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

Today in Science History - Quickie Quiz
Who said: “I was going to record talking... the foil was put on; I then shouted 'Mary had a little lamb',... and the machine reproduced it perfectly.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index D > Category: Demonstrate

Demonstrate Quotes (76 quotes)

Nature and nurture are an inseparable blend of influences that work together to produce our behavior. A growing band of researchers are demonstrating that the bedrock of behaviors that make up the concerns of everyday life, such as sex, language, cooperation, and violence have been carved out by evolution over the eons, and this Stone Age legacy continues to influence modern life today.
In Stone Age Present: How Evolution Has Shaped Modern Life: From Sex, Violence and Language to Emotions, Morals and Communities, (1995), 25-26.
Science quotes on:  |  Age (499)  |  Bedrock (2)  |  Behavior (84)  |  Blend (9)  |  Concern (228)  |  Continue (165)  |  Cooperation (32)  |  Eon (11)  |  Everyday (32)  |  Everyday Life (14)  |  Evolution (590)  |  Growing (98)  |  Influence (222)  |  Inseparable (16)  |  Language (293)  |  Legacy (14)  |  Life (1795)  |  Modern (385)  |  Modern Life (3)  |  Nature (1926)  |  Nurture (16)  |  Researcher (33)  |  Sex (69)  |  Stone (162)  |  Stone Age (12)  |  Today (314)  |  Together (387)  |  Violence (34)  |  Work (1351)

That the Sun will not rise Tomorrow is no less intelligible a Proposition and implies no more contradiction than the Affirmation that it will rise. We should in vain, therefore, attempt to demonstrate its falsehood.
An Enquiry Concerning Human Understanding (1748), 48.
Science quotes on:  |  Affirmation (7)  |  Attempt (251)  |  Contradiction (68)  |  Falsehood (28)  |  Intelligible (34)  |  More (2559)  |  Proposition (123)  |  Rise (166)  |  Sun (385)  |  Tomorrow (60)  |  Vain (83)  |  Will (2355)

According to the theory of aerodynamics, as may be readily demonstrated through wind tunnel experiments, the bumblebee is unable to fly. This is because the size, weight and shape of his body in relation to the total wingspread make flying impossible. But the bumblebee, being ignorant of these scientific truths, goes ahead and flies anyway—and makes a little honey every day.
Anonymous
Sign in a General Motors Corporation factory. As quoted in Ralph L. Woods, The Businessman's Book of Quotations (1951), 249-50. Cited in Suzy Platt (ed)., Respectfully Quoted: A Dictionary of Quotations (1989), 118.
Science quotes on:  |  According (237)  |  Being (1278)  |  Body (537)  |  Bumblebee (4)  |  Experiment (695)  |  Fly (146)  |  Flying (72)  |  Honey (15)  |  Ignorant (90)  |  Impossible (251)  |  Little (707)  |  Scientific (941)  |  Scientific Truth (23)  |  Shape (72)  |  Size (60)  |  Theory (970)  |  Through (849)  |  Total (94)  |  Truth (1057)  |  Tunnel (13)  |  Unable (24)  |  Weight (134)  |  Wind (128)

All the work of the crystallographers serves only to demonstrate that there is only variety everywhere where they suppose uniformity … that in nature there is nothing absolute, nothing perfectly regular.
In Histoire Naturelle des Minéraux (1783-88), Vol. 3, 433.
Science quotes on:  |  Absolute (145)  |  All (4108)  |  Crystallographer (4)  |  Everywhere (94)  |  Mineral (59)  |  Nature (1926)  |  Nothing (966)  |  Regular (46)  |  Suppose (156)  |  Uniformity (37)  |  Variety (132)  |  Work (1351)

Any time you wish to demonstrate something, the number of faults is proportional to the number of viewers.
Anonymous
Bye's First Law of Model Railroading. In Paul Dickson, The Official Rules, (1978), 23.
Science quotes on:  |  Demonstration (113)  |  Failure (161)  |  Fault (54)  |  Number (699)  |  Something (719)  |  Time (1877)  |  Wish (212)

As soon as somebody demonstrates the art of flying, settlers from our species of man will not be lacking [on the moon and Jupiter]… Given ships or sails adapted to the breezes of heaven, there will be those who will not shrink from even that vast expanse.
(1610) As translated by Edward Rosen in Kepler’s Conversation with Galileo’s Sidereal Messenger (1965), 39.
Science quotes on:  |  Adapt (66)  |  Art (657)  |  Breeze (6)  |  Expanse (6)  |  Fly (146)  |  Flying (72)  |  Give (202)  |  Heaven (258)  |  Jupiter (26)  |  Lack (119)  |  Man (2251)  |  Moon (237)  |  Sail (36)  |  Settler (2)  |  Ship (62)  |  Shrink (23)  |  Somebody (8)  |  Soon (186)  |  Species (401)  |  Vast (177)  |  Will (2355)

