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

Today in Science History - Quickie Quiz
Who said: “A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index E > Category: Examine

Examine Quotes (44 quotes)

...the scientific cast of mind examines the world critically, as if many alternative worlds might exist, as if other things might be here which are not. Then we are forced to ask why what we see is present and not something else. Why are the Sun and moon and the planets spheres? Why not pyramids, or cubes, or dodecahedra? Why not irregular, jumbly shapes? Why so symmetrical, worlds? If you spend any time spinning hypotheses, checking to see whether they make sense, whether they conform to what else we know. Thinking of tests you can pose to substantiate or deflate hypotheses, you will find yourself doing science.
…...
Science quotes on:  |  Alternative (29)  |  Ask (156)  |  Cast (25)  |  Check (24)  |  Conform (11)  |  Critical (40)  |  Cube (11)  |  Deflate (2)  |  Exist (144)  |  Find (400)  |  Force (248)  |  Hypothesis (249)  |  Irregular (6)  |  Jumble (8)  |  Know (536)  |  Mind (733)  |  Moon (199)  |  Planet (261)  |  Pose (9)  |  Present (173)  |  Pyramid (9)  |  Science (2017)  |  Scientific (230)  |  See (368)  |  Sense (310)  |  Shape (69)  |  Spend (42)  |  Sphere (56)  |  Spin (15)  |  Substantiate (4)  |  Sun (276)  |  Symmetrical (2)  |  Test (122)  |  Think (338)  |  Time (586)  |  World (877)

A disease which new and obscure to you, Doctor, will be known only after death; and even then not without an autopsy will you examine it with exacting pains. But rare are those among the extremely busy clinicians who are willing or capable of doing this correctly.
In Atrocis, nee Descipti Prius, Morbi Historia as translated in Bulletin of the Medical Library Association (1944), 43, 217.
Science quotes on:  |  Autopsy (2)  |  Busy (27)  |  Capable (49)  |  Clinician (2)  |  Correct (79)  |  Death (297)  |  Disease (275)  |  Doctor (101)  |  Exacting (2)  |  Known (16)  |  New (477)  |  Obscure (30)  |  Pain (99)  |  Rare (41)  |  Willing (8)

A modern branch of mathematics, having achieved the art of dealing with the infinitely small, can now yield solutions in other more complex problems of motion, which used to appear insoluble. This modern branch of mathematics, unknown to the ancients, when dealing with problems of motion, admits the conception of the infinitely small, and so conforms to the chief condition of motion (absolute continuity) and thereby corrects the inevitable error which the human mind cannot avoid when dealing with separate elements of motion instead of examining continuous motion. In seeking the laws of historical movement just the same thing happens. The movement of humanity, arising as it does from innumerable human wills, is continuous. To understand the laws of this continuous movement is the aim of history. … Only by taking an infinitesimally small unit for observation (the differential of history, that is, the individual tendencies of man) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.
War and Peace (1869), Book 11, Chap. 1.
Science quotes on:  |  Absolute (96)  |  Aim (85)  |  Ancient (102)  |  Appear (113)  |  Arise (47)  |  Arrive (35)  |  Attain (41)  |  Avoid (50)  |  Branch (100)  |  Chief (37)  |  Complex (94)  |  Concept (142)  |  Condition (157)  |  Conform (11)  |  Continuity (29)  |  Continuous (38)  |  Correct (79)  |  Deal (47)  |  Differential (7)  |  Element (162)  |  Error (272)  |  Find (400)  |  History (366)  |  Hope (174)  |  Human (544)  |  Human Mind (80)  |  Humanity (123)  |  Individual (215)  |  Inevitable (27)  |  Infinite (128)  |  Infinitesimal (15)  |  Innumerable (23)  |  Insoluble (15)  |  Integrate (5)  |  Law (511)  |  Mathematics (1130)  |  Modern (156)  |  Motion (157)  |  Movement (81)  |  Observation (444)  |  Problem (483)  |  Seek (101)  |  Separate (69)  |  Small (160)  |  Solution (208)  |  Sum (41)  |  Tendency (54)  |  Understand (320)  |  Unit (30)  |  Unknown (104)  |  Yield (35)

A scientist works largely by intuition. Given enough experience, a scientist examining a problem can leap to an intuition as to what the solution ‘should look like.’ ... Science is ultimately based on insight, not logic.
…...
Science quotes on:  |  Base (70)  |  Experience (329)  |  Give (197)  |  Insight (69)  |  Intuition (57)  |  Largely (13)  |  Leap (34)  |  Logic (244)  |  Problem (483)  |  Science (2017)  |  Scientist (511)  |  Solution (208)  |  Ultimately (15)  |  Work (615)

