Celebrating 18 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “We are here to celebrate the completion of the first survey of the entire human genome. Without a doubt, this is the most important, most wondrous map ever produced by human kind.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index P > Category: Purely

Purely Quotes (28 quotes)

A principle of induction would be a statement with the help of which we could put inductive inferences into a logically acceptable form. In the eyes of the upholders of inductive logic, a principle of induction is of supreme importance for scientific method: “... this principle”, says Reichenbach, “determines the truth of scientific theories. To eliminate it from science would mean nothing less than to deprive science of the power to decide the truth or falsity of its theories. Without it, clearly, science would no longer have the right to distinguish its theories from the fanciful and arbitrary creations of the poet’s mind.” Now this principle of induction cannot be a purely logical truth like a tautology or an analytic statement. Indeed, if there were such a thing as a purely logical principle of induction, there would be no problem of induction; for in this case, all inductive inferences would have to be regarded as purely logical or tautological transformations, just like inferences in inductive logic. Thus the principle of induction must be a synthetic statement; that is, a statement whose negation is not self-contradictory but logically possible. So the question arises why such a principle should be accepted at all, and how we can justify its acceptance on rational grounds.
…...
Science quotes on:  |  Accept (65)  |  Acceptable (6)  |  Acceptance (45)  |  Analytic (10)  |  Arbitrary (20)  |  Arise (49)  |  Case (98)  |  Clearly (41)  |  Creation (239)  |  Decide (40)  |  Deprive (11)  |  Determine (72)  |  Distinguish (61)  |  Eliminate (21)  |  Eye (218)  |  Falsity (13)  |  Fanciful (6)  |  Form (308)  |  Ground (90)  |  Help (101)  |  Importance (216)  |  Induction (59)  |  Inductive (10)  |  Inference (31)  |  Justify (23)  |  Less (102)  |  Logic (247)  |  Logical (54)  |  Long (172)  |  Mean (101)  |  Mind (743)  |  Negation (2)  |  Nothing (385)  |  Poet (78)  |  Possible (155)  |  Power (358)  |  Principle (285)  |  Problem (490)  |  Question (404)  |  Rational (56)  |  Regard (93)  |  Right (196)  |  Say (228)  |  Science (2043)  |  Scientific (232)  |  Scientific Method (166)  |  Scientific Theory (24)  |  Statement (72)  |  Supreme (37)  |  Synthetic (16)  |  Tautological (2)  |  Tautology (4)  |  Theory (690)  |  Transformation (54)  |  Truth (914)

Boundaries which mark off one field of science from another are purely artificial, are set up only for temporary convenience. Let chemists and physicists dig deep enough, and they reach common ground.
From chapter 'Jottings from a Note-Book', in Canadian Stories (1918), 183.
Science quotes on:  |  Artificial (32)  |  Boundary (38)  |  Chemist (88)  |  Common Ground (3)  |  Convenience (34)  |  Deep (121)  |  Dig (11)  |  Field (170)  |  Physicist (160)  |  Reach (119)  |  Science (2043)  |  Set (97)  |  Temporary (16)

Descartes is the completest type which history presents of the purely mathematical type of mind—that in which the tendencies produced by mathematical cultivation reign unbalanced and supreme.
In An Examination of Sir William Hamilton’s Philosophy (1878), 626.
Science quotes on:  |  Complete (84)  |  Cultivation (27)  |  René Descartes (81)  |  History (368)  |  Mathematicians and Anecdotes (123)  |  Mathematics (1149)  |  Mind (743)  |  Present (174)  |  Produce (100)  |  Reign (11)  |  Supreme (37)  |  Tendency (54)  |  Type (51)  |  Unbalanced (2)

Engineering is an activity other than purely manual and physical work which brings about the utilization of the materials and laws of nature for the good of humanity.
1929
Science quotes on:  |  Activity (128)  |  Bring (90)  |  Engineering (141)  |  Good (345)  |  Humanity (125)  |  Law (513)  |  Manual (7)  |  Material (154)  |  Nature (1211)  |  Physical (129)  |  Utilization (9)  |  Work (626)

Every definition implies an axiom, since it asserts the existence of the object defined. The definition then will not be justified, from the purely logical point of view, until we have ‘proved’ that it involves no contradiction either in its terms or with the truths previously admitted.
…...
Science quotes on:  |  Admit (44)  |  Assert (21)  |  Axiom (52)  |  Contradiction (54)  |  Define (49)  |  Definition (191)  |  Existence (296)  |  Imply (15)  |  Involve (47)  |  Justify (23)  |  Logical (54)  |  Object (169)  |  Point Of View (41)  |  Previously (11)  |  Prove (108)  |  Term (120)  |  Truth (914)