Each species has evolved a special set of solutions to the general problems that all organisms must face. By the fact of its existence, a species demonstrates that its members are able to carry out adequately a series of general functions. … These general functions offer a framework within which one can integrate one’s view of biology and focus one’s research. Such a view helps one to avoid becoming lost in a morass of unstructured detail—even though the ways in which different species perform these functions may differ widely. A few obvious examples will suffice. Organisms must remain functionally integrated. They must obtain materials from their environments, and process and release energy from these materials. … They must differentiate and grow, and they must reproduce. By focusing one’s questions on one or another of these obligatory and universal capacities, one can ensure that one’s research will not be trivial and that it will have some chance of achieving broad general applicability.
In 'Integrative Biology: An Organismic Biologist’s Point of View', Integrative and Comparative Biology (2005), 45, 331.
Science quotes on:  |   (2863)  |  Achieve (66)  |  Adequately (3)  |  All (4108)  |  Applicability (6)  |  Avoid (116)  |  Become (815)  |  Becoming (96)  |  Biology (216)  |  Broad (27)  |  Capacity (100)  |  Carry (127)  |  Chance (239)  |  Detail (146)  |  Differ (85)  |  Different (577)  |  Differentiate (19)  |  Energy (344)  |  Ensure (26)  |  Environment (216)  |  Evolution (590)  |  Example (94)  |  Existence (456)  |  Face (212)  |  Fact (1210)  |  Focus (35)  |  Framework (31)  |  Function (228)  |  General (511)  |  Grow (238)  |  Help (105)  |  Integrate (7)  |  Integrated (10)  |  Lose (159)  |  Material (353)  |  Member (41)  |  Morass (2)  |  Must (1526)  |  Obligatory (3)  |  Obtain (163)  |  Obvious (126)  |  Offer (141)  |  Organism (220)  |  Perform (121)  |  Problem (676)  |  Process (423)  |  Question (621)  |  Release (27)  |  Remain (349)  |  Reproduce (11)  |  Research (664)  |  Series (149)  |  Set (394)  |  Solution (267)  |  Solution. (53)  |  Special (184)  |  Species (401)  |  Suffice (7)  |  Trivial (57)  |  Universal (189)  |  View (488)  |  Way (1217)  |  Widely (9)  |  Will (2355)

Euclid and Archimedes are allowed to be knowing, and to have demonstrated what they say: and yet whosoever shall read over their writings without perceiving the connection of their proofs, and seeing what they show, though he may understand all their words, yet he is not the more knowing. He may believe, indeed, but does not know what they say, and so is not advanced one jot in mathematical knowledge by all his reading of those approved mathematicians.
In Conduct of the Understanding, sect. 24.
Science quotes on:  |  Advance (280)  |  All (4108)  |  Allow (45)  |  Approve (3)  |  Archimedes (55)  |  Belief (578)  |  Connection (162)  |  Euclid (54)  |  Indeed (324)  |  Jot (3)  |  Know (1518)  |  Knowing (137)  |  Knowledge (1529)  |  Mathematician (387)  |  Mathematics (1328)  |  More (2559)  |  Perceive (40)  |  Proof (287)  |  Read (287)  |  Reading (133)  |  Say (984)  |  See (1081)  |  Seeing (142)  |  Show (346)  |  Study And Research In Mathematics (61)  |  Understand (606)  |  Word (619)  |  Writing (189)

Exobiology—a curious development in view of the fact that this “science” has yet to demonstrate that its subject matter exists!
In This View of Life: The World of the Evolutionist (1964), 254.
Science quotes on:  |  Curious (91)  |  Development (422)  |  Exist (443)  |  Exobiology (2)  |  Fact (1210)  |  Matter (798)  |  Science (3879)  |  Subject (521)  |  View (488)

Geometry is founded in mechanical practice, and is nothing but that part of universal mechanics which accurately proposes and demonstrates the art of measuring.
In Principia (1687), Preface, translated by Andrew Motte (1729), in Florian Cajori (ed.), Sir Isaac Newton's Mathematical Principles of Natural Philosophy (1934), xvii.
Science quotes on:  |  Accuracy (78)  |  Art (657)  |  Founded (20)  |  Geometry (255)  |  Measurement (174)  |  Mechanic (119)  |  Mechanical (140)  |  Mechanics (131)  |  Nothing (966)  |  Practice (204)  |  Propose (23)  |  Universal (189)

Gravitation is demonstrable by leaving a body unsupported.
In Sir William Withey Gull and Theodore Dyke Acland (ed.), A Collection of the Published Writings of William Withey Gull (1896), xlix.
Science quotes on:  |  Body (537)  |  Gravitation (70)  |  Support (147)

He made an instrument to know If the moon shine at full or no;
That would, as soon as e’er she shone straight,
Whether ‘twere day or night demonstrate;
Tell what her d’ameter to an inch is,
And prove that she’s not made of green cheese.
Science quotes on:  |   (2863)  |  Cheese (9)  |  Day (42)  |  Diameter (28)  |  Full (66)  |  Green (63)  |  Inch (9)  |  Instrument (144)  |  Know (1518)  |  Moon (237)  |  Night (120)  |  Prove (250)  |  Shine (45)  |  Soon (186)  |  Straight (73)  |  Tell (340)

Here lies Sir Isaac Newton, Knight, who by a vigour of mind almost supernatural, first demonstrated, the motions and Figures of the Planets, the Paths of the comets, and the Tides of the Oceans ... Let Mortals rejoice that there has existed such and so great an ornament of Nature.
Epitaph
Inscribed on the tomb of Isaac Newton in Westminster Abbey.
Science quotes on:  |  Comet (54)  |  Exist (443)  |  Figure (160)  |  First (1283)  |  Great (1574)  |  Knight (6)  |  Lie (364)  |  Mind (1338)  |  Mortal (54)  |  Motion (310)  |  Nature (1926)  |  Ocean (202)  |  Orbit (81)  |  Ornament (20)  |  Path (144)  |  Planet (356)  |  Rejoice (11)  |  Supernatural (25)  |  Tide (34)  |  Vigour (18)