Archimedes possessed so high a spirit, so profound a soul, and such treasures of highly scientific knowledge, that though these inventions [used to defend Syracuse against the Romans] had now obtained him the renown of more than human sagacity, he yet would not deign to leave behind him any commentary or writing on such subjects; but, repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit, he placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life; studies, the superiority of which to all others is unquestioned, and in which the only doubt can be whether the beauty and grandeur of the subjects examined, or the precision and cogency of the methods and means of proof, most deserve our admiration.
Plutarch
In John Dryden (trans.), Life of Marcellus.
Science quotes on:  |  Admiration (43)  |  Affection (18)  |  Ambition (34)  |  Archimedes (52)  |  Art (280)  |  Beauty (236)  |  Behind (38)  |  Commentary (3)  |  Defend (28)  |  Deserve (24)  |  Doubt (158)  |  Engineering (126)  |  Grandeur (21)  |  High (150)  |  Highly (16)  |  Human (544)  |  Ignoble (2)  |  Invention (316)  |  Leave (126)  |  Lend (3)  |  Life (1113)  |  Mathematicians and Anecdotes (120)  |  Means (167)  |  Mere (74)  |  Method (225)  |  Need (275)  |  Obtain (45)  |  Place (171)  |  Possess (48)  |  Precision (49)  |  Profit (38)  |  Profound (57)  |  Proof (242)  |  Pure (97)  |  Reference (32)  |  Renown (2)  |  Repudiate (3)  |  Roman (26)  |  Sagacity (8)  |  Scientific Knowledge (9)  |  Sort (46)  |  Soul (163)  |  Speculation (102)  |  Spirit (152)  |  Study (456)  |  Subject (231)  |  Superiority (12)  |  Syracuse (5)  |  Trade (30)  |  Treasure (45)  |  Unquestioned (6)  |  Vulgar (15)  |  Whole (186)  |  Write (150)

At this point, however, I have no intention whatever of criticizing the false teachings of Galen, who is easily first among the professors of dissection, for I certainly do not wish to start off by gaining a reputation for impiety toward him, the author of all good things, or by seeming insubordinate to his authority. For I am well aware how upset the practitioners (unlike the followers of Aristotle) invariably become nowadays, when they discover in the course of a single dissection that Galen has departed on two hundred or more occasions from the true description of the harmony, function, and action of the human parts, and how grimly they examine the dissected portions as they strive with all the zeal at their command to defend him. Yet even they, drawn by their love of truth, are gradually calming down and placing more faith in their own not ineffective eyes and reason than in Galen’s writings.
From De Humani Corporis Fabrica Libri Septem: (1543), Book I, iv, as translated by William Frank Richardson, in On The Fabric of the Human Body: Book I: The Bones and Cartilages (1998), Preface, liv.
Science quotes on:  |  Aristotle (161)  |  Author (58)  |  Authority (63)  |  Criticism (60)  |  Description (81)  |  Discovery (675)  |  Dissection (28)  |  Eye (215)  |  Faith (156)  |  False (96)  |  Follower (10)  |  Galen (19)  |  Harmony (69)  |  Human (544)  |  Ineffective (4)  |  Practitioner (13)  |  Professor (54)  |  Reason (449)  |  Reputation (27)  |  Teaching (107)  |  Truth (901)  |  Writing (76)  |  Zeal (11)

Common sense … may be thought of as a series of concepts and conceptual schemes which have proved highly satisfactory for the practical uses of mankind. Some of those concepts and conceptual schemes were carried over into science with only a little pruning and whittling and for a long time proved useful. As the recent revolutions in physics indicate, however, many errors can be made by failure to examine carefully just how common sense ideas should be defined in terms of what the experimenter plans to do.
In Science and Common Sense (1951), 32-33.
Science quotes on:  |  Careful (24)  |  Common Sense (74)  |  Concept (142)  |  Define (49)  |  Error (272)  |  Experimenter (20)  |  Failure (136)  |  Idea (573)  |  Mankind (238)  |  Physics (342)  |  Plan (87)  |  Practical (123)  |  Prune (7)  |  Revolution (69)  |  Satisfactory (16)  |  Science (2017)

Education must be subversive if it is to be meaningful. By this I mean that it must challenge all the things we take for granted, examine all accepted assumptions, tamper with every sacred cow, and instil a desire to question and doubt.
As quoted, without citation, in Ronald William Clark, The Life of Bertrand Russell (1976), 423.
Science quotes on:  |  Accepted (6)  |  Assumption (57)  |  Challenge (59)  |  Desire (139)  |  Doubt (158)  |  Education (328)  |  Instil (3)  |  Meaningful (15)  |  Question (399)  |  Sacred Cow (3)  |  Subversive (2)  |  Tamper (5)

Examine Language; what, if you except some few primitive elements (of natural sound), what is it all but Metaphors, recognized as such, or no longer recognized?
Science quotes on:  |  Language (214)  |  Metaphor (25)  |  Primitive (41)  |  Recognize (64)  |  Sound (86)

Examine Venus and the Moon
Who stole a thimble or a spoon.
From poem 'Hudibras' (1684), Line 591. In Hudibras: In Three Parts, Written in the Time of the Late Wars (1806), 119.
Science quotes on:  |  Moon (199)  |  Spoon (2)  |  Steal (13)  |  Venus (15)

Examine your words well, and you will find that even when you have no motive to be false, it is a very hard thing to say the exact truth, even about your own immediate feelings—much harder than to say something fine about them which is not the exact truth.
In Adam Bede (1859, 1860), 151.
Science quotes on:  |  Exact (63)  |  False (96)  |  Feeling (91)  |  Find (400)  |  Fine (33)  |  Hard (98)  |  Harder (6)  |  Immediate (42)  |  Motive (33)  |  Say (226)  |  Truth (901)  |  Word (296)

