  |  Rare (50)  |  Require (85)  |  Result (389)  |  See (369)  |  Separate (74)  |  Set Down (2)  |  Talent (63)  |  Uncertain (14)  |  Vague (26)  |  Whole (192)  |  Worse (24)  |  Wrong (139)

The person who did most to give to analysis the generality and symmetry which are now its pride, was also the person who made mechanics analytical; I mean Euler.
From History of the Inductive Sciences from the Earliest to the Present (1837), Vol. 2, 93.
Science quotes on:  |  Leonhard Euler (35)  |  Generality (34)  |  Mechanics (57)  |  Pride (64)  |  Symmetry (37)

The philosopher of science is not much interested in the thought processes which lead to scientific discoveries; he looks for a logical analysis of the completed theory, including the establishing its validity. That is, he is not interested in the context of discovery, but in the context of justification.
'The Philosophical Significance of the Theory of Relativity' (1938). Collected in P.A. Schillp (ed.). Albert Einstein: Philosopher-Scientist (1949, 1970), 292. Cited in G. Holton, Thematic Origins of Scientific Thought (1973), 7.
Science quotes on:  |  Completion (17)  |  Context (22)  |  Discovery (680)  |  Establishment (35)  |  Interest (237)  |  Justification (40)  |  Logic (260)  |  Philosophy (259)  |  Process (267)  |  Theory (696)  |  Validity (31)

The philosopher of science is not much interested in the thought processes which lead to scientific discoveries; he looks for a logical analysis of the completed theory, including the relationships establishing its validity. That is, he is not interested in the context of discovery, but in the context of justification.
In'The Philosophical Significance of the Theory of Relativity' (1949), collected in P.A. Schilpp (ed), Albert Einstein: Philosopher-Scientist (1969), 292. As quoted and cited in Stanley Goldberg, Understanding Relativity: Origin and Impact of a Scientific Revolution (1984, 2013), 306.
Science quotes on:  |  Context (22)  |  Discovery (680)  |  Justification (40)  |  Logic (260)  |  Process (267)  |  Relationship (71)  |  Science And Philosophy (5)  |  Theory (696)  |  Thought (546)  |  Validity (31)

The precise equivalence of the chromosomes contributed by the two sexes is a physical correlative of the fact that the two sexes play, on the whole, equal parts in hereditary transmission, and it seems to show that the chromosomal substance, the chromatin, is to be regarded as the physical basis of inheritance. Now, chromatin is known to be closely similar to, if not identical with, a substance known as nuclein (C29H49N9O22, according to Miescher), which analysis shows to be a tolerably definite chemical compased of nucleic acid (a complex organic acid rich in phosphorus) and albumin. And thus we reach the remarkable conclusion that inheritance may, perhaps, be effected by the physical transmission of a particular chemical compound from parent to offspring.
In An Atlas of the Fertilization and Karyokinesis of the Ovum (1895), 4.
Science quotes on:  |  Albumin (2)  |  Chromatin (4)  |  Chromosome (19)  |  Heredity (53)  |  Inheritance (19)  |  Offspring (16)  |  Parent (46)  |  Phosphorus (15)  |  Sex (49)  |  Transmission (25)

The present rate of progress [in X-ray crystallography] is determined, not so much by the lack of problems to investigate or the limited power of X-ray analysis, as by the restricted number of investigators who have had a training in the technique of the new science, and by the time it naturally takes for its scientific and technical importance to become widely appreciated.
Concluding remark in Lecture (1936) on 'Forty Years of Crystal Physics', collected in Needham and Pagel (eds.) in Background to Modern Science: Ten Lectures at Cambridge Arranged by the History of Science Committee, (1938), 89.
Science quotes on:  |  Appreciate (30)  |  Become (172)  |  Determine (76)  |  Importance (218)  |  Investigation (176)  |  Investigator (35)  |  Lack (77)  |  Limited (18)  |  Naturally (11)  |  New (496)  |  Number (282)  |  Power (366)  |  Present (176)  |  Problem (497)  |  Progress (368)  |  Rate (29)  |  Restricted (2)  |  Science (2067)  |  Scientific (236)  |  Take (10)  |  Technical (42)  |  Technique (49)  |  Time (595)  |  Training (66)  |  Widely (8)  |  X-ray Crystallography (11)