Homo sapiens is a compulsive communicator. Look at the number of people you see walking around talking on mobile phones. We seem to have an infinite capacity for communicating and being communicated with. I’m not sure how admirable it is, but it certainly demonstrates that we are social organisms.
From interview with Michael Bond, 'It’s a Wonderful Life', New Scientist (14 Dec 2002), 176, No. 2373, 48.
Science quotes on:  |  Being (1278)  |  Capacity (100)  |  Cell Phone (5)  |  Certainly (185)  |  Communicate (36)  |  Compulsive (3)  |  Homo Sapiens (23)  |  Infinite (231)  |  Look (582)  |  Number (699)  |  Organism (220)  |  People (1005)  |  See (1081)  |  Social (252)  |  Talking (76)  |  Walk (124)

I am delighted that I have found a new reaction to demonstrate even to the blind the structure of the interstitial stroma of the cerebral cortex. I let the silver nitrate react with pieces of brain hardened in potassium dichromate. I have already obtained magnificent results and hope to do even better in the future.
Letter to Nicolo Manfredi, 16 Feb 1873. Archive source. Quoted in Paolo Mazzarello, The Hidden Structure: A Scientific Biography of Camillo Golgi, trans. and ed. Henry A. Buchtel and Aldo Badiani (1999), 63.
Science quotes on:  |  Already (222)  |  Better (486)  |  Blind (95)  |  Brain (270)  |  Delight (108)  |  Do (1908)  |  Future (429)  |  Hope (299)  |  Magnificent (43)  |  Neurobiology (4)  |  New (1216)  |  Obtain (163)  |  Potassium (11)  |  Reaction (104)  |  Result (677)  |  Silver (46)  |  Stain (9)  |  Structure (344)

I do not claim that intelligence, however defined, has no genetic basis–I regard it as trivially true, uninteresting, and unimportant that it does. The expression of any trait represents a complex interaction of heredity and environment ... a specific claim purporting to demonstrate a mean genetic deficiency in the intelligence of American blacks rests upon no new facts whatever and can cite no valid data in its support. It is just as likely that blacks have a genetic advantage over whites. And, either way, it doesn’t matter a damn. An individual can’t be judged by his group mean.
…...
Science quotes on:  |  Advantage (134)  |  American (46)  |  Basis (173)  |  Black (42)  |  Cite (8)  |  Claim (146)  |  Complex (188)  |  Damn (12)  |  Data (156)  |  Deficiency (12)  |  Define (49)  |  Do (1908)  |  Environment (216)  |  Expression (175)  |  Fact (1210)  |  Facts (553)  |  Genetic (108)  |  Group (78)  |  Heredity (60)  |  Individual (404)  |  Intelligence (211)  |  Interaction (46)  |  Judge (108)  |  Likely (34)  |  Matter (798)  |  Mean (809)  |  New (1216)  |  Purport (3)  |  Regard (305)  |  Represent (155)  |  Rest (280)  |  Specific (95)  |  Support (147)  |  Trait (22)  |  True (212)  |  Unimportant (6)  |  Uninteresting (9)  |  Valid (11)  |  Way (1217)  |  Whatever (234)  |  White (127)

I have always loved to begin with the facts, to observe them, to walk in the light of experiment and demonstrate as much as possible, and to discuss the results.
Quoted in Francesco Rodolico, 'Arduino', In Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography (1970), Vol. 1, 234.
Science quotes on:  |  Begin (260)  |  Experiment (695)  |  Fact (1210)  |  Facts (553)  |  Light (607)  |  Observation (555)  |  Observe (168)  |  Possible (552)  |  Result (677)  |  Walk (124)

I never really paused for a moment to question the idea that the progressive Spiritualization of Matter—so clearly demonstrated to me by Paleontology—could be anything other, or anything less, than an irreversible process. By its gravitational nature, the Universe, I saw, was falling—falling forwards—in the direction of spirit as upon its stable form. In other words, Matter was not ultra-materialized as I would at first have believed, but was instead metamorphosed in Psyche.
In The Heart of Matter (1978), 27-28.
Science quotes on:  |  Direction (175)  |  Fall (230)  |  First (1283)  |  Form (959)  |  Forward (102)  |  Gravitation (70)  |  Idea (843)  |  Irreversible (12)  |  Materialize (2)  |  Matter (798)  |  Metamorphose (2)  |  Moment (253)  |  Nature (1926)  |  Never (1087)  |  Other (2236)  |  Paleontology (31)  |  Process (423)  |  Progressive (17)  |  Psyche (9)  |  Question (621)  |  Saw (160)  |  Spirit (265)  |  Spiritualization (2)  |  Stable (30)  |  Universe (857)  |  Word (619)

I was inspired by the remarks in those books; not by the parts in which everything was proved and demonstrated [but by] the remarks about the fact that this doesn’t make any sense. … So I had this as a challenge and an inspiration.
In his Nobel Prize Lecture (11 Dec 1965), 'The Development of the Space-Time View of Quantum Electrodynamics'. Collected in Stig Lundqvist, Nobel Lectures: Physics, 1963-1970 (1998), 156.
Science quotes on:  |  Book (392)  |  Challenge (85)  |  Everything (476)  |  Fact (1210)  |  Inspiration (75)  |  Proof (287)  |  Remark (28)  |  Sense (770)