I view the major features of my own odyssey as a set of mostly fortunate contingencies. I was not destined by inherited mentality or family tradition to become a paleontologist. I can locate no tradition for scientific or intellectual careers anywhere on either side of my eastern European Jewish background ... I view my serious and lifelong commitment to baseball in entirely the same manner: purely as a contingent circumstance of numerous, albeit not entirely capricious, accidents.
…...
Science quotes on:  |  Accident (65)  |  Anywhere (13)  |  Background (30)  |  Baseball (3)  |  Become (172)  |  Capricious (4)  |  Career (57)  |  Circumstance (66)  |  Commitment (20)  |  Contingency (11)  |  Contingent (10)  |  Destined (11)  |  Eastern (3)  |  Entirely (33)  |  European (5)  |  Family (45)  |  Feature (43)  |  Fortunate (10)  |  Inherit (16)  |  Intellectual (120)  |  Jewish (10)  |  Lifelong (8)  |  Locate (7)  |  Major (32)  |  Manner (57)  |  Mentality (5)  |  Numerous (29)  |  Paleontologist (15)  |  Same (155)  |  Scientific (232)  |  Serious (52)  |  Set (97)  |  Side (51)  |  Tradition (49)  |  View (171)

If a mathematician of the past, an Archimedes or even a Descartes, could view the field of geometry in its present condition, the first feature to impress him would be its lack of concreteness. There are whole classes of geometric theories which proceed not only without models and diagrams, but without the slightest (apparent) use of spatial intuition. In the main this is due, to the power of the analytic instruments of investigations as compared with the purely geometric.
In 'The Present Problems in Geometry', Bulletin American Mathematical Society (1906), 286.
Science quotes on:  |  Analytic (10)  |  Apparent (39)  |  Archimedes (53)  |  Class (83)  |  Compare (37)  |  Concreteness (4)  |  Condition (160)  |  René Descartes (81)  |  Diagram (13)  |  Due (20)  |  Feature (43)  |  Field (170)  |  First (313)  |  Geometric (5)  |  Geometry (215)  |  Impress (16)  |  Instrument (92)  |  Intuition (57)  |  Investigation (175)  |  Lack (77)  |  Main (27)  |  Mathematician (364)  |  Model (80)  |  Modern Mathematics (36)  |  Past (150)  |  Power (358)  |  Present (174)  |  Proceed (41)  |  Slight (30)  |  Spatial (8)  |  Theory (690)  |  View (171)  |  Whole (189)

Mathematics gives the young man a clear idea of demonstration and habituates him to form long trains of thought and reasoning methodically connected and sustained by the final certainty of the result; and it has the further advantage, from a purely moral point of view, of inspiring an absolute and fanatical respect for truth. In addition to all this, mathematics, and chiefly algebra and infinitesimal calculus, excite to a high degree the conception of the signs and symbols—necessary instruments to extend the power and reach of the human mind by summarizing an aggregate of relations in a condensed form and in a kind of mechanical way. These auxiliaries are of special value in mathematics because they are there adequate to their definitions, a characteristic which they do not possess to the same degree in the physical and mathematical [natural?] sciences.
There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching was directed so as to leave free play to the personal work of the student.
In 'Science as an Instrument of Education', Popular Science Monthly (1897), 253.
Science quotes on:  |  Absolute (97)  |  Addition (29)  |  Adequate (25)  |  Advantage (73)  |  Aggregate (14)  |  Algebra (92)  |  Auxiliary (6)  |  Available (25)  |  Calculus (48)  |  Certainty (129)  |  Characteristic (94)  |  Chiefly (12)  |  Clear (97)  |  Conception (88)  |  Condense (11)  |  Connect (30)  |  Definition (191)  |  Degree (81)  |  Demonstration (81)  |  Direct (82)  |  Excite (15)  |  Extend (41)  |  Fact (725)  |  Faculty (65)  |  Fanatical (3)  |  Far (154)  |  Final (49)  |  Form (308)  |  Free (90)  |  Full (63)  |  Give (200)  |  Habituate (3)  |  High (152)  |  Human Mind (80)  |  Idea (577)  |  Infinitesimal (15)  |  Inspire (49)  |  Instruction (72)  |  Instrument (92)  |  Kind (138)  |  Leave (127)  |  Long (172)  |  Mass (78)  |  Mathematics (1149)  |  Mechanical (48)  |  Mental (78)  |  Methodically (2)  |  Moral (123)  |  Natural (167)  |  Necessary (147)  |  Personal (66)  |  Physical (129)  |  Play (110)  |  Point Of View (41)  |  Possess (53)  |  Power (358)  |  Reach (119)  |  Reason (454)  |  Relation (149)  |  Respect (86)  |  Result (376)  |  Same (155)  |  Science (2043)  |  Sign (56)  |  Special (74)  |  Student (201)  |  Summarize (10)  |  Sustain (23)  |  Symbol (65)  |  Teach (179)  |  Thought (536)  |  Train (45)  |  Truth (914)  |  Value (240)  |  Value Of Mathematics (55)  |  Work (626)  |  Young (98)