For the saving the long progression of the thoughts to remote and first principles in every case, the mind should provide itself several stages; that is to say, intermediate principles, which it might have recourse to in the examining those positions that come in its way. These, though they are not self-evident principles, yet, if they have been made out from them by a wary and unquestionable deduction, may be depended on as certain and infallible truths, and serve as unquestionable truths to prove other points depending upon them, by a nearer and shorter view than remote and general maxims. … And thus mathematicians do, who do not in every new problem run it back to the first axioms through all the whole train of intermediate propositions. Certain theorems that they have settled to themselves upon sure demonstration, serve to resolve to them multitudes of propositions which depend on them, and are as firmly made out from thence as if the mind went afresh over every link of the whole chain that tie them to first self-evident principles.
In The Conduct of the Understanding, Sect. 21.
Science quotes on:  |  Afresh (4)  |  Axiom (52)  |  Back (103)  |  Case (98)  |  Certain (121)  |  Chain (50)  |  Deduction (67)  |  Demonstration (81)  |  Depend (85)  |  Firmly (6)  |  First (306)  |  General (154)  |  Infallible (8)  |  Intermediate (20)  |  Link (41)  |  Long (167)  |  Mathematician (361)  |  Maxim (17)  |  Mind (733)  |  Multitude (20)  |  Nature Of Mathematics (72)  |  New (477)  |  Point (122)  |  Position (75)  |  Principle (279)  |  Problem (483)  |  Progression (12)  |  Proposition (78)  |  Prove (107)  |  Provide (64)  |  Recourse (12)  |  Remote (39)  |  Resolve (19)  |  Run (56)  |  Save (56)  |  Self-Evident (12)  |  Serve (56)  |  Settle (18)  |  Several (31)  |  Short (46)  |  Stage (53)  |  Theorem (88)  |  Thought (531)  |  Tie (23)  |  Train (42)  |  Truth (901)  |  Unquestionable (8)  |  View (169)  |  Wary (3)  |  Whole (186)

Gates is the ultimate programming machine. He believes everything can be defined, examined, reduced to essentials, and rearranged into a logical sequence that will achieve a particular goal.
Science quotes on:  |  Achieve (63)  |  Belief (500)  |  Define (49)  |  Bill Gates (10)  |  Goal (100)  |  Logic (244)  |  Machine (154)  |  Programming (2)  |  Rearrange (3)  |  Sequence (40)  |  Ultimate (83)

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)  |  Analysis (158)  |  Arrive (35)  |  Combination (88)  |  Command (26)  |  Comparison (61)  |  Complicated (61)  |  Contradict (11)  |  Cut (39)  |  Disguise (10)  |  Element (162)  |  Enter (29)  |  Geometry (213)  |  Inconvenient (3)  |  Labour (45)  |  Less (101)  |  Mechanical (46)  |  Nature (1199)  |  Obey (16)  |  Painful (10)  |  Physics (342)  |  Question (399)  |  Real (144)  |  Result (361)  |  Separate (69)  |  Short (46)  |  Sometimes (42)  |  Substitute (27)  |  Surprise (70)  |  Troublesome (7)  |  United (14)

If he [Thomas Edison] had a needle to find in a haystack, he would not stop to reason where it was most likely to be, but would proceed at once with the feverish diligence of a bee, to examine straw after straw until he found the object of his search. … [J]ust a little theory and calculation would have saved him ninety percent of his labor.
As quoted in 'Tesla Says Edison Was an Empiricist', The New York Times (19 Oct 1931), 25. In 1884, Tesla had moved to America to assist Edison in the designing of motors and generators.
Science quotes on:  |  Bee (26)  |  Calculation (98)  |  Diligence (16)  |  Thomas Edison (82)  |  Feverish (3)  |  Labor (68)  |  Needle (5)  |  Proceed (41)  |  Reason (449)  |  Saving (20)  |  Search (103)  |  Straw (7)  |  Theory (687)

If the entire Mandelbrot set were placed on an ordinary sheet of paper, the tiny sections of boundary we examine would not fill the width of a hydrogen atom. Physicists think about such tiny objects; only mathematicians have microscopes fine enough to actually observe them.
In 'Can We See the Mandelbrot Set?', The College Mathematics Journal (Mar 1995), 26, No. 2, 90.
Science quotes on:  |  Actual (47)  |  Atom (280)  |  Boundary (38)  |  Entire (46)  |  Fill (58)  |  Fine (33)  |  Hydrogen (43)  |  Mandelbrot Set (2)  |  Mathematician (361)  |  Microscope (73)  |  Object (167)  |  Observe (75)  |  Physicist (159)  |  Section (11)  |  Think (338)  |  Tiny (36)  |  Width (5)

If there is anything that we wish to change in a child, we should first examine it and see whether it is not something that could be better changed in ourselves.
Carl Jung
…...
Science quotes on:  |  Better (185)  |  Change (358)  |  Child (244)  |  First (306)  |  Ourselves (51)  |  See (368)  |  Wish (91)

If thou examinest a man having a break in the column of his nose, his nose being disfigured, and a [depression] being in it, while the swelling that is on it protrudes, [and] he had discharged blood from both his nostrils, thou shouldst say concerning him: “One having a break in the column of his nose. An ailment which I will treat. “Thou shouldst cleanse [it] for him [with] two plugs of linen. Thou shouldst place two [other] plugs of linen saturated with grease in the inside of his two nostrils. Thou shouldst put [him] at his mooring stakes until the swelling is drawn out. Thou shouldst apply for him stiff rolls of linen by which his nose is held fast. Thou shouldst treat him afterward [with] lint, every day until he recovers.
Anonymous
(circa 1700 B.C.) From “The Edwin Smith Surgical Papyrus”, an ancient Egyptian document regarded as the earliest known historical record of scientific thought. As translated in James Henry Breasted, The Edwin Smith Surgical Papyrus: Published in Facsimile and Hieroglyphic Transliteration with Translation and Commentary (1930), 440.
Science quotes on:  |  Ailment (6)  |  Blood (103)  |  Cleanse (5)  |  Medicine (340)  |  Nostril (4)  |  Recover (11)  |  Swelling (5)  |  Treatment (100)