I wish that one would be persuaded that psychological experiments, especially those on the complex functions, are not improved [by large studies]; the statistical method gives only mediocre results; some recent examples demonstrate that. The American authors, who love to do things big, often publish experiments that have been conducted on hundreds and thousands of people; they instinctively obey the prejudice that the persuasiveness of a work is proportional to the number of observations. This is only an illusion.
L' Études expérimentale de l'intelligence (1903), 299.
Science quotes on:  |  Author (167)  |  Complex (188)  |  Conduct (69)  |  Do (1908)  |  Experiment (695)  |  Function (228)  |  Hundred (229)  |  Illusion (66)  |  Large (394)  |  Love (309)  |  Mediocre (14)  |  Method (505)  |  Number (699)  |  Obey (40)  |  Observation (555)  |  People (1005)  |  Prejudice (87)  |  Psychological (42)  |  Recent (77)  |  Result (677)  |  Thing (1915)  |  Thousand (331)  |  Wish (212)  |  Work (1351)

I would think I knew nothing in physics if I could say only how things could be but, without demonstrating that they can’t be otherwise.
From the original French, “Pour la Physique, ie croyrois n’y rien sçauoir, si ie ne sçauois que dire comment les choses peuuent estre, sans demonstrer qu’elles ne peuuent estre autrement,” in letter (11 Mar 1640) to Père Marin Mersenne, collected in Lettres de Mr Descartes (1659), Vol. 2, 213. As translated by John Cottingham, et al., (trans.), in The Philosophical Writings of Descartes: Volume 3, The Correspondence (1991), 145.
Science quotes on:  |  Can’t (9)  |  Know (1518)  |  Nothing (966)  |  Otherwise (24)  |  Physic (517)  |  Physics (533)  |  Say (984)  |  Thing (1915)  |  Think (1086)

Iamblichus in his treatise On the Arithmetic of Nicomachus observes p. 47- “that certain numbers were called amicable by those who assimilated the virtues and elegant habits to numbers.” He adds, “that 284 and 220 are numbers of this kind; for the parts of each are generative of each other according to the nature of friendship, as was shown by Pythagoras. For some one asking him what a friend was, he answered, another I (ετεϑος εγω) which is demonstrated to take place in these numbers.” [“Friendly” thus: Each number is equal to the sum of the factors of the other.]
In Theoretic Arithmetic (1816), 122. (Factors of 284 are 1, 2, 4 ,71 and 142, which give the sum 220. Reciprocally, factors of 220 are 1, 2, 4, 5, 10, 11 ,22, 44, 55 and 110, which give the sum 284.) Note: the expression “alter ego” is Latin for “the other I.”
Science quotes on:  |  According (237)  |  Addition (66)  |  Answer (366)  |  Arithmetic (136)  |  Asking (73)  |  Assimilate (9)  |  Call (769)  |  Certain (550)  |  Elegant (36)  |  Factor (46)  |  Friend (168)  |  Friendship (18)  |  Generative (2)  |  Habit (168)  |  Kind (557)  |  Nature (1926)  |  Nomenclature (146)  |  Number (699)  |  Observe (168)  |  Other (2236)  |  Place (177)  |  Pythagoras (38)  |  Sum (102)  |  Treatise (44)  |  Virtue (109)

If diphtheria is a disease caused by a microorganism, it is essential that three postulates be fulfilled. The fulfilment of these postulates is necessary in order to demonstrate strictly the parasitic nature of a disease:
1) The organism must be shown to be constantly present in characteristic form and arrangement in the diseased tissue.
2) The organism which, from its behaviour appears to be responsible for the disease, must be isolated and grown in pure culture.
3) The pure culture must be shown to induce the disease experimentally.
An early statement of Koch's postulates.
Mittheilungen aus den Kaiserliche Gesundheitsamt (1884) Vol. 2. Trans. T. D. Brock, Robert Koch: A Life in Medicine and Bacteriology (1988), 180.
Science quotes on:  |   (2863)  |  Arrangement (91)  |  Behaviour (41)  |  Characteristic (148)  |  Culture (143)  |  Diphtheria (2)  |  Disease (328)  |  Early (185)  |  Essential (199)  |  Experiment (695)  |  Form (959)  |  Induce (22)  |  Isolation (31)  |  Microorganism (28)  |  Must (1526)  |  Nature (1926)  |  Necessary (363)  |  Order (632)  |  Organism (220)  |  Parasite (33)  |  Postulate (38)  |  Present (619)  |  Pure (291)  |  Statement (142)  |  Tissue (45)

If it were always necessary to reduce everything to intuitive knowledge, demonstration would often be insufferably prolix. This is why mathematicians have had the cleverness to divide the difficulties and to demonstrate separately the intervening propositions. And there is art also in this; for as the mediate truths (which are called lemmas, since they appear to be a digression) may be assigned in many ways, it is well, in order to aid the understanding and memory, to choose of them those which greatly shorten the process, and appear memorable and worthy in themselves of being demonstrated. But there is another obstacle, viz.: that it is not easy to demonstrate all the axioms, and to reduce demonstrations wholly to intuitive knowledge. And if we had chosen to wait for that, perhaps we should not yet have the science of geometry.
In Gottfried Wilhelm Leibnitz and Alfred Gideon Langley (trans.), New Essays Concerning Human Understanding (1896), 413-414.
Science quotes on:  |  Aid (97)  |  All (4108)  |  Appear (118)  |  Art (657)  |  Assign (13)  |  Axiom (63)  |  Being (1278)  |  Call (769)  |  Choose (112)  |  Chosen (48)  |  Cleverness (15)  |  Demonstration (113)  |  Difficulty (196)  |  Digression (3)  |  Divide (75)  |  Easy (204)  |  Everything (476)  |  Geometry (255)  |  Insufferable (2)  |  Intervene (8)  |  Intuitive (14)  |  Knowledge (1529)  |  Lemma (2)  |  Mathematician (387)  |  Mediate (4)  |  Memorable (4)  |  Memory (134)  |  Nature Of Mathematics (80)  |  Necessary (363)  |  Obstacle (42)  |  Often (106)  |  Order (632)  |  Process (423)  |  Prolix (2)  |  Proposition (123)  |  Reduce (94)  |  Science (3879)  |  Separate (143)  |  Shorten (5)  |  Themselves (433)  |  Truth (1057)  |  Understand (606)  |  Understanding (513)  |  Wait (58)  |  Way (1217)  |  Wholly (88)  |  Why (491)  |  Worthy (34)