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 (92)  |  Analysis (159)  |  Appear (115)  |  Arithmetical (11)  |  Author (61)  |  Authority (65)  |  Automaton (10)  |  Become (172)  |  Branch (102)  |  Calculus (48)  |  Cause (283)  |  Chair (11)  |  Characterize (17)  |  Compound (58)  |  Connect (30)  |  Construction (83)  |  Continue (63)  |  Demonstration (81)  |  Development (276)  |  Discovery (676)  |  Doctrine (75)  |  Double (15)  |  Effort (143)  |  Elasticity (5)  |  Equation (93)  |  Leonhard Euler (34)  |  Face (108)  |  Fact (725)  |  Feel (165)  |  Pierre de Fermat (15)  |  Flame (26)  |  Form (308)  |  Foundation (105)  |  Fraction (12)  |  Fresh (30)  |  Carl Friedrich Gauss (73)  |  Genius (243)  |  Geometry (215)  |  Great (524)  |  Christiaan Huygens (10)  |  Idea (577)  |  Influence (137)  |  Inform (16)  |  Instance (32)  |  Integral Calculus (4)  |  Investigation (175)  |  Karl Jacobi (9)  |  Count Joseph-Louis de Lagrange (24)  |  Laid (7)  |  Law (513)  |  Lead (158)  |  Leave (127)  |  Adrien-Marie Legendre (3)  |  Light (345)  |  Lip (4)  |  Mathematician (364)  |  Mathematics (1149)  |  Mechanic (23)  |  Mechanical (48)  |  Memory (105)  |  Method (230)  |  Midst (7)  |  Modern (159)  |  Molecular (7)  |  Moment (106)  |  Motion (158)  |  Nature Of Mathematics (77)  |  New (483)  |  Observation (445)  |  Origin (86)  |  Pendulum (15)  |  Periodicity (5)  |  Physics (346)  |  Planetary (9)  |  Predecessor (21)  |  Present (174)  |  Principal (28)  |  Proof (243)  |  Reach (119)  |  Reason (454)  |  Reciprocity (2)  |  Reduce (53)  |  Resist (15)  |  Result (376)  |  Right (196)  |  Root (60)  |  Say (228)  |  Serve (57)  |  Speak (90)  |  William Spottiswoode (3)  |  Stare (9)  |  Theorem (88)  |  Theory (690)  |  Transcendent (2)  |  Transfigure (2)  |  Transformation (54)  |  Turn (118)  |  Variation (61)  |  Year (299)  |  Yield (35)

On the day of Cromwell’s death, when Newton was sixteen, a great storm raged all over England. He used to say, in his old age, that on that day he made his first purely scientific experiment. To ascertain the force of the wind, he first jumped with the wind and then against it; and, by comparing these distances with the extent of his own jump on a calm day, he was enabled to compute the force of the storm. When the wind blew thereafter, he used to say it was so many feet strong.
In 'Sir Isaac Newton', People’s Book of Biography: Or, Short Lives of the Most Interesting Persons of All Ages and Countries (1868), 248.
Science quotes on:  |  Ascertain (15)  |  Blow (22)  |  Calm (22)  |  Compare (37)  |  Compute (18)  |  Oliver Cromwell (3)  |  Death (302)  |  Distance (76)  |  Experiment (600)  |  Extent (49)  |  First (313)  |  Foot (60)  |  Force (249)  |  Jump (17)  |  Mathematicians and Anecdotes (123)  |  Sir Isaac Newton (327)  |  Scientific (232)  |  Storm (30)  |  Strong (72)  |  Wind (80)