If you wish to learn from the theoretical physicist anything about the methods which he uses, I would give you the following piece of advice: Don’t listen to his words, examine his achievements. For to the discoverer in that field, the constructions of his imagination appear so necessary and so natural that he is apt to treat them not as the creations of his thoughts but as given realities.
In Herbert Spencer Lecture at Oxford (10 Jun 1933), 'On the Methods of Theoretical Physics'. Printed inPhilosophy of Science (Apr 1934), 1, No. 2, 163.
Science quotes on:  |  Achievement (149)  |  Advice (39)  |  Appearance (85)  |  Construction (83)  |  Creation (239)  |  Discovery (675)  |  Field (170)  |  Imagination (268)  |  Learn (277)  |  Listen (38)  |  Method (225)  |  Necessity (141)  |  Reality (184)  |  Theoretical Physicist (12)  |  Thought (531)  |  Wish (91)  |  Word (296)

In order to comprehend and fully control arithmetical concepts and methods of proof, a high degree of abstraction is necessary, and this condition has at times been charged against arithmetic as a fault. I am of the opinion that all other fields of knowledge require at least an equally high degree of abstraction as mathematics,—provided, that in these fields the foundations are also everywhere examined with the rigour and completeness which is actually necessary.
In 'Die Theorie der algebraischen Zahlkorper', Vorwort, Jahresbericht der Deutschen Mathematiker Vereinigung, Bd. 4.
Science quotes on:  |  Abstraction (38)  |  Actually (27)  |  Arithmetic (114)  |  Arithmetical (11)  |  Charge (33)  |  Completeness (14)  |  Comprehend (38)  |  Concept (142)  |  Condition (157)  |  Control (111)  |  Degree (79)  |  Equally (25)  |  Everywhere (24)  |  Fault (33)  |  Field (170)  |  Foundation (105)  |  Fully (21)  |  High (150)  |  Knowledge (1275)  |  Least (72)  |  Mathematics (1130)  |  Method (225)  |  Necessary (142)  |  Opinion (173)  |  Order (238)  |  Proof (242)  |  Provide (64)  |  Require (78)  |  Rigour (15)  |  Study And Research In Mathematics (55)  |  Time (586)

In the context of biological research one can reasonably identify creativity with the capacity 1 to ask new and incisive questions, 2 to form new hypotheses, 3 to examine old questions in new ways or with new techniques, and 4 to perceive previously unnoticed relationships.
In 'Scientific innovation and creativity: a zoologist’s point of view', American Zoologist (1982), 22, 231.
Science quotes on:  |  Ask (156)  |  Biological (35)  |  Capacity (62)  |  Context (22)  |  Creativity (70)  |  Form (305)  |  Hypothesis (249)  |  Identify (12)  |  Incisive (2)  |  New (477)  |  Old (143)  |  Perceive (39)  |  Previously (11)  |  Question (399)  |  Reasonably (3)  |  Relationship (71)  |  Research (583)  |  Technique (48)  |  Unnoticed (5)

It is from this absolute indifference and tranquility of the mind, that mathematical speculations derive some of their most considerable advantages; because there is nothing to interest the imagination; because the judgment sits free and unbiased to examine the point. All proportions, every arrangement of quantity, is alike to the understanding, because the same truths result to it from all; from greater from lesser, from equality and inequality.
In On the Sublime and Beautiful, Part 3, sect. 2.
Science quotes on:  |  Absolute (96)  |  Advantage (73)  |  Alike (22)  |  Arrangement (57)  |  Considerable (20)  |  Derive (33)  |  Equality (21)  |  Free (88)  |  Great (517)  |  Imagination (268)  |  Indifference (13)  |  Inequality (8)  |  Interest (234)  |  Judgment (96)  |  Lesser (5)  |  Mathematics (1130)  |  Mind (733)  |  Nothing (376)  |  Point (122)  |  Proportion (70)  |  Quantity (64)  |  Result (361)  |  Same (154)  |  Sit (46)  |  Speculation (102)  |  Tranquility (8)  |  Truth (901)  |  Unbiased (5)  |  Understand (320)  |  Value Of Mathematics (51)