The present state of the system of nature is evidently a consequence of what it was in the preceding moment, and if we conceive of an intelligence that at a given instant comprehends all the relations of the entities of this universe, it could state the respective position, motions, and general affects of all these entities at any time in the past or future. Physical astronomy, the branch of knowledge that does the greatest honor to the human mind, gives us an idea, albeit imperfect, of what such an intelligence would be. The simplicity of the law by which the celestial bodies move, and the relations of their masses and distances, permit analysis to follow their motions up to a certain point; and in order to determine the state of the system of these great bodies in past or future centuries, it suffices for the mathematician that their position and their velocity be given by observation for any moment in time. Man owes that advantage to the power of the instrument he employs, and to the small number of relations that it embraces in its calculations. But ignorance of the different causes involved in the production of events, as well as their complexity, taken together with the imperfection of analysis, prevents our reaching the same certainty about the vast majority of phenomena. Thus there are things that are uncertain for us, things more or less probable, and we seek to compensate for the impossibility of knowing them by determining their different degrees of likelihood. So it was that we owe to the weakness of the human mind one of the most delicate and ingenious of mathematical theories, the science of chance or probability.
'Recherches, 1º, sur l'Intégration des Équations Différentielles aux Différences Finies, et sur leur Usage dans la Théorie des Hasards' (1773, published 1776). In Oeuvres complètes de Laplace, 14 Vols. (1843-1912), Vol. 8, 144-5, trans. Charles Coulston Gillispie, Pierre-Simon Laplace 1749-1827: A Life in Exact Science (1997), 26.
Science quotes on:  |  Astronomy (204)  |  Calculation (100)  |  Celestial (21)  |  Certainty (131)  |  Chance (160)  |  Complexity (91)  |  Difference (246)  |  Distance (77)  |  Event (116)  |  Honour (25)  |  Human Mind (82)  |  Ignorance (213)  |  Impossibility (53)  |  Instrument (95)  |  Intelligence (168)  |  Knowledge (1306)  |  Law (515)  |  Likelihood (10)  |  Mass (78)  |  Mathematician (384)  |  Motion (160)  |  Nature (1223)  |  Observation (450)  |  Phenomenon (278)  |  Position (76)  |  Prediction (71)  |  Probability (106)  |  Relation (154)  |  Simplicity (147)  |  Theory (696)  |  Time (595)  |  Uncertainty (42)  |  Universe (686)  |  Velocity (16)  |  Weakness (36)

The problems of analyzing war operations are … rather nearer, in general, to many problems, say of biology or of economics, than to most problems of physics, where usually a great deal of numerical data are ascertainable about relatively simple phenomena.
In report at the British Association Annual Meeting, Dundee (30 Aug 1947), published in 'Operational Research in War and Peace', The Advancement of Science (1948), 17, 320-332. Collected in P.M.S. Blackett, Studies of War: Nuclear and Conventional (1962), 177.
Science quotes on:  |  Biology (168)  |  Data (120)  |  Economics (34)  |  Operation (121)  |  Physics (348)  |  Problem (497)  |  War (161)

The proof given by Wright, that non-adaptive differentiation will occur in small populations owing to “drift,” or the chance fixation of some new mutation or recombination, is one of the most important results of mathematical analysis applied to the facts of neo-mendelism. It gives accident as well as adaptation a place in evolution, and at one stroke explains many facts which puzzled earlier selectionists, notably the much greater degree of divergence shown by island than mainland forms, by forms in isolated lakes than in continuous river-systems.
Evolution: The Modern Synthesis (1942), 199-200.
Science quotes on:  |  Accident (66)  |  Adaptation (49)  |  Chance (160)  |  Differentiation (18)  |  Divergence (4)  |  Drift (13)  |  Evolution (535)  |  Island (24)  |  Lake (18)  |  Mainland (3)  |  Mathematics (1205)  |  Mutation (30)  |  Population (79)  |  Proof (245)  |  River (79)

The reason Dick's [Richard Feynman] physics was so hard for ordinary people to grasp was that he did not use equations. The usual theoretical physics was done since the time of Newton was to begin by writing down some equations and then to work hard calculating solutions of the equations. This was the way Hans [Bethe] and Oppy [Oppenheimer] and Julian Schwinger did physics. Dick just wrote down the solutions out of his head without ever writing down the equations. He had a physical picture of the way things happen, and the picture gave him the solutions directly with a minimum of calculation. It was no wonder that people who had spent their lives solving equations were baffled by him. Their minds were analytical; his was pictorial.
Quoted in Michio Kaku and Jennifer Trainer Thompson, Beyond Einstein: the Cosmic Quest for the Theory of the Universe (1987, 1999), 56-57, citing Freeman Dyson, Disturbing the Universe (1979, 1981), 55-56.
Science quotes on:  |  Bafflement (2)  |  Hans Albrecht Bethe (5)  |  Biography (232)  |  Calculation (100)  |  Difficulty (146)  |  Equation (96)  |  Richard P. Feynman (122)  |  Happening (32)  |  Hard (99)  |  Life (1131)  |  Minimum (12)  |  Sir Isaac Newton (333)  |  J. Robert Oppenheimer (39)  |  Physics (348)  |  Picture (77)  |  Solution (216)  |  Theoretical Physics (18)  |  Understanding (325)  |  Wonder (169)  |  Writing (81)