Our first endeavors are purely instinctive prompting of an imagination vivid and undisciplined. As we grow older reason asserts itself and we become more and more systematic and designing. But those early impulses, though not immediately productive, are o
http://web.archive.org/web/20070109161311/http://www.knowprose.com/node/12961
Science quotes on:  |  Assert (21)  |  Become (172)  |  Design (113)  |  Early (61)  |  Endeavor (41)  |  First (313)  |  Grow (98)  |  Imagination (268)  |  Immediately (21)  |  Impulse (33)  |  Instinctive (3)  |  Old (147)  |  Productive (12)  |  Prompt (6)  |  Reason (454)  |  Systematic (32)  |  Undisciplined (2)  |  Vivid (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)  |  Analysis (159)  |  Apparently (19)  |  Association (20)  |  Atmosphere (79)  |  Attention (115)  |  Become (172)  |  Berlin (10)  |  Brain (209)  |  Century (130)  |  Confidently (2)  |  Discipline (53)  |  Domain (40)  |  Effect (165)  |  Find (405)  |  Fire (132)  |  France (26)  |  Function (128)  |  Furnish (40)  |  Germany (12)  |  Grant (32)  |  Great (524)  |  Half (56)  |  Helpful (15)  |  Human (548)  |  Incapable (17)  |  Influence (137)  |  Laurel (2)  |  Live (269)  |  Mathematician (364)  |  Mathematicians and Anecdotes (123)  |  Mathematics (1149)  |  Mere (78)  |  Modern (159)  |  Peculiarly (4)  |  Power (358)  |  Present (174)  |  Prevail (16)  |  Prime (10)  |  Read (144)  |  Receptive (4)  |  Restless (11)  |  Retain (19)  |  Second (59)  |  Splendid (12)  |  Stimulus (19)  |  Subject (235)  |  Supply (46)  |  Surround (29)  |  James Joseph Sylvester (48)  |  Temperament (11)  |  Theory (690)  |  Thought (536)  |  Train (45)  |  Work (626)

That mathematics “do not cultivate the power of generalization,”; … will be admitted by no person of competent knowledge, except in a very qualified sense. The generalizations of mathematics, are, no doubt, a different thing from the generalizations of physical science; but in the difficulty of seizing them, and the mental tension they require, they are no contemptible preparation for the most arduous efforts of the scientific mind. Even the fundamental notions of the higher mathematics, from those of the differential calculus upwards are products of a very high abstraction. … To perceive the mathematical laws common to the results of many mathematical operations, even in so simple a case as that of the binomial theorem, involves a vigorous exercise of the same faculty which gave us Kepler’s laws, and rose through those laws to the theory of universal gravitation. Every process of what has been called Universal Geometry—the great creation of Descartes and his successors, in which a single train of reasoning solves whole classes of problems at once, and others common to large groups of them—is a practical lesson in the management of wide generalizations, and abstraction of the points of agreement from those of difference among objects of great and confusing diversity, to which the purely inductive sciences cannot furnish many superior. Even so elementary an operation as that of abstracting from the particular configuration of the triangles or other figures, and the relative situation of the particular lines or points, in the diagram which aids the apprehension of a common geometrical demonstration, is a very useful, and far from being always an easy, exercise of the faculty of generalization so strangely imagined to have no place or part in the processes of mathematics.
In An Examination of Sir William Hamilton’s Philosophy (1878), 612-13.
Science quotes on:  |  Abstract (79)  |  Abstraction (38)  |  Admit (44)  |  Agreement (39)  |  Aid (41)  |  Apprehension (15)  |  Arduous (3)  |  Binomial Theorem (3)  |  Call (127)  |  Case (98)  |  Class (83)  |  Common (118)  |  Competent (18)  |  Configuration (7)  |  Confuse (18)  |  Contemptible (8)  |  Creation (239)  |  Cultivate (19)  |  Demonstration (81)  |  René Descartes (81)  |  Diagram (13)  |  Difference (246)  |  Different (178)  |  Differential Calculus (8)  |  Difficulty (144)  |  Diversity (51)  |  Doubt (159)  |  Easy (98)  |  Effort (143)  |  Elementary (45)  |  Exercise (64)  |  Faculty (65)  |  Far (154)  |  Figure (68)  |  Fundamental (158)  |  Furnish (40)  |  Generalization (41)  |  Geometrical (10)  |  Geometry (215)  |  Give (200)  |  Gravitation (38)  |  Great (524)  |  Group (72)  |  High (152)  |  Higher Mathematics (6)  |  Imagine (74)  |  Inductive (10)  |  Involve (47)  |  Johannes Kepler (90)  |  Knowledge (1293)  |  Large (130)  |  Law (513)  |  Lesson (41)  |  Line (89)  |  Management (12)  |  Mathematics (1149)  |  Mental (78)  |  Nature Of Mathematics (77)  |  Notion (57)  |  Object (169)  |  Operation (118)  |  Part (220)  |  Particular (75)  |  Perceive (40)  |  Person (153)  |  Physical Science (65)  |  Place (174)  |  Point (122)  |  Power (358)  |  Practical (129)  |  Preparation (41)  |  Problem (490)  |  Process (261)  |  Product (82)  |  Qualify (4)  |  Reason (454)  |  Relative (39)  |  Require (79)  |  Result (376)  |  Rise (70)  |  Same (155)  |  Science (2043)  |  Scientific Mind (5)  |  Seize (14)  |  Sense (315)  |  Simple (172)  |  Single (119)  |  Situation (52)  |  Solve (76)  |  Strangely (5)  |  Successor (9)  |  Superior (40)  |  Tension (9)  |  Theory (690)  |  Train (45)  |  Triangle (10)  |  Universal (100)  |  Upwards (6)  |  Useful (98)  |  Vigorous (20)  |  Whole (189)  |  Wide (27)