It is said that the composing of the Lilavati was occasioned by the following circumstance. Lilavati was the name of the author’s daughter, concerning whom it appeared, from the qualities of the ascendant at her birth, that she was destined to pass her life unmarried, and to remain without children. The father ascertained a lucky hour for contracting her in marriage, that she might be firmly connected and have children. It is said that when that hour approached, he brought his daughter and his intended son near him. He left the hour cup on the vessel of water and kept in attendance a time-knowing astrologer, in order that when the cup should subside in the water, those two precious jewels should be united. But, as the intended arrangement was not according to destiny, it happened that the girl, from a curiosity natural to children, looked into the cup, to observe the water coming in at the hole, when by chance a pearl separated from her bridal dress, fell into the cup, and, rolling down to the hole, stopped the influx of water. So the astrologer waited in expectation of the promised hour. When the operation of the cup had thus been delayed beyond all moderate time, the father was in consternation, and examining, he found that a small pearl had stopped the course of the water, and that the long-expected hour was passed. In short, the father, thus disappointed, said to his unfortunate daughter, I will write a book of your name, which shall remain to the latest times—for a good name is a second life, and the ground-work of eternal existence.
In Preface to the Persian translation of the Lilavati by Faizi (1587), itself translated into English by Strachey and quoted in John Taylor (trans.) Lilawati, or, A Treatise on Arithmetic and Geometry by Bhascara Acharya (1816), Introduction, 3. [The Lilavati is the 12th century treatise on mathematics by Indian mathematician, Bhaskara Acharya, born 1114.]
Science quotes on:  |  Accord (36)  |  Appear (113)  |  Approach (53)  |  Arrangement (57)  |  Ascendant (2)  |  Ascertain (14)  |  Astrologer (10)  |  Author (58)  |  Beyond (104)  |  Birth (92)  |  Book (255)  |  Bring (89)  |  Chance (156)  |  Child (244)  |  Circumstance (64)  |  Compose (16)  |  Concern (106)  |  Connect (29)  |  Contract (11)  |  Course (83)  |  Cup (7)  |  Curiosity (105)  |  Daughter (15)  |  Delay (10)  |  Destined (11)  |  Destiny (36)  |  Disappointed (6)  |  Down (86)  |  Dress (8)  |  Eternal (66)  |  Existence (294)  |  Expectation (54)  |  Fall (118)  |  Father (57)  |  Find (400)  |  Firmly (6)  |  Follow (121)  |  Girl (20)  |  Good (336)  |  Happen (82)  |  Hole (15)  |  Hour (70)  |  Indian (20)  |  Influx (2)  |  Intend (16)  |  Jewel (10)  |  Keep (97)  |  Late (50)  |  Leave (126)  |  Life (1113)  |  Lucky (12)  |  Marriage (35)  |  Mathematician (361)  |  Mathematicians and Anecdotes (120)  |  Mathematics (1130)  |  Moderate (6)  |  Name (164)  |  Natural (161)  |  Observe (75)  |  Occasion (22)  |  Operation (118)  |  Order (238)  |  Pass (90)  |  Pearl (6)  |  Precious (30)  |  Promise (37)  |  Quality (92)  |  Remain (109)  |  Roll (16)  |  Say (226)  |  Second (57)  |  Separate (69)  |  Short (46)  |  Small (160)  |  Son (23)  |  Stop (73)  |  Subside (5)  |  Time (586)  |  Treatise (31)  |  Unfortunate (13)  |  United (14)  |  Unmarried (3)  |  Vessel (28)  |  Wait (57)  |  Water (289)  |  Write (150)

Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined
In CRC Concise Encyclopedia of Mathematics (1998, 2nd ed. 2002 ), 1862.
Science quotes on:  |  Broad (26)  |  Field (170)  |  Ideal (69)  |  Interaction (30)  |  Mathematics (1130)  |  Object (167)  |  Property (122)  |  Study (456)

Mathematics may be likened to a large rock whose interior composition we wish to examine. The older mathematicians appear as persevering stone cutters slowly attempting to demolish the rock from the outside with hammer and chisel. The later mathematicians resemble expert miners who seek vulnerable veins, drill into these strategic places, and then blast the rock apart with well placed internal charges.
From In Mathematical Circles (1969), 7.
Science quotes on:  |  Appear (113)  |  Attempt (119)  |  Blast (10)  |  Charge (33)  |  Chisel (2)  |  Composition (54)  |  Cutter (2)  |  Demolish (4)  |  Drill (10)  |  Expert (49)  |  Hammer (21)  |  Interior (19)  |  Internal (22)  |  Later (17)  |  Mathematician (361)  |  Mathematics (1130)  |  Miner (9)  |  Older (7)  |  Outside (48)  |  Place (171)  |  Resemble (25)  |  Rock (125)  |  Seek (101)  |  Stone (76)  |  Vein (13)  |  Vulnerable (5)  |  Wish (91)

Metals are the great agents by which we can examine the recesses of nature; and their uses are so multiplied, that they have become of the greatest importance in every occupation of life. They are the instruments of all our improvements, of civilization itself, and are even subservient to the progress of the human mind towards perfection. They differ so much from each other, that nature seems to have had in view all the necessities of man, in order that she might suit every possible purpose his ingenuity can invent or his wants require.
From 'Artist and Mechanic', The artist & Tradesman’s Guide: embracing some leading facts & principles of science, and a variety of matter adapted to the wants of the artist, mechanic, manufacturer, and mercantile community (1827), 16.
Science quotes on:  |  Agent (32)  |  Civilization (174)  |  Difference (242)  |  Human Mind (80)  |  Importance (213)  |  Improvement (73)  |  Ingenuity (27)  |  Instrument (90)  |  Invent (49)  |  Life (1113)  |  Metal (41)  |  Nature (1199)  |  Necessity (141)  |  Occupation (40)  |  Perfection (87)  |  Progress (360)  |  Purpose (188)  |  Recess (7)  |  Require (78)  |  Use (76)  |  Want (173)

No man who has not a decently skeptical mind can claim to be civilized. Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions. Then, in the alleged proof, be alert for inexplicit assumptions. Euclid’s notorious oversights drove this lesson home. Thanks to him, I am (I hope!) immune to all propaganda, including that of mathematics itself.
In 'What Mathematics Has Meant to Me', Mathematics Magazine (Jan-Feb 1951), 24, 161.
Science quotes on:  |  Alert (6)  |  Argument (80)  |  Assumption (57)  |  Civilized (17)  |  Euclid (52)  |  Explicit (3)  |  Immune (3)  |  Lesson (41)  |  Mathematics (1130)  |  Mind (733)  |  Notorious (8)  |  Oversight (4)  |  Proof (242)  |  Propaganda (12)  |  Skeptical (11)  |  Teach (177)  |  Thank (12)