The science of optics, like every other physical science, has two different directions of progress, which have been called the ascending and the descending scale, the inductive and the deductive method, the way of analysis and of synthesis. In every physical science, we must ascend from facts to laws, by the way of induction and analysis; and we must descend from laws to consequences, by the deductive and synthetic way. We must gather and group appearances, until the scientific imagination discerns their hidden law, and unity arises from variety; and then from unity must reduce variety, and force the discovered law to utter its revelations of the future.
In On a General Method of Expressing the Paths of Light, & of the Planets, by the Coefficients of a Characteristic Function (1833), 7-8. [The spelling as “groupe” in the original text, has her been corrected to “group” to avoid an intrusive “sic”.]
Science quotes on:  |  Appearance (85)  |  Arise (49)  |  Ascend (12)  |  Ascent (7)  |  Consequence (114)  |  Deductive (11)  |  Descend (11)  |  Different (186)  |  Direction (76)  |  Discern (17)  |  Discover (199)  |  Fact (733)  |  Force (249)  |  Future (287)  |  Gather (39)  |  Group (72)  |  Hide (53)  |  Imagination (275)  |  Induction (60)  |  Inductive (10)  |  Law (515)  |  Method (239)  |  Optics (20)  |  Physical Science (66)  |  Progress (368)  |  Reduce (53)  |  Revelation (34)  |  Scale (63)  |  Scientific (236)  |  Synthesis (44)  |  Synthetic (16)  |  Unity (54)  |  Utter (7)  |  Variety (71)

The science of the modern school … is in effect … the acquisition of imperfectly analyzed misstatements about entrails, elements, and electricity…
Mankind in the Making (1903), 206.
Science quotes on:  |  Acquisition (42)  |  Electricity (136)  |  Element (162)  |  Entrail (2)  |  Imperfect (20)  |  School (119)  |  Science (2067)

The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.
Elementary Mathematics From an Advanced Standpoint (1908). 3rd edition (1924), trans. E. R. Hedrick and C. A. Noble (1932), Vol. 1, 155.
Science quotes on:  |  18th Century (19)  |  Algebra (104)  |  Calculus (51)  |  Difficulty (146)  |  Imperfection (24)  |  Infinitesimal (15)  |  Teacher (120)

The union of philosophical and mathematical productivity, which besides in Plato we find only in Pythagoras, Descartes and Leibnitz, has always yielded the choicest fruits to mathematics; To the first we owe scientific mathematics in general, Plato discovered the analytic method, by means of which mathematics was elevated above the view-point of the elements, Descartes created the analytical geometry, our own illustrious countryman discovered the infinitesimal calculus—and just these are the four greatest steps in the development of mathematics.
In Geschichte der Mathematik im Altertum und im Mittelalter (1874), 149-150. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 210. From the original German, “Die Verbindung philosophischer und mathematischer Productivität, wie wir sie ausser in Platon wohl nur noch in Pythagoras, Descartes, Leibnitz vorfinden, hat der Mathematik immer die schönsten Früchte gebracht: Ersterem verdanken wir die wissenschaftliche Mathematik überhaupt, Platon erfand die analytische Methode, durch welche sich die Mathematik über den Standpunct der Elemente erhob, Descartes schuf die analytische Geometrie, unser berühmter Landsmann den Infinitesimalcalcül—und eben daß sind die vier grössten Stufen in der Entwickelung der Mathematik.”
Science quotes on:  |  Analytic (10)  |  Calculus (51)  |  Countryman (4)  |  Create (153)  |  René Descartes (81)  |  Development (289)  |  Discover (199)  |  Element (162)  |  Elevate (12)  |  Find (408)  |  Fruit (71)  |  General (160)  |  Geometry (232)  |  Greatest (63)  |  Illustrious (5)  |  Infinitesimal (15)  |  Gottfried Wilhelm Leibniz (49)  |  Mathematics (1205)  |  Means (176)  |  Method (239)  |  Philosophy (259)  |  Plato (76)  |  Productivity (17)  |  Pythagoras (38)  |  Scientific (236)  |  Step (110)  |  Union (21)  |  Viewpoint (8)  |  Yield (38)

The whole art of making experiments in chemistry is founded on the principle: we must always suppose an exact equality or equation between the principles of the body examined and those of the products of its analysis.
From Traité Élémentaire de Chimie (1789), 140. Translation as given in James Riddick Partington, A Short History of Chemistry (1960), 124. This is an alternate translation of part of the same passage on this page that begins “We may lay it down as an incontestible axiom…”
Science quotes on:  |  Body (247)  |  Chemistry (252)  |  Conservation Of Matter (7)  |  Equality (22)  |  Equation (96)  |  Exact (68)  |  Examined (3)  |  Experiment (602)  |  Principle (292)  |  Product (82)  |  Reactant (2)

The whole of the developments and operations of analysis are now capable of being executed by machinery ... As soon as an Analytical Engine exists, it will necessarily guide the future course of science.
Passages From the Life of a Philosopher (1864), 136-137.
Science quotes on:  |  Analytical Engine (5)  |  Computer (105)  |  Development (289)  |  Execution (19)  |  Future (287)  |  Guide (65)  |  Machine (157)  |  Necessity (143)  |  Operation (121)  |  Science (2067)