The aim of science is to apprehend this purely intelligible world as a thing in itself, an object which is what it is independently of all thinking, and thus antithetical to the sensible world.... The world of thought is the universal, the timeless and spaceless, the absolutely necessary, whereas the world of sense is the contingent, the changing and moving appearance which somehow indicates or symbolizes it.
'Outlines of a Philosophy of Art,' Essays in the Philosophy of Art, Indiana University Press (1964).
Science quotes on:  |  Absolutely (39)  |  Aim (88)  |  Antithetical (2)  |  Appearance (85)  |  Apprehend (5)  |  Change (363)  |  Contingent (10)  |  Independently (6)  |  Indicate (18)  |  Intelligible (18)  |  Move (94)  |  Necessary (147)  |  Object (169)  |  Science (2043)  |  Sense (315)  |  Sensible (25)  |  Spaceless (2)  |  Symbolize (6)  |  Think (341)  |  Thought (536)  |  Timeless (6)  |  Universal (100)  |  World (892)

The antagonism between science and religion, about which we hear so much, appears to me purely factitious, fabricated on the one hand by short-sighted religious people, who confound theology with religion; and on the other by equally short-sighted scientific people who forget that science takes for its province only that which is susceptible of clear intellectual comprehension.
…...
Science quotes on:  |  Antagonism (4)  |  Appear (115)  |  Clear (97)  |  Comprehension (57)  |  Confound (14)  |  Equally (25)  |  Fabricate (5)  |  Forget (63)  |  Hand (141)  |  Hear (60)  |  Intellectual (120)  |  People (388)  |  Province (14)  |  Religion (239)  |  Religious (49)  |  Science (2043)  |  Science And Religion (302)  |  Scientific (232)  |  Short-Sighted (2)  |  Susceptible (6)  |  Theology (40)

The degree of exactness of the intuition of space may be different in different individuals, perhaps even in different races. It would seem as if a strong naive space-intuition were an attribute pre-eminently of the Teutonic race, while the critical, purely logical sense is more fully developed in the Latin and Hebrew races. A full investigation of this subject, somewhat on the lines suggested by Francis Gallon in his researches on heredity, might be interesting.
In The Evanston Colloquium Lectures (1894), 46.
Science quotes on:  |  Attribute (38)  |  Critical (40)  |  Degree (81)  |  Developed (11)  |  Different (178)  |  Exactness (21)  |  Hebrew (6)  |  Heredity (53)  |  Individual (215)  |  Interest (235)  |  Intuition (57)  |  Investigation (175)  |  Latin (33)  |  Line (89)  |  Logical (54)  |  Mathematician (364)  |  Naive (10)  |  Preeminent (5)  |  Race (103)  |  Research (589)  |  Sense (315)  |  Space (257)  |  Strong (72)  |  Subject (235)  |  Suggest (32)

The Jewish scriptures admirably illustrate the development from the religion of fear to moral religion, a development continued in the New Testament. The religions of all civilized peoples, especially the peoples of the Orient, are primarily moral religions. The development from a religion of fear to moral religion is a great step in peoples’ lives. And yet, that primitive religions are based entirely on fear and the religions of civilized peoples purely on morality is a prejudice against which we must be on our guard. The truth is that all religions are a varying blend of both types, with this differentiation: that on the higher levels of social life the religion of morality predominates.
…...
Science quotes on:  |  Admirably (3)  |  Base (71)  |  Blend (9)  |  Both (81)  |  Civilized (17)  |  Continue (63)  |  Development (276)  |  Differentiation (17)  |  Entirely (33)  |  Especially (30)  |  Fear (141)  |  Great (524)  |  Guard (18)  |  High (152)  |  Illustrate (9)  |  Jewish (10)  |  Level (67)  |  Live (269)  |  Moral (123)  |  Morality (42)  |  New Testament (3)  |  Orient (4)  |  People (388)  |  Predominate (5)  |  Prejudice (66)  |  Primarily (12)  |  Primitive (41)  |  Religion (239)  |  Scripture (11)  |  Social Life (3)  |  Step (109)  |  Truth (914)  |  Type (51)  |  Vary (25)