One of the most curious and interesting reptiles which I met with in Borneo was a large tree-frog, which was brought me by one of the Chinese workmen. He assured me that he had seen it come down in a slanting direction from a high tree, as if it flew. On examining it, I found the toes very long and fully webbed to their very extremity, so that when expanded they offered a surface much larger than the body. The forelegs were also bordered by a membrane, and the body was capable of considerable inflation. The back and limbs were of a very deep shining green colour, the undersurface and the inner toes yellow, while the webs were black, rayed with yellow. The body was about four inches long, while the webs of each hind foot, when fully expanded, covered a surface of four square inches, and the webs of all the feet together about twelve square inches. As the extremities of the toes have dilated discs for adhesion, showing the creature to be a true tree frog, it is difficult to imagine that this immense membrane of the toes can be for the purpose of swimming only, and the account of the Chinaman, that it flew down from the tree, becomes more credible. This is, I believe, the first instance known of a “flying frog,” and it is very interesting to Darwinians as showing that the variability of the toes which have been already modified for purposes of swimming and adhesive climbing, have been taken advantage of to enable an allied species to pass through the air like the flying lizard. It would appear to be a new species of the genus Rhacophorus, which consists of several frogs of a much smaller size than this, and having the webs of the toes less developed.
Malay Archipelago
Science quotes on:  |  Account (67)  |  Adhesion (5)  |  Adhesive (2)  |  Advantage (73)  |  Air (187)  |  Ally (6)  |  Already (28)  |  Appear (113)  |  Assure (15)  |  Back (103)  |  Become (173)  |  Belief (500)  |  Black (42)  |  Body (240)  |  Border (9)  |  Borneo (3)  |  Bring (89)  |  Capable (49)  |  Chinese (7)  |  Climb (34)  |  Color (98)  |  Considerable (20)  |  Consist (45)  |  Cover (37)  |  Creature (153)  |  Credible (3)  |  Curious (41)  |  Darwinian (9)  |  Deep (119)  |  Develop (102)  |  Difficult (114)  |  Direction (73)  |  Disk (3)  |  Down (86)  |  Enable (41)  |  Expand (22)  |  Extremity (4)  |  Find (400)  |  First (306)  |  Fly (99)  |  Foot (57)  |  Frog (33)  |  Fully (21)  |  Genus (18)  |  Green (32)  |  High (150)  |  Hind (3)  |  Imagine (74)  |  Immense (42)  |  Inch (9)  |  Inflation (5)  |  Inner (39)  |  Instance (32)  |  Interest (234)  |  Know (536)  |  Large (129)  |  Less (101)  |  Limb (7)  |  Lizard (6)  |  Long (167)  |  Meet (29)  |  Membrane (12)  |  Modify (15)  |  New (477)  |  Offer (40)  |  Pass (90)  |  Purpose (188)  |  Ray (41)  |  Reptile (25)  |  See (368)  |  Several (31)  |  Shine (43)  |  Show (90)  |  Size (60)  |  Small (160)  |  Species (217)  |  Square (23)  |  Surface (100)  |  Swim (16)  |  Toe (7)  |  Together (75)  |  Tree (169)  |  True (192)  |  Underside (2)  |  Variability (5)  |  Web (15)  |  Workman (13)  |  Yellow (17)

Only for you, children of doctrine and learning, have we written this work. Examine this book, ponder the meaning we have dispersed in various places and gathered again; what we have concealed in one place we have disclosed in another, that it may be understood by your wisdom.
In De Occulta Philosophia (1531), Vol. 3, 65. As quoted and cited in epigraph, Umberto Eco and William Weaver (trans.), Foucault’s Pendulum (2007), Front matter before title page.
Science quotes on:  |  Conceal (17)  |  Dedication (11)  |  Disclose (11)  |  Learning (177)  |  Meaning (110)  |  Ponder (9)  |  Understand (320)  |  Wisdom (178)

Our ancestors, when about to build a town or an army post, sacrificed some of the cattle that were wont to feed on the site proposed and examined their livers. If the livers of the first victims were dark-coloured or abnormal, they sacrificed others, to see whether the fault was due to disease or their food. They never began to build defensive works in a place until after they had made many such trials and satisfied themselves that good water and food had made the liver sound and firm. …healthfulness being their chief object.
Vitruvius
In De Architectura, Book 1, Chap 4, Sec. 9. As translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 20.
Science quotes on:  |  Abnormal (5)  |  Ancestor (40)  |  Cattle (13)  |  Disease (275)  |  Feed (26)  |  Firm (24)  |  Food (150)  |  Healthy (25)  |  Liver (14)  |  Sacrifice (32)  |  Sound (86)  |  Town (24)  |  Water (289)

The dispute between evolutionists and creation scientists offers textbook writers and teachers a wonderful opportunity to provide students with insights into the philosophy and methods of science. … What students really need to know is … how scientists judge the merit of a theory. Suppose students were taught the criteria of scientific theory evaluation and then were asked to apply these criteria … to the two theories in question. Wouldn’t such a task qualify as authentic science education? … I suspect that when these two theories are put side by side, and students are given the freedom to judge their merit as science, creation theory will fail ignominiously (although natural selection is far from faultless). … It is not only bad science to allow disputes over theory to go unexamined, but also bad education.
In Building a Bridge to the 18th Century: How the Past Can Improve Our Future (1999), 168.
Science quotes on:  |  Allow (43)  |  Authentic (4)  |  Bad Science (5)  |  Creationist (15)  |  Criterion (17)  |  Dispute (22)  |  Education (328)  |  Evaluation (7)  |  Evolutionist (7)  |  Fail (58)  |  Fault (33)  |  Freedom (100)  |  Insight (69)  |  Judge (60)  |  Merit (32)  |  Natural Selection (88)  |  Opportunity (61)  |  Philosophy (251)  |  Science And Education (15)  |  Scientific Method (164)  |  Scientific Theory (24)  |  Student (198)  |  Teacher (117)  |  Textbook (27)  |  Theory (687)  |  Writer (44)