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:  |   (2863)  |  Analysis (233)  |  Certain (550)  |  Chemical (292)  |  Composition (84)  |  Difference (337)  |  Different (577)  |  Fascinating (37)  |  First (1283)  |  Helium (11)  |  Hydrogen (75)  |  Late (118)  |  Living (491)  |  Mystery (177)  |  Neon (4)  |  Nitrogen (26)  |  Sense (770)  |  Spectroscopy (11)  |  Star (427)  |  Start (221)  |  Still (613)  |  Sun (385)  |  Understanding (513)  |  Understood (156)  |  Way (1217)  |  Year (933)

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:  |  Actual (117)  |  Advanced (11)  |  Analysis (233)  |  Attempt (251)  |  Avoid (116)  |  Chance (239)  |  Concentrate (26)  |  Course (409)  |  Effort (227)  |  Elaborate (28)  |  Experience (467)  |  Fact (1210)  |  Finding (30)  |  Form (959)  |  Key (50)  |  Know (1518)  |  Law (894)  |  Method (505)  |  Methods (204)  |  More (2559)  |  Obvious (126)  |  Order (632)  |  Possible (552)  |  Probability (130)  |  Research (664)  |  Result (677)  |  Sense (770)  |  Simple (406)  |  Something (719)  |  Sophisticated (15)  |  Statistics (155)  |  Theory (970)  |  Truth (1057)  |  Use (766)  |  Warfare (11)  |  Wise (131)  |  Work (1351)

In Pure Mathematics, where all the various truths are necessarily connected with each other, (being all necessarily connected with those hypotheses which are the principles of the science), an arrangement is beautiful in proportion as the principles are few; and what we admire perhaps chiefly in the science, is the astonishing variety of consequences which may be demonstrably deduced from so small a number of premises.
In Elements of the Philosophy of the Human Mind (1827), Vol. 3, Chap. 1, Sec. 8, 186.
Science quotes on:  |  Admire (18)  |  All (4108)  |  Arrangement (91)  |  Astonishing (27)  |  Beautiful (258)  |  Being (1278)  |  Chiefly (47)  |  Connect (125)  |  Consequence (203)  |  Deduce (25)  |  Hypothesis (296)  |  Mathematics (1328)  |  Nature Of Mathematics (80)  |  Necessarily (135)  |  Number (699)  |  Other (2236)  |  Premise (37)  |  Principle (507)  |  Proportion (136)  |  Pure (291)  |  Pure Mathematics (67)  |  Science (3879)  |  Small (477)  |  Truth (1057)  |  Variety (132)  |  Various (200)

In the discovery of hidden things and the investigation of hidden causes, stronger reasons are obtained from sure experiments and demonstrated arguments than from probable conjectures and the opinions of philosophical speculators of the common sort...
De Magnete (1600). In William Gilbert and P. Fleury Mottelay (trans.), William Gilbert of Colchester, physician of London: On the load stone and magnetic bodies (1893), xlvii.
Science quotes on:  |  Argument (138)  |  Cause (541)  |  Common (436)  |  Conjecture (49)  |  Discovery (780)  |  Experiment (695)  |  Hidden (42)  |  Investigation (230)  |  Obtain (163)  |  Opinion (281)  |  Philosopher (258)  |  Probable (20)  |  Reason (744)  |  Stronger (36)  |  Thing (1915)

In the mathematical investigations I have usually employed such methods as present themselves naturally to a physicist. The pure mathematician will complain, and (it must be confessed) sometimes with justice, of deficient rigour. But to this question there are two sides. For, however important it may be to maintain a uniformly high standard in pure mathematics, the physicist may occasionally do well to rest content with arguments which are fairly satisfactory and conclusive from his point of view. To his mind, exercised in a different order of ideas, the more severe procedure of the pure mathematician may appear not more but less demonstrative. And further, in many cases of difficulty to insist upon the highest standard would mean the exclusion of the subject altogether in view of the space that would be required.
In Preface to second edition, The Theory of Sound (1894), Vol. 1, vii.
Science quotes on:  |  Appear (118)  |  Argument (138)  |  Complain (8)  |  Conclusive (11)  |  Confess (42)  |  Deficient (3)  |  Demonstrative (14)  |  Different (577)  |  Difficulty (196)  |  Do (1908)  |  Employ (113)  |  Exclusion (16)  |  High (362)  |  Idea (843)  |  Insist (20)  |  Investigation (230)  |  Justice (39)  |  Maintain (105)  |  Mathematics (1328)  |  Mean (809)  |  Method (505)  |  Methods (204)  |  Mind (1338)  |  More (2559)  |  Must (1526)  |  Order (632)  |  Physicist (259)  |  Point (580)  |  Point Of View (80)  |  Present (619)  |  Procedure (41)  |  Pure (291)  |  Pure Mathematics (67)  |  Question (621)  |  Required (108)  |  Rest (280)  |  Rigour (21)  |  Satisfactory (17)  |  Severe (16)  |  Side (233)  |  Space (500)  |  Standard (57)  |  Subject (521)  |  Themselves (433)  |  Two (937)  |  Usually (176)  |  View (488)  |  Will (2355)