The progress of synthesis, or the building up of natural materials from their constituent elements, proceeds apace. Even some of the simpler albuminoids, a class of substances of great importance in the life process, have recently been artificially prepared. ... Innumerable entirely new compounds have been produced in the last century. The artificial dye-stuffs, prepared from materials occurring in coal-tar, make the natural colours blush. Saccharin, which is hundreds of times sweeter than sugar, is a purely artificial substance. New explosives, drugs, alloys, photographic substances, essences, scents, solvents, and detergents are being poured out in a continuous stream.
In Matter and Energy (1912), 45-46.
Science quotes on:  |  Alloy (2)  |  Artificial (32)  |  Blush (3)  |  Building (52)  |  Century (130)  |  Chemistry (250)  |  Class (83)  |  Coal Tar (2)  |  Color (99)  |  Compound (58)  |  Constituent (16)  |  Continuous (38)  |  Detergent (2)  |  Drug (43)  |  Element (162)  |  Entirely (33)  |  Essence (54)  |  Explosive (18)  |  Great (524)  |  Hundred (64)  |  Importance (216)  |  Innumerable (23)  |  Last (19)  |  Life (1124)  |  Material (154)  |  Natural (167)  |  New (483)  |  Occurrence (32)  |  Photograph (19)  |  Pour (10)  |  Preparation (41)  |  Proceeding (13)  |  Process (261)  |  Production (115)  |  Progress (362)  |  Recent (29)  |  Saccharin (2)  |  Scent (5)  |  Simplicity (146)  |  Solvent (5)  |  Stream (40)  |  Substance (85)  |  Sugar (14)  |  Synthesis (43)

The purely formal Sciences, logic and mathematics, deal with those relations which are, or can be, independent of the particular content or the substance of objects. To mathematics in particular fall those relations between objects which involve the concepts of magnitude, of measure and of number.
In Theorie der Complexen Zahlensysteme (1867), 1. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 4. From the original German, “Die rein formalen Wissenschaften, Logik und Mathematik, haben solche Relationen zu behandeln, welche unabhängig von dem bestimmten Inhalte, der Substanz der Objecte sind oder es wenigstens sein können. Der Mathematik fallen ins Besondere diejenigen Beziehungen der Objecte zu einander zu, die den Begriff der Grösse, des Maasses, der Zahl involviren.”
Science quotes on:  |  Concept (143)  |  Content (66)  |  Deal (49)  |  Formal (29)  |  Independent (65)  |  Involve (47)  |  Logic (247)  |  Magnitude (41)  |  Mathematics (1149)  |  Measure (102)  |  Number (276)  |  Object (169)  |  Relation (149)  |  Science (2043)  |  Substance (85)

The school of Plato has advanced the interests of the race as much through geometry as through philosophy. The modern engineer, the navigator, the astronomer, built on the truths which those early Greeks discovered in their purely speculative investigations. And if the poetry, statesmanship, oratory, and philosophy of our day owe much to Plato’s divine Dialogues, our commerce, our manufactures, and our science are equally indebted to his Conic Sections. Later instances may be abundantly quoted, to show that the labors of the mathematician have outlasted those of the statesman, and wrought mightier changes in the condition of the world. Not that we would rank the geometer above the patriot, but we claim that he is worthy of equal honor.
In 'Imagination in Mathematics', North American Review, 85, 228.
Science quotes on:  |  Advance (162)  |  Astronomer (68)  |  Build (117)  |  Change (363)  |  Claim (70)  |  Commerce (15)  |  Condition (160)  |  Conic Section (7)  |  Dialogue (8)  |  Discover (196)  |  Divine (60)  |  Early (61)  |  Engineer (97)  |  Equal (77)  |  Equally (25)  |  Estimates of Mathematics (30)  |  Geometer (22)  |  Geometry (215)  |  Greek (71)  |  Honor (30)  |  Indebted (7)  |  Instance (32)  |  Interest (235)  |  Investigation (175)  |  Labor (71)  |  Late (52)  |  Manufacture (15)  |  Mathematician (364)  |  Mighty (13)  |  Modern (159)  |  Navigator (8)  |  Outlast (3)  |  Owe (23)  |  Patriot (4)  |  Philosophy (257)  |  Plato (73)  |  Poetry (120)  |  Quote (18)  |  Race (103)  |  Rank (32)  |  School (117)  |  Science (2043)  |  Show (90)  |  Speculative (8)  |  Statesman (18)  |  Statesmanship (2)  |  Truth (914)  |  Work (626)  |  World (892)  |  Worthy (34)