The facts once classified, once understood, the judgment based upon them ought to be independent of the individual mind which examines them.
From The Grammar of Science (1892), 7.
Science quotes on:  |  Base (70)  |  Classify (5)  |  Fact (717)  |  Independent (65)  |  Individual (215)  |  Judgment (96)  |  Mind (733)  |  Understand (320)

The hypothetical character of continual creation has been pointed out, but why is it more of a hypothesis to say that creation is taking place now than that it took place in the past? On the contrary, the hypothesis of continual creation is more fertile in that it answers more questions and yields more results, and results that are, at least in principle, observable. To push the entire question of creation into the past is to restrict science to a discussion of what happened after creation while forbidding it to examine creation itself. This is a counsel of despair to be taken only if everything else fails.
From Cosmology (), 152.
Science quotes on:  |  Answer (243)  |  Continual (18)  |  Counsel (6)  |  Creation (239)  |  Despair (27)  |  Discussion (47)  |  Fail (58)  |  Fertile (15)  |  Happened (2)  |  Hypothesis (249)  |  Observable (5)  |  Past (150)  |  Present (173)  |  Question (399)  |  Restrict (12)  |  Result (361)  |  Science (2017)  |  Yield (35)

The more I examine the universe and study the details of its architecture, the more evidence I find that the universe in some sense must have known that we were coming.
In Disturbing the Universe (1979), 250. As cited in Daniel C. Dennett, Darwin's Dangerous Idea: Evolution and the Meaning of Life (1996), 163.
Science quotes on:  |  Architecture (42)  |  Coming (10)  |  Detail (84)  |  Evidence (179)  |  Find (400)  |  Know (536)  |  Sense (310)  |  Study (456)  |  Universe (678)

The more the subject is examined the more complex must we suppose the constitution of matter in order to explain the remarkable effects observed.
In Radio-activity (1905), 1.
Science quotes on:  |  Complex (94)  |  Constitution (31)  |  Effect (164)  |  Explain (104)  |  Matter (336)  |  Observe (75)  |  Remarkable (48)  |  Subject (231)  |  Suppose (48)

The native intellectual powers of men in different times, are not so much the causes of the different success of their labours, as the peculiar nature of the means and artificial resources in their possession‎. Independent of vessels of glass, there could have been no accurate manipulations in common chemistry: the air pump was necessary for live investigation of the properties of gaseous matter; and without the Voltaic apparatus, there was no possibility of examining the relations of electrical polarities to chemical attractions.
In Elements of Chemical Philosophy (1812), Vol. 1, Part 1, 28-29.
Science quotes on:  |  Accurate (32)  |  Air Pump (2)  |  Apparatus (36)  |  Artificial (31)  |  Attraction (36)  |  Cause (283)  |  Chemical (79)  |  Chemistry (250)  |  Common (117)  |  Different (176)  |  Electrical (12)  |  Gas (49)  |  Glass (44)  |  Independent (65)  |  Intellectual (116)  |  Investigation (170)  |  Labour (45)  |  Live (266)  |  Manipulation (14)  |  Matter (336)  |  Means (167)  |  Native (15)  |  Nature (1199)  |  Necessary (142)  |  Peculiar (43)  |  Polarity (3)  |  Possession (45)  |  Possibility (115)  |  Power (355)  |  Property (122)  |  Relation (146)  |  Resource (60)  |  Success (245)  |  Vessel (28)  |  Voltaic (2)

The philosophic spirit of inquiry may be traced to brute curiosity, and that to the habit of examining all things in search of food. Artistic genius is an expansion of monkey imitativeness.
In The Martyrdom of Man (14th ed., 1892), 392.
Science quotes on:  |  Artistic (15)  |  Brute (15)  |  Curiosity (105)  |  Expansion (26)  |  Food (150)  |  Genius (230)  |  Habit (104)  |  Imitation (21)  |  Inquiry (40)  |  Monkey (40)  |  Philosophic (4)  |  Search (103)  |  Spirit (152)  |  Trace (50)

The X-ray spectrometer opened up a new world. It proved to be a far more powerful method of analysing crystal structure…. One could examine the various faces of a crystal in succession, and by noting the angles at which and the intensity with which they reflected the X-rays, one could deduce the way in which the atoms were arranged in sheets parallel to these faces. The intersections of these sheets pinned down the positions of the atoms in space.… It was like discovering an alluvial gold field with nuggets lying around waiting to be picked up.… It was a glorious time when we worked far into every night with new worlds unfolding before us in the silent laboratory.
In The History of X-ray Analysis (1943), 9.
Science quotes on:  |  Alluvial (2)  |  Analyse (3)  |  Angle (19)  |  Arrangement (57)  |  Atom (280)  |  Crystal (53)  |  Deduce (22)  |  Discover (190)  |  Face (108)  |  Glorious (22)  |  Gold (68)  |  Intensity (19)  |  Intersection (2)  |  Laboratory (131)  |  Located (2)  |  Lying (6)  |  Method (225)  |  New (477)  |  Night (117)  |  Nugget (3)  |  Parallel (17)  |  Pick Up (4)  |  Position (75)  |  Powerful (65)  |  Reflect (31)  |  Sheet (7)  |  Space (256)  |  Structure (219)  |  Waiting (9)  |  Work (615)  |  World (877)