In this manner the whole substance of our geometry is reduced to the definitions and axioms which we employ in our elementary reasonings; and in like manner we reduce the demonstrative truths of any other science to the definitions and axioms which we there employ.
In The Philosophy of the Inductive Sciences: Founded Upon Their History (1840), Vol. 1, 67.
Science quotes on:  |  Axiom (63)  |  Definition (221)  |  Demonstrative (14)  |  Elementary (96)  |  Employ (113)  |  Geometry (255)  |  Other (2236)  |  Reasoning (207)  |  Reduce (94)  |  Science (3879)  |  Substance (248)  |  Truth (1057)  |  Whole (738)

Little could Plato have imagined, when, indulging his instinctive love of the true and beautiful for their own sakes, he entered upon these refined speculations and revelled in a world of his own creation, that he was writing the grammar of the language in which it would be demonstrated in after ages that the pages of the universe are written.
From Lecture (4 Dec 1854) delivered to the Gresham Committee and the members of the Common Council of the City of London, 'A Probationary Lecture on Geometry', collected in Collected Mathematical Papers of James Joseph Sylvester (1908), Vol. 2, 7.
Science quotes on:  |  Age (499)  |  Beautiful (258)  |  Creation (327)  |  Enter (141)  |  Grammar (14)  |  Imagine (164)  |  Indulge (14)  |  Instinctive (4)  |  Language (293)  |  Little (707)  |  Love (309)  |  Page (30)  |  Plato (76)  |  Refine (8)  |  Revel (5)  |  Sake (58)  |  Speculation (126)  |  True (212)  |  Universe (857)  |  World (1774)  |  Write (230)  |  Writing (189)

Mathematic is either Pure or Mixed: To Pure Mathematic belong those sciences which handle Quantity entirely severed from matter and from axioms of natural philosophy. These are two, Geometry and Arithmetic; the one handling quantity continued, the other dissevered. … Mixed Mathematic has for its subject some axioms and parts of natural philosophy, and considers quantity in so far as it assists to explain, demonstrate and actuate these.
In De Augmentis, Bk. 3; Advancement of Learning, Bk. 2.
Science quotes on:  |  Arithmetic (136)  |  Assist (9)  |  Axiom (63)  |  Belong (162)  |  Consider (416)  |  Continue (165)  |  Definitions and Objects of Mathematics (33)  |  Entirely (34)  |  Explain (322)  |  Far (154)  |  Geometry (255)  |  Handle (28)  |  Matter (798)  |  Mixed (6)  |  Natural (796)  |  Natural Philosophy (52)  |  Other (2236)  |  Part (222)  |  Philosophy (380)  |  Pure (291)  |  Quantity (132)  |  Science (3879)  |  Sever (2)  |  Subject (521)  |  Two (937)

Mathematics, from the earliest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the safe way of science. But it must not be supposed that it was as easy for mathematics as for logic, in which reason is concerned with itself alone, to find, or rather to make for itself that royal road. I believe, on the contrary, that there was a long period of tentative work (chiefly still among the Egyptians), and that the change is to be ascribed to a revolution, produced by the happy thought of a single man, whose experiments pointed unmistakably to the path that had to be followed, and opened and traced out for the most distant times the safe way of a science. The history of that intellectual revolution, which was far more important than the passage round the celebrated Cape of Good Hope, and the name of its fortunate author, have not been preserved to us. … A new light flashed on the first man who demonstrated the properties of the isosceles triangle (whether his name was Thales or any other name), for he found that he had not to investigate what he saw in the figure, or the mere concepts of that figure, and thus to learn its properties; but that he had to produce (by construction) what he had himself, according to concepts a priori, placed into that figure and represented in it, so that, in order to know anything with certainty a priori, he must not attribute to that figure anything beyond what necessarily follows from what he has himself placed into it, in accordance with the concept.
In Critique of Pure Reason, Preface to the Second Edition, (1900), 690.
Science quotes on:  |  A Priori (26)  |  Accord (36)  |  Accordance (10)  |  According (237)  |  Alone (311)  |  Ascribe (17)  |  Attribute (61)  |  Author (167)  |  Belief (578)  |  Beyond (308)  |  Celebrate (19)  |  Certainty (174)  |  Change (593)  |  Chiefly (47)  |  Concept (221)  |  Concern (228)  |  Construction (112)  |  Contrary (141)  |  Distant (33)  |  Early (185)  |  Easy (204)  |  Egyptian (5)  |  Experiment (695)  |  Far (154)  |  Figure (160)  |  Find (998)  |  First (1283)  |  Flash (49)  |  Follow (378)  |  Fortunate (26)  |  Good (889)  |  Greek (107)  |  Happy (105)  |  Himself (461)  |  History (673)  |  Hope (299)  |  Human (1468)  |  Important (209)  |  Intellectual (255)  |  Investigate (103)  |  Isosceles Triangle (3)  |  Know (1518)  |  Learn (629)  |  Light (607)  |  Logic (287)  |  Long (790)  |  Man (2251)  |  Mathematics (1328)  |  Mere (84)  |  More (2559)  |  Most (1731)  |  Must (1526)  |  Name (333)  |  Nature Of Mathematics (80)  |  Necessarily (135)  |  New (1216)  |  Open (274)  |  Order (632)  |  Other (2236)  |  Passage (50)  |  Path (144)  |  People (1005)  |  Period (198)  |  Place (177)  |  Point (580)  |  Preserve (83)  |  Produce (104)  |  Produced (187)  |  Property (168)  |  Reach (281)  |  Reason (744)  |  Represent (155)  |  Revolution (129)  |  Round (26)  |  Royal (57)  |  Royal Road (4)  |  Safe (54)  |  Saw (160)  |  Science (3879)  |  See (1081)  |  Single (353)  |  Still (613)  |  Suppose (156)  |  Tentative (16)  |  Thales (9)  |  Thought (953)  |  Time (1877)  |  Trace (103)  |  Triangle (18)  |  Unmistakably (2)  |  Way (1217)  |  Wonderful (149)  |  Work (1351)