The study of mathematics cannot be replaced by any other activity that will train and develop man’s purely logical faculties to the same level of rationality.
In The American Mathematical Monthly (1949), 56, 19. Excerpted in John Ewing (ed,), A Century of Mathematics: Through the Eyes of the Monthly (1996), 186.
Science quotes on:  |  Activity (128)  |  Develop (103)  |  Faculty (65)  |  Level (67)  |  Logical (54)  |  Mathematics (1149)  |  Rationality (15)  |  Replace (30)  |  Same (155)  |  Study (461)  |  Train (45)

Through purely logical thinking we can attain no knowledge whatsoever of the empirical world.
In Francis Crick, The Astonishing Hypothesis: the Scientific Search for the Soul (1995), 215.
Science quotes on:  |  Attain (42)  |  Empirical (27)  |  Knowledge (1293)  |  Logical (54)  |  Think (341)  |  Whatsoever (9)  |  World (892)

To characterize the import of pure geometry, we might use the standard form of a movie-disclaimer: No portrayal of the characteristics of geometrical figures or of the spatial properties of relationships of actual bodies is intended, and any similarities between the primitive concepts and their customary geometrical connotations are purely coincidental.
From 'Geometry and Empirical Science', collected in Carl Hempel and James H. Fetzer (ed.), The Philosophy of Carl G. Hempel: Studies in Science, Explanation, and Rationality (2001), Chap. 2, 24. Also Carl Hempel, 'Geometry and Empirical Science', collected in J.R. Newman (ed.), The World of Mathematics (1956), Vol. 3, 1641.
Science quotes on:  |  Actual (47)  |  Body (243)  |  Characteristic (94)  |  Characterize (17)  |  Concept (143)  |  Connotation (2)  |  Customary (4)  |  Disclaimer (2)  |  Figure (68)  |  Geometrical (10)  |  Geometry (215)  |  Importance (216)  |  Intend (16)  |  Movie (16)  |  Portrayal (2)  |  Primitive (41)  |  Property (123)  |  Pure (98)  |  Relationship (71)  |  Similarity (20)  |  Spatial (8)

To emphasize this opinion that mathematicians would be unwise to accept practical issues as the sole guide or the chief guide in the current of their investigations, ... let me take one more instance, by choosing a subject in which the purely mathematical interest is deemed supreme, the theory of functions of a complex variable. That at least is a theory in pure mathematics, initiated in that region, and developed in that region; it is built up in scores of papers, and its plan certainly has not been, and is not now, dominated or guided by considerations of applicability to natural phenomena. Yet what has turned out to be its relation to practical issues? The investigations of Lagrange and others upon the construction of maps appear as a portion of the general property of conformal representation; which is merely the general geometrical method of regarding functional relations in that theory. Again, the interesting and important investigations upon discontinuous two-dimensional fluid motion in hydrodynamics, made in the last twenty years, can all be, and now are all, I believe, deduced from similar considerations by interpreting functional relations between complex variables. In the dynamics of a rotating heavy body, the only substantial extension of our knowledge since the time of Lagrange has accrued from associating the general properties of functions with the discussion of the equations of motion. Further, under the title of conjugate functions, the theory has been applied to various questions in electrostatics, particularly in connection with condensers and electrometers. And, lastly, in the domain of physical astronomy, some of the most conspicuous advances made in the last few years have been achieved by introducing into the discussion the ideas, the principles, the methods, and the results of the theory of functions. … the refined and extremely difficult work of Poincare and others in physical astronomy has been possible only by the use of the most elaborate developments of some purely mathematical subjects, developments which were made without a thought of such applications.
In Presidential Address British Association for the Advancement of Science, Section A, (1897), Nature, 56, 377.
Science quotes on:  |  Accept (65)  |  Accrue (3)  |  Achieve (63)  |  Advance (162)  |  Appear (115)  |  Applicability (6)  |  Application (166)  |  Apply (76)  |  Associate (14)  |  Astronomy (203)  |  Belief (503)  |  Body (243)  |  Build (117)  |  Certainly (31)  |  Chief (37)  |  Choose (59)  |  Complex (94)  |  Condenser (4)  |  Connection (107)  |  Consideration (85)  |  Conspicuous (7)  |  Construction (83)  |  Current (54)  |  Deduce (22)  |  Deem (6)  |  Develop (103)  |  Development (276)  |  Difficult (116)  |  Discontinuous (5)  |  Discussion (47)  |  Domain (40)  |  Dominate (19)  |  Dynamics (9)  |  Elaborate (20)  |  Electrostatic (5)  |  Emphasize (12)  |  Equation (93)  |  Extension (30)  |  Extremely (15)  |  Far (154)  |  Fluid Motion (2)  |  Function (128)  |  Functional (10)  |  General (156)  |  Geometrical (10)  |  Guide (62)  |  Heavy (22)  |  Hydrodynamics (4)  |  Idea (577)  |  Important (202)  |  Initiate (6)  |  Instance (32)  |  Interest (235)  |  Interpret (18)  |  Introduce (41)  |  Investigation (175)  |  Issue (42)  |  Knowledge (1293)  |  Count Joseph-Louis de Lagrange (24)  |  Least (74)  |  Let (61)  |  Map (30)  |  Mathematician (364)  |  Mathematics (1149)  |  Merely (82)  |  Method (230)  |  Motion (158)  |  Natural (167)  |  Opinion (176)  |  Paper (82)  |  Particularly (21)  |  Phenomenon (276)  |  Physical (129)  |  Plan (87)  |  Henri Poincaré (93)  |  Portion (24)  |  Possible (155)  |  Practical (129)  |  Principle (285)  |  Property (123)  |  Pure Mathematics (63)  |  Question (404)  |  Refine (4)  |  Regard (93)  |  Region (35)  |  Relation (149)  |  Representation (35)  |  Result (376)  |  Rotate (6)  |  Score (7)  |  Similar (35)  |  Sole (20)  |  Study And Research In Mathematics (59)  |  Subject (235)  |  Substantial (14)  |  Supreme (37)  |  Theory (690)  |  Thought (536)  |  Time (594)  |  Title (18)  |  Turned Out (4)  |  Unwise (4)  |  Variable (16)  |  Various (46)  |  Work (626)  |  Year (299)