There are also two kinds of truths, those of reasoning and those of fact. Truths of reasoning are necessary and their opposite is impossible: truths of fact are contingent and their opposite is possible. When a truth is necessary, reason can be found by analysis, resolving it into more simple ideas and truths, until we come to those which are primary.
The Monadology and Other Philosophical Writings (1714), trans. Robert Latta (1898), 235-6.
Science quotes on:  |  Fact (733)  |  Idea (580)  |  Impossible (113)  |  Opposite (50)  |  Reasoning (100)  |  Truth (928)

There are very few theorems in advanced analysis which have been demonstrated in a logically tenable manner. Everywhere one finds this miserable way of concluding from the special to the general and it is extremely peculiar that such a procedure has led to so few of the so-called paradoxes.
From letter to his professor Christoffer Hansteen (1826) in Oeuvres, 2, 263-65. In Morris Kline, Mathematical Thought from Ancient to Modern Times (1990), Vol. 3, 947.
Science quotes on:  |  General (160)  |  Logic (260)  |  Special (77)  |  Theorem (90)

There can be but one opinion as to the beauty and utility of this analysis of Laplace; but the manner in which it has been hitherto presented has seemed repulsive to the ablest mathematicians, and difficult to ordinary mathematical students.[Co-author with Peter Guthrie Tait.]
In William Thomson Baron Kelvin, Peter Guthrie Tait, Treatise on Natural Philosophy (1879), Vol. 1, Preface, vii.
Science quotes on:  |  Ability (108)  |  Beauty (248)  |  Difficult (121)  |  Pierre-Simon Laplace (62)  |  Mathematician (384)  |  Mathematics (1205)  |  Opinion (176)  |  Ordinary (73)  |  Repulsive (7)  |  Student (203)  |  Utility (33)

There is synthesis when, in combining therein judgments that are made known to us from simpler relations, one deduces judgments from them relative to more complicated relations.
There is analysis when from a complicated truth one deduces more simple truths.
In James R. Hofmann, André-Marie Ampère (1996), 158. Cites Académie des Sciences Ampère Archives, lecture notes, box 261.
Science quotes on:  |  Combination (91)  |  Complication (24)  |  Deduction (69)  |  Judgment (101)  |  Relation (154)  |  Simplicity (147)  |  Synthesis (44)  |  Truth (928)

There is a certain way of searching for the truth in mathematics that Plato is said first to have discovered. Theon called this analysis.
…...
Science quotes on:  |  Call (128)  |  Certain (126)  |  Discover (199)  |  First (314)  |  Mathematics (1205)  |  Plato (76)  |  Search (105)  |  Theon (2)  |  Truth (928)

There is only one subject matter for education, and that is Life in all its manifestations. Instead of this single unity, we offer children—Algebra, from which nothing follows; Geometry, from which nothing follows; Science, from which nothing follows; History, from which nothing follows; a Couple of Languages, never mastered; and lastly, most dreary of all, Literature, represented by plays of Shakespeare, with philological notes and short analyses of plot and character to be in substance committed to memory.
In 'The Aims of Education', The Aims of Education: & Other Essays (1917), 10.
Science quotes on:  |  Algebra (104)  |  Character (118)  |  Dreary (5)  |  Education (347)  |  Geometry (232)  |  History (369)  |  Language (228)  |  Life (1131)  |  Literature (79)  |  Manifestation (35)  |  Mastery (28)  |  Memory (106)  |  Nothing (395)  |  Plot (10)  |  Science (2067)  |  William Shakespeare (102)  |  Subject (240)

Those of us who were familiar with the state of inorganic chemistry in universities twenty to thirty years ago will recall that at that time it was widely regarded as a dull and uninteresting part of the undergraduate course. Usually, it was taught almost entirely in the early years of the course and then chiefly as a collection of largely unconnected facts. On the whole, students concluded that, apart from some relationships dependent upon the Periodic table, there was no system in inorganic chemistry comparable with that to be found in organic chemistry, and none of the rigour and logic which characterised physical chemistry. It was widely believed that the opportunities for research in inorganic chemistry were few, and that in any case the problems were dull and uninspiring; as a result, relatively few people specialized in the subject... So long as inorganic chemistry is regarded as, in years gone by, as consisting simply of the preparations and analysis of elements and compounds, its lack of appeal is only to be expected. The stage is now past and for the purpose of our discussion we shall define inorganic chemistry today as the integrated study of the formation, composition, structure and reactions of the chemical elements and compounds, excepting most of those of carbon.
Inaugural Lecture delivered at University College, London (1 Mar 1956). In The Renaissance of Inorganic Chemistry (1956), 4-5.
Science quotes on:  |  Appeal (45)  |  Carbon (49)  |  Composition (60)  |  Compound (58)  |  Dull (32)  |  Element (162)  |  Expectation (55)  |  Few (13)  |  Formation (59)  |  Inorganic Chemistry (4)  |  Integrated (2)  |  Opportunity (63)  |  Preparation (43)  |  Reaction (62)  |  Recall (10)  |  Research (590)  |  Result (389)  |  Specialization (17)  |  Structure (225)  |  Study (476)  |  Uninteresting (6)  |  University (81)