We may have three principal objects in the study of truth: one to discover it when it is sought; another to demonstrate it when it is possessed; and a third, to discriminate it from the false when it is examined.
As translated in Blaise Pascal and G.W. Wight (trans.), Of the Geometrical Spirit, collected in Charles William Eliot, The Harvard Classics (1910), Vol. 48, 427. From the original French, “On peut avoir trois principaux objets dans l’etude de la vérité: l’un, de la découvrir quand on la cherche; l’autre, de la démontrer quand on la possède; le dernier, de la discerner d'avec le faux quand on l’examine,” in 'De l'Ésprit Géométrique', Pascal: Opuscules Philosophiques (1887), 82. For an alternative translation, see the quote beginning, “There are three leading objects…” on the Blaise Pascal Quotes page of this website.
Science quotes on:  |  Demonstrate (49)  |  Discover (190)  |  Discriminate (4)  |  False (96)  |  Object (167)  |  Possess (48)  |  Principal (28)  |  Seek (101)  |  Study (456)  |  Truth (901)

When asked what it was like to set about proving something, the mathematician likened proving a theorem to seeing the peak of a mountain and trying to climb to the top. One establishes a base camp and begins scaling the mountain’s sheer face, encountering obstacles at every turn, often retracing one’s steps and struggling every foot of the journey. Finally when the top is reached, one stands examining the peak, taking in the view of the surrounding countryside and then noting the automobile road up the other side!
Space-filler in The Two-Year College Mathematics Journal (Nov 1980), 11, No. 5, 295.
Science quotes on:  |  Automobile (20)  |  Base (70)  |  Camp (4)  |  Climb (34)  |  Countryside (5)  |  Encounter (22)  |  Establish (55)  |  Face (108)  |  Journey (28)  |  Mathematician (361)  |  Mountain (144)  |  Obstacle (31)  |  Other (27)  |  Peak (20)  |  Prove (107)  |  Reach (119)  |  Retrace (3)  |  Road (62)  |  Scale (61)  |  Sheer (9)  |  Side (51)  |  Stand (106)  |  Step (108)  |  Struggle (76)  |  Surrounding (13)  |  Theorem (88)  |  Top (34)  |  View (169)

When I examine myself and my methods of thought, I come to the conclusion that the gift of fantasy has meant more to me that my talent for absorbing positive knowledge.
…...
Science quotes on:  |  Absorb (16)  |  Conclusion (156)  |  Fantasy (9)  |  Gift (60)  |  Knowledge (1275)  |  Mean (101)  |  Method (225)  |  Myself (36)  |  Positive (42)  |  Talent (61)  |  Thought (531)

Whereas in The Two Towers you have different races, nations, cultures coming together and examining their conscience and unifying against a very real and terrifying enemy. What the United States has been doing for the past year is bombing innocent civilians without having come anywhere close to catching Osama bin Laden or any presumed enemy.
…...
Science quotes on:  |  Anywhere (13)  |  Bomb (18)  |  Catch (30)  |  Civilian (2)  |  Close (66)  |  Conscience (38)  |  Culture (101)  |  Different (176)  |  Enemy (60)  |  Innocent (10)  |  Load (11)  |  Nation (132)  |  Past (150)  |  Presume (7)  |  Race (102)  |  Real (144)  |  Terrify (11)  |  Together (75)  |  Tower (17)  |  Unify (4)  |  United States (19)  |  Year (297)

[E.H.] Moore was presenting a paper on a highly technical topic to a large gathering of faculty and graduate students from all parts of the country. When half way through he discovered what seemed to be an error (though probably no one else in the room observed it). He stopped and re-examined the doubtful step for several minutes and then, convinced of the error, he abruptly dismissed the meeting—to the astonishment of most of the audience. It was an evidence of intellectual courage as well as honesty and doubtless won for him the supreme admiration of every person in the group—an admiration which was in no wise diminished, but rather increased, when at a later meeting he announced that after all he had been able to prove the step to be correct.
In Obituary, 'Eliakim Hastings Moore', The American Mathematical Monthly (Apr 1933), 40, 191.
Science quotes on:  |  Admiration (43)  |  Announce (9)  |  Astonishment (23)  |  Audience (16)  |  Convinced (21)  |  Correct (79)  |  Courage (55)  |  Diminish (15)  |  Dismiss (10)  |  Doubtful (9)  |  Doubtless (8)  |  Error (272)  |  Evidence (179)  |  Faculty (64)  |  Graduate Student (4)  |  Honesty (19)  |  Increase (143)  |  Intellectual (116)  |  Meeting (20)  |  Eliakim Hastings Moore (2)  |  Paper (81)  |  Present (173)  |  Prove (107)  |  Step (108)  |  Stop (73)  |  Technical (40)  |  Topic (12)

[Science] is not perfect. It can be misused. It is only a tool. But it is by far the best tool we have, self-correcting, ongoing, applicable to everything. It has two rules. First: there are no sacred truths; all assumptions must be critically examined; arguments from authority are worthless. Second: whatever is inconsistent with the facts must be discarded or revised. ... The obvious is sometimes false; the unexpected is sometimes true.
Cosmos (1985), 277.
Science quotes on:  |  Argument (80)  |  Assumption (57)  |  Authority (63)  |  Discard (19)  |  Fact (717)  |  False (96)  |  Inconsistent (8)  |  Misuse (10)  |  Obvious (77)  |  Perfect (80)  |  Revise (6)  |  Rule (170)  |  Sacred (17)  |  Scientific Method (164)  |  Self-Correction (2)  |  Tool (85)  |  Truth (901)  |  Unexpected (35)  |  Worthless (21)


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.