True rigor is productive, being distinguished in this from another rigor which is purely formal and tiresome, casting a shadow over the problems it touches.
From address to the section of Algebra and Analysis, International Congress of Arts and Sciences, St. Louis (22 Sep 1904), 'On the Development of Mathematical Analysis and its Relation to Certain Other Sciences,' as translated by M.W. Haskell in Bulletin of the American Mathematical Society (May 1905), 11, 417.
Science quotes on:  |  Casting (3)  |  Distinguish (61)  |  Formal (29)  |  Problem (490)  |  Productive (12)  |  Rigor (21)  |  Shadow (52)  |  Tiresome (2)  |  Touch (76)  |  True (201)

Truth and falsity, indeed understanding, is not necessarily something purely intellectual, remote from feelings and attitudes. ... It is in the total conduct of men rather than in their statements that truth or falsehood lives, more in what a man does, in his real reaction to other men and to things, in his will to do them justice, to live at one with them. Here lies the inner connection between truth and justice. In the realm of behavior and action, the problem recurs as to the difference between piece and part.
From 'On Truth', collected in Mary Henle (ed.), Documents of Gestalt Psychology (1961), 28.
Science quotes on:  |  Action (184)  |  Attitude (59)  |  Behavior (60)  |  Conduct (31)  |  Connection (107)  |  Difference (246)  |  Falsehood (25)  |  Falsity (13)  |  Feeling (91)  |  Inner (39)  |  Intellectual (120)  |  Life (1124)  |  Man (373)  |  Part (220)  |  Piece (38)  |  Problem (490)  |  Reaction (61)  |  Real (148)  |  Realm (54)  |  Recur (4)  |  Remote (39)  |  Statement (72)  |  Total (36)  |  Truth (914)  |  Understanding (325)

Whether you take the doughnut hole as a blank space or as an entity unto itself is a purely metaphysical question and does not affect the taste of the doughnut one bit.
A Wild Sheep Chase. Quoted in Kim Lim (ed.), 1,001 Pearls of Spiritual Wisdom: Words to Enrich, Inspire, and Guide Your Life (2014), 45
Science quotes on:  |  Affect (17)  |  Bit (22)  |  Blank (11)  |  Doughnut (3)  |  Entity (31)  |  Hole (16)  |  Metaphysical (11)  |  Question (404)  |  Space (257)  |  Taste (48)  |  Unto (8)

[Cantor’s set theory:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.
As quoted in Constance Reid, Hilbert (1970), 176.
Science quotes on:  |  Achievement (150)  |  Activity (128)  |  Fine (33)  |  Genius (243)  |  Human (548)  |  Intellectual (120)  |  Mathematics (1149)  |  Product (82)  |  Set Theory (5)  |  Supreme (37)


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.