To Descartes, the great philosopher of the 17th century, is due the undying credit of having removed the bann which until then rested upon geometry. The analytical geometry, as Descartes’ method was called, soon led to an abundance of new theorems and principles, which far transcended everything that ever could have been reached upon the path pursued by the ancients.
In Die Entwickelung der Mathematik in den letzten Jahrhunderten (1884), 10.
Science quotes on:  |  17th Century (16)  |  Abundance (21)  |  Ancient (106)  |  Call (128)  |  Credit (20)  |  René Descartes (81)  |  Due (20)  |  Everything (181)  |  Far (154)  |  Geometry (232)  |  Great (534)  |  Lead (160)  |  Mathematicians and Anecdotes (141)  |  Method (239)  |  New (496)  |  Path (84)  |  Philosopher (166)  |  Principle (292)  |  Pursue (23)  |  Reach (121)  |  Remove (26)  |  Rest (93)  |  Soon (34)  |  Theorem (90)  |  Transcend (17)  |  Undying (2)

To eliminate the discrepancy between men's plans and the results achieved, a new approach is necessary. Morphological thinking suggests that this new approach cannot be realized through increased teaching of specialized knowledge. This morphological analysis suggests that the essential fact has been overlooked that every human is potentially a genius. Education and dissemination of knowledge must assume a form which allows each student to absorb whatever develops his own genius, lest he become frustrated. The same outlook applies to the genius of the peoples as a whole.
Halley Lecture for 1948, delivered at Oxford (12 May 1948). In "Morphological Astronomy", The Observatory (1948), 68, 143.
Science quotes on:  |  Achievement (150)  |  Approach (54)  |  Discrepancy (5)  |  Dissemination (2)  |  Education (347)  |  Elimination (18)  |  Essential (117)  |  Fact (733)  |  Frustration (9)  |  Genius (249)  |  Knowledge (1306)  |  Necessity (143)  |  New (496)  |  Outlook (14)  |  Overlooking (3)  |  People (390)  |  Plan (87)  |  Potential (39)  |  Realization (37)  |  Result (389)  |  Specialization (17)  |  Student (203)

Until that afternoon, my thoughts on planetary atmospheres had been wholly concerned with atmospheric analysis as a method of life detection and nothing more. Now that I knew the composition of the Martian atmosphere was so different from that of our own, my mind filled with wonderings about the nature of the Earth. If the air is burning, what sustains it at a constant composition? I also wondered about the supply of fuel and the removal of the products of combustion. It came to me suddenly, just like a flash of enlightenment, that to persist and keep stable, something must be regulating the atmosphere and so keeping it at its constant composition. Moreover, if most of the gases came from living organisms, then life at the surface must be doing the regulation.
Homage to Gaia: The Life of an Independent Scholar (2000), 253.
Science quotes on:  |  Air (190)  |  Atmosphere (79)  |  Combustion (10)  |  Composition (60)  |  Enlightenment (12)  |  Extraterrestrial Life (20)  |  Fuel (31)  |  Gaia (3)  |  Mars (34)  |  Organism (150)  |  Planet (263)

We are Marxists, and Marxism teaches that in our approach to a problem we should start from objective facts, not from abstract definitions, and that we should derive our guiding principles, policies, and measures from an analysis of these facts.
As quoted in William Theodore De Bary, Sources of Chinese Tradition (1960), 929.
Science quotes on:  |  Abstract (86)  |  Definition (192)  |  Derive (33)  |  Fact (733)  |  Measure (104)  |  Objective (66)  |  Policy (24)  |  Principle (292)  |  Problem (497)  |  Start (97)

We have here no esoteric theory of the ultimate nature of concepts, nor a philosophical championing of the primacy of the 'operation'. We have merely a pragmatic matter, namely that we have observed after much experience that if we want to do certain kinds of things with our concepts, our concepts had better be constructed in certain ways. In fact one can see that the situation here is no different from what we always find when we push our analysis to the limit; operations are not ultimately sharp or irreducible any more than any other sort of creature. We always run into a haze eventually, and all our concepts are describable only in spiralling approximation.
Reflections of a Physicist (1950 ), 9.
Science quotes on:  |  Philosophy (259)