Nature never “fails.” Nature complies with its own laws. Nature is the law. When Man lacks understanding of Nature’s laws and a Man-contrived structure buckles unexpectedly, it does not fail. It only demonstrates that Man did not understand Nature’s laws and behaviors. Nothing failed. Man’s knowledge or estimating was inadequate.
In "How Little I Know", in Saturday Review (12 Nov 1966), 152. Excerpted in Buckminster Fuller and Answar Dil, Humans in Universe (1983), 31.
Science quotes on:  |   (2863)  |  Behavior (84)  |  Buckle (4)  |  Compliance (7)  |  Contrive (10)  |  Engineering (175)  |  Estimate (57)  |  Fail (185)  |  Failure (161)  |  Inadequate (19)  |  Knowledge (1529)  |  Lack (119)  |  Law (894)  |  Man (2251)  |  Nature (1926)  |  Never (1087)  |  Nothing (966)  |  Structure (344)  |  Understand (606)  |  Understanding (513)  |  Unexpected (52)

Our failure to discern a universal good does not record any lack of insight or ingenuity, but merely demonstrates that nature contains no moral messages framed in human terms. Morality is a subject for philosophers, theologians, students of the humanities, indeed for all thinking people. The answers will not be read passively from nature; they do not, and cannot, arise from the data of science. The factual state of the world does not teach us how we, with our powers for good and evil, should alter or preserve it in the most ethical manner.
…...
Science quotes on:  |  All (4108)  |  Alter (62)  |  Answer (366)  |  Arise (158)  |  Contain (68)  |  Data (156)  |  Discern (33)  |  Do (1908)  |  Ethical (34)  |  Evil (116)  |  Factual (8)  |  Failure (161)  |  Frame (26)  |  Good (889)  |  Good And Evil (3)  |  Human (1468)  |  Humanities (20)  |  Indeed (324)  |  Ingenuity (39)  |  Insight (102)  |  Lack (119)  |  Manner (58)  |  Merely (316)  |  Message (49)  |  Moral (195)  |  Morality (52)  |  Most (1731)  |  Nature (1926)  |  Passively (3)  |  People (1005)  |  Philosopher (258)  |  Power (746)  |  Preserve (83)  |  Read (287)  |  Record (154)  |  Science (3879)  |  State (491)  |  Student (300)  |  Subject (521)  |  Teach (277)  |  Term (349)  |  Terms (184)  |  Theologian (22)  |  Think (1086)  |  Thinking (414)  |  Universal (189)  |  Will (2355)  |  World (1774)

Our present work sets forth mathematical principles of philosophy. For the basic problem of philosophy seems to be to discover the forces of nature from the phenomena of motions and then to demonstrate the other phenomena from these forces. It is to these ends that the general propositions in books 1 and 2 are directed, while in book 3 our explanation of the system of the world illustrates these propositions.
The Principia: Mathematical Principles of Natural Philosophy (1687), 3rd edition (1726), trans. I. Bernard Cohen and Anne Whitman (1999), Preface to the first edition, 382.
Science quotes on:  |  Basic (138)  |  Book (392)  |  Direct (225)  |  Discover (553)  |  Discovery (780)  |  End (590)  |  Explanation (234)  |  Force (487)  |  General (511)  |  Mathematics (1328)  |  Motion (310)  |  Nature (1926)  |  Other (2236)  |  Phenomenon (318)  |  Philosophy (380)  |  Present (619)  |  Principle (507)  |  Problem (676)  |  Proposition (123)  |  Set (394)  |  System (537)  |  Work (1351)  |  World (1774)

Perhaps a species that has accumulated ... tons of explosive per capita has already demonstrated its biological unfitness beyond any further question.
…...
Science quotes on:  |  Accumulate (26)  |  Already (222)  |  Beyond (308)  |  Biological (137)  |  Explosive (23)  |  Far (154)  |  Question (621)  |  Species (401)  |  Ton (21)

Politics is a science. You can demonstrate that you are right and that others are wrong.
Jean Paul
…...
Science quotes on:  |  Other (2236)  |  Politics (112)  |  Right (452)  |  Science (3879)  |  Wrong (234)

Samoa culture demonstrates how much the tragic or the easy solution of the Oedipus situation depends upon the inter-relationship between parents and children, and is not created out of whole cloth by the young child’s biological impulses.
Male and Female: A Study of the Sexes in a Changing World (1949), 119.
Science quotes on:  |   (2863)  |  Biological (137)  |  Child (307)  |  Children (200)  |  Culture (143)  |  Demonstration (113)  |  Depend (228)  |  Easy (204)  |  Impulse (48)  |  Inter (11)  |  Inter-Relationship (2)  |  Oedipus (2)  |  Parent (76)  |  Relationship (104)  |  Situation (113)  |  Solution (267)  |  Tragic (17)  |  Whole (738)  |  Young (227)

Sample recommendation letter:
Dear Search Committee Chair,
I am writing this letter for Mr. John Smith who has applied for a position in your department. I should start by saying that I cannot recommend him too highly.
In fact, there is no other student with whom I can adequately compare him, and I am sure that the amount of mathematics he knows will surprise you.
His dissertation is the sort of work you don’t expect to see these days.
It definitely demonstrates his complete capabilities.
In closing, let me say that you will be fortunate if you can get him to work for you.
Sincerely,
A. D. Visor (Prof.)
In A Mathematician Reads the Newspaper (1995), 43
Science quotes on:  |  Amount (151)  |  Applied (177)  |  Capability (41)  |  Chair (24)  |  Committee (15)  |  Compare (69)  |  Complete (204)  |  Department (92)  |  Dissertation (2)  |  Expect (200)  |  Fact (1210)  |  Fortunate (26)  |  Know (1518)  |  Letter (109)  |  Mathematics (1328)  |  Other (2236)  |  Recommend (24)  |  Recommendation (12)  |  Reference (33)  |  Sample (19)  |  Say (984)  |  Search (162)  |  See (1081)  |  Start (221)  |  Student (300)  |  Surprise (86)  |  Will (2355)  |  Work (1351)  |  Writing (189)

Science has sometimes been said to be opposed to faith and inconsistent with it. But all science in fact rests on a basis of faith for it assumes the permanence and uniformity of natural laws—a thing which can never be demonstrated.
In Tryon Edwards (ed.), A Dictionary of Thoughts: Being a Cyclopedia of Laconic Quotations from the Best Authors of the World, Both Ancient and Modern (1891), 165.
Science quotes on:  |  All (4108)  |  Assume (38)  |  Basis (173)  |  Fact (1210)  |  Faith (203)  |  Inconsistent (9)  |  Law (894)  |  Natural (796)  |  Natural Law (41)  |  Never (1087)  |  Oppose (24)  |  Permanence (24)  |  Rest (280)  |  Science (3879)  |  Thing (1915)  |  Uniformity (37)

So the astronomer is on common ground with the physicist both in the subject and in the predicate of the conclusion, but the physicist demonstrates the predicate to belong to the subject by nature, whereas the astronomer does not care whether it belongs by nature or not. What, therefore, is the predicate for the physicist, is abstracted as the subject for the pure mathematician.
As quoted in Alistair Cameron Crombie, Robert Grosseteste and the Origins of Experimental Science, 1100-1700 (1971), 94.
Science quotes on:  |  Abstract (124)  |  Astronomer (93)  |  Belong (162)  |  Both (493)  |  Care (186)  |  Common (436)  |  Common Ground (4)  |  Conclusion (254)  |  Ground (217)  |  Mathematician (387)  |  Nature (1926)  |  Physicist (259)  |  Predicate (3)  |  Pure (291)  |  Scientist (820)  |  Subject (521)

Some recent philosophers seem to have given their moral approval to these deplorable verdicts that affirm that the intelligence of an individual is a fixed quantity, a quantity that cannot be augmented. We must protest and react against this brutal pessimism; we will try to demonstrate that it is founded on nothing.
Les idées modernes sur les enfants (1909), 141.
Science quotes on:  |  Against (332)  |  Augment (12)  |  Deplorable (4)  |  Individual (404)  |  Intelligence (211)  |  Moral (195)  |  Must (1526)  |  Nothing (966)  |  Pessimism (4)  |  Philosopher (258)  |  Protest (9)  |  Quantity (132)  |  Recent (77)  |  Try (283)  |  Verdict (8)  |  Will (2355)

Spong and I had also several fine discourses upon the globes this afternoon, particularly why the fixed stars do not rise and set at the same hour all the year long, which he could not demonstrate nor I neither.
Entry for 19 Aug 1666. In Samuel Pepys and Henry B. Wheatley (ed.), The Diary of Samuel Pepys (1895, 1900), Vol. 5, 382. He spent the day with Mr Reeves and Mr Spong.
Science quotes on:  |  All (4108)  |  Discourse (18)  |  Do (1908)  |  Explain (322)  |  Fixed (17)  |  Hour (186)  |  Long (790)  |  Rise (166)  |  Set (394)  |  Star (427)  |  Stars (304)  |  Why (491)  |  Year (933)

Surely the claim of mathematics to take a place among the liberal arts must now be admitted as fully made good. Whether we look at the advances made in modern geometry, in modern integral calculus, or in modern algebra, in each of these three a free handling of the material employed is now possible, and an almost unlimited scope is left to the regulated play of fancy. It seems to me that the whole of aesthetic (so far as at present revealed) may be regarded as a scheme having four centres, which may be treated as the four apices of a tetrahedron, namely Epic, Music, Plastic, and Mathematic. There will be found a common plane to every three of these, outside of which lies the fourth; and through every two may be drawn a common axis opposite to the axis passing through the other two. So far is certain and demonstrable. I think it also possible that there is a centre of gravity to each set of three, and that the line joining each such centre with the outside apex will intersect in