We ought then to consider the present state of the universe as the effect of its previous state and as the cause of that which is to follow. An intelligence that, at a given instant, could comprehend all the forces by which nature is animated and the respective situation of the beings that make it up, if moreover it were vast enough to submit these data to analysis, would encompass in the same formula the movements of the greatest bodies of the universe and those of the lightest atoms. For such an intelligence nothing would be uncertain, and the future, like the past, would be open to its eyes.
Philosophical Essay on Probabilities (1814), 5th edition (1825), trans. Andrew I. Dale (1995), 2.
Science quotes on:  |  Animation (4)  |  Atom (280)  |  Cause (285)  |  Data (120)  |  Force (249)  |  Formula (80)  |  Future (287)  |  Intelligence (168)  |  Movement (83)  |  Nature (1223)  |  Past (152)  |  State (137)  |  Uncertainty (42)  |  Universe (686)

We praise the eighteenth century for concerning itself chiefly with analysis. The task remaining to the nineteenth is to discover the false syntheses which prevail, and to analyse their contents anew.
In The Maxims and Reflections of Goethe (1906), 198.
Science quotes on:  |  18th Century (19)  |  19th Century (27)  |  Analyse (3)  |  Anew (8)  |  Chiefly (12)  |  Concern (110)  |  Content (69)  |  Discover (199)  |  False (99)  |  Praise (26)  |  Prevail (17)  |  Remain (113)  |  Synthesis (44)  |  Task (83)

We regard as 'scientific' a method based on deep analysis of facts, theories, and views, presupposing unprejudiced, unfearing open discussion and conclusions. The complexity and diversity of all the phenomena of modern life, the great possibilities and dangers linked with the scientific-technical revolution and with a number of social tendencies demand precisely such an approach, as has been acknowledged in a number of official statements.
Progress, Coexistence and Intellectual Freedom (1968), 25.
Science quotes on:  |  Acknowledgment (11)  |  Approach (54)  |  Danger (78)  |  Demand (76)  |  Fact (733)  |  Life (1131)  |  Method (239)  |  Modern (162)  |  Official (6)  |  Phenomenon (278)  |  Possibility (116)  |  Revolution (69)  |  Science (2067)  |  Society (228)  |  Statement (76)  |  Technology (222)  |  Tendency (56)  |  Theory (696)  |  View (171)

We see it [the as-yet unseen, probable new planet, Neptune] as Columbus saw America from the coast of Spain. Its movements have been felt, trembling along the far-reaching line of our analysis with a certainty hardly inferior to that of ocular demonstration.
Address to the British Association, Southampton (10 Sep 1845). Quoted in Memoirs of the Royal Astronomical Society (1847), 16, 400.
Science quotes on:  |  America (87)  |  Certainty (131)  |  Coast (13)  |  Christopher Columbus (15)  |  Demonstration (86)  |  Far-Reaching (8)  |  Feeling (91)  |  Inferior (19)  |  Movement (83)  |  Neptune (11)  |  New (496)  |  Ocular (3)  |  Planet (263)  |  Spain (4)  |  Tremble (6)

What I then got hold of, something frightful and dangerous, a problem with horns but not necessarily a bull, in any case a new problem—today I should say that it was the problem of science itself, science considered for the first time as problematic, as questionable. But the book in which my youthful courage and suspicion found an outlet—what an impossible book had to result from a task so uncongenial to youth! Constructed from a lot of immature, overgreen personal experiences, all of them close to the limits of communication, presented in the context of art—for the problem of science cannot be recognized in the context of science—a book perhaps for artists who also have an analytic and retrospective penchant (in other words, an exceptional type of artist for whom one might have to look far and wide and really would not care to look) …
In The Birth of Tragedy (1872). Collected in Friedrich Nietzsche and Walter Kaufmann (trans.), The Birth of Tragedy and The Case of Wagner (1967), 18.
Science quotes on:  |  Art (294)  |  Book (257)  |  Bull (3)  |  Communication (76)  |  Courage (55)  |  Dangerous (60)  |  Experience (342)  |  Frightful (3)  |  Horn (12)  |  Immature (4)  |  Impossible (113)  |  Outlet (3)  |  Problem (497)  |  Questionable (3)  |  Result (389)  |  Science (2067)  |  Suspicion (28)  |  Uncongenial (2)  |  Youth (77)

When Aloisio Galvani first stimulated the nervous fiber by the accidental contact of two heterogeneous metals, his contemporaries could never have anticipated that the action of the voltaic pile would discover to us, in the alkalies, metals of a silvery luster, so light as to swim on water, and eminently inflammable; or that it would become a powerful instrument of chemical analysis, and at the same time a thermoscope and a magnet.
In 'Introduction' Cosmos: A Sketch of a Physical Description of the Universe (1860), Vol. 1, 52, as translated by E.C. Otté.
Science quotes on:  |  Alkali (6)  |  Chemistry (252)  |  Discover (199)  |  Instrument (95)  |  Magnet (10)  |  Nerve (70)  |  Stimulate (18)

When Ramanujan was sixteen, he happened upon a copy of Carr’s Synopsis of Mathematics. This chance encounter secured immortality for the book, for it was this book that suddenly woke Ramanujan into full mathematical activity and supplied him essentially with his complete mathematical equipment in analysis and number theory. The book also gave Ramanujan his general direction as a dealer in formulas, and it furnished Ramanujan the germs of many of his deepest developments.
In Mathematical Circles Squared (1972), 158. George Shoobridge Carr (1837-1914) wrote his Synopsis of Elementary Results in Mathematics in 1886.
Science quotes on:  |  Activity (135)  |  Book (257)  |  Chance (160)  |  Complete (87)  |  Deep (124)  |  Development (289)  |  Encounter (22)  |  Equipment (29)  |  Essential (117)  |  Formula (80)  |  Furnish (42)  |  Germ (32)  |  Immortality (11)  |  Mathematics (1205)  |  Number Theory (6)  |  Srinivasa Ramanujan (17)  |  Suddenly (17)  |  Supply (47)  |  Synopsis (2)  |  Wake (13)

Whenever the essential nature of things is analysed by the intellect, it must seem absurd or paradoxical. This has always been recognized by the mystics, but has become a problem in science only very recently.
In The Tao of Physics (1975), 50.
Science quotes on:  |  Absurdity (22)  |  Essential (117)  |  Intellect (192)  |  Paradox (43)  |  Problem (497)  |  Recent (30)  |  Recognition (70)  |  Science (2067)

While the unique crystal stands on its shelf unmeasured by the goniometer, unslit by the optical lapidary, unanalysed by the chemist,—it is merely a piece of furniture, and has no more right to be considered as anything pertaining to science, than a curious china tea-cup on a chimney-piece.
In 'Report on the Progress and Present State of Mineralogy', Report of the British Association for the Advancement of Science (1831 -32), 364-365.
Science quotes on:  |  Chemist (89)  |  Chimney (2)  |  China (20)  |  Consideration (85)  |  Crystal (53)  |  Furniture (8)  |  Measurement (161)  |  Optics (20)  |  Right (197)  |  Science (2067)  |  Shelf (7)  |  Teacup (2)  |  Unique (41)

Without analysis, no synthesis.
Herr Eugen Dühring's Revolution in Science (Anti-Dühring), First Publication (1878). Trans. Emile Burns and ed. C.P. Dutt (1935), 52.

Without the slightest doubt there is something through which material and spiritual energy hold togehter and are complementary. In the last analysis, somehow or other, there must be a single energy operating in the world. And the first idea that occurs to us is that the 'soul' must be as it were the focal point of transformation at which, from all the points of nature, the forces of bodies converge, to become interiorised and sublimated in beauty and truth.
In Teilhard de Chardin and Bernard Wall (trans.), The Phenomenon of Man (1959, 2008), 63. Originally published in French as Le Phénomene Humain (1955).
Science quotes on:  |  Beauty (248)  |  Become (172)  |  Body (247)  |  Complementary (8)  |  Converge (4)  |  Doubt (160)  |  Energy (214)  |  First (314)  |  Force (249)  |  Hold (94)  |  Idea (580)  |  Material (156)  |  Nature (1223)  |  Occur (43)  |  Operating (4)  |  Point (123)  |  Single (120)  |  Slightest (2)  |  Somehow (3)  |  Soul (166)  |  Spiritual (57)  |  Together (79)  |  Transformation (54)  |  Truth (928)  |  World (898)

You are urgently warned against allowing yourself to be influenced in any way by theories or by other preconceived notions in the observation of phenomena, the performance of analyses and other determinations.
Laboratory Rules at Munich. Quoted by M. Bergmann, 'Fischer', in Bugge's Das Buch der Grosse Chemiker. Trans. Joseph S. Froton, Contrasts in Scientific Style: Research Groups in the Chemical and Biomedical Sciences (1990), 172.
Science quotes on:  |  Experiment (602)  |  Laboratory (132)  |  Observation (450)

[Gauss calculated the elements of the planet Ceres] and his analysis proved him to be the first of theoretical astronomers no less than the greatest of “arithmeticians.”
In History of Mathematics (3rd Ed., 1901), 458.
Science quotes on:  |  Anecdote (20)  |  Arithmetician (3)  |  Astronomer (68)  |  Calculate (33)  |  Carl Friedrich Gauss (77)  |  Mathematicians and Anecdotes (141)  |  Planet (263)  |  Theory (696)

[My favourite fellow of the Royal Society is the Reverend Thomas Bayes, an obscure 18th-century Kent clergyman and a brilliant mathematician who] devised a complex equation known as the Bayes theorem, which can be used to work out probability distributions. It had no practical application in his lifetime, but today, thanks to computers, is routinely used in the modelling of climate change, astrophysics and stock-market analysis.
Quoted in Max Davidson, 'Bill Bryson: Have faith, science can solve our problems', Daily Telegraph (26 Sep 2010)
Science quotes on:  |  Application (170)  |  Astrophysics (14)  |  Climate Change (60)  |  Computer (105)  |  Equation (96)  |  Mathematician (384)  |  Model (81)  |  Practicality (6)  |  Probability (106)  |  Routine (19)  |  Royal Society (10)  |  Theorem (90)

[T]he habit of scientific analysis … exhausts the material offered to it…
Entry for 1 Sep 1875 in Amiel’s Journal: The Journal Intime of Henri-Frédéric Amiel, trans. Humphry Ward (1893), 225.
Science quotes on:  |  Scientific Method (166)

… just as the astronomer, the physicist, the geologist, or other student of objective science looks about in the world of sense, so, not metaphorically speaking but literally, the mind of the mathematician goes forth in the universe of logic in quest of the things that are there; exploring the heights and depths for facts—ideas, classes, relationships, implications, and the rest; observing the minute and elusive with the powerful microscope of his Infinitesimal Analysis; observing the elusive and vast with the limitless telescope of his Calculus of the Infinite; making guesses regarding the order and internal harmony of the data observed and collocated; testing the hypotheses, not merely by the complete induction peculiar to mathematics, but, like his colleagues of the outer world, resorting also to experimental tests and incomplete induction; frequently finding it necessary, in view of unforeseen disclosures, to abandon one hopeful hypothesis or to transform it by retrenchment or by enlargement:—thus, in his own domain, matching, point for point, the processes, methods and experience familiar to the devotee of natural science.
In Lectures on Science, Philosophy and Art (1908), 26
Science quotes on:  |  Abandon (48)  |  Astronomer (68)  |  Calculus (51)  |  Class (84)  |  Colleague (23)  |  Complete (87)  |  Data (120)  |  Depth (51)  |  Devotee (5)  |  Disclosure (5)  |  Domain (42)  |  Elusive (8)  |  Enlargement (7)  |  Experience (342)  |  Experimental (20)  |  Exploration (123)  |  Fact (733)  |  Familiar (43)  |  Find (408)  |  Forth (13)  |  Frequently (21)  |  Geologist (47)  |  Guess (48)  |  Harmony (72)  |  Height (32)  |  Hopeful (2)  |  Hypothesis (252)  |  Idea (580)  |  Implication (22)  |  Incomplete (15)  |  Induction (60)  |  Infinite (130)  |  Infinitesimal (15)  |  Internal (25)  |  Limitless (8)  |  Literally (8)  |  Located (2)  |  Logic (260)  |  Match (16)  |  Mathematician (384)  |  Mathematics (1205)  |  Merely (82)  |  Metaphor (25)  |  Method (239)  |  Microscope (74)  |  Mind (760)  |  Minute (44)  |  Natural Science (90)  |  Nature Of Mathematics (80)  |  Necessary (154)  |  Objective (66)  |  Observe (76)  |  Order (242)  |  Outer (13)  |  Peculiar (45)  |  Physicist (161)  |  Point (123)  |  Powerful (68)  |  Process (267)  |  Quest (32)  |  Regard (95)  |  Relationship (71)  |  Resort (8)  |  Rest (93)  |  Science (2067)  |  Sense (321)  |  Speak (92)  |  Student (203)  |  Telescope (82)  |  Test (125)  |  Transform (35)  |  Unforeseen (6)  |  Universe (686)  |  Vast (89)  |  View (171)  |  World (898)


Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
Quotations by:Albert EinsteinIsaac NewtonLord KelvinCharles DarwinSrinivasa RamanujanCarl SaganFlorence NightingaleThomas EdisonAristotleMarie CurieBenjamin FranklinWinston ChurchillGalileo GalileiSigmund FreudRobert BunsenLouis PasteurTheodore RooseveltAbraham LincolnRonald ReaganLeonardo DaVinciMichio KakuKarl PopperJohann GoetheRobert OppenheimerCharles Kettering  ... (more people)

Quotations about:Atomic  BombBiologyChemistryDeforestationEngineeringAnatomyAstronomyBacteriaBiochemistryBotanyConservationDinosaurEnvironmentFractalGeneticsGeologyHistory of ScienceInventionJupiterKnowledgeLoveMathematicsMeasurementMedicineNatural ResourceOrganic ChemistryPhysicsPhysicianQuantum TheoryResearchScience and ArtTeacherTechnologyUniverseVolcanoVirusWind PowerWomen ScientistsX-RaysYouthZoology  ... (more topics)
Sitewide search within all Today In Science History pages:
Visit our Science and Scientist Quotations index for more Science Quotes from archaeologists, biologists, chemists, geologists, inventors and inventions, mathematicians, physicists, pioneers in medicine, science events and technology.

Names index: | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

Categories index: | 1 | 2 | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



who invites your feedback
Thank you for sharing.
Today in Science History
Sign up for Newsletter
with quiz, quotes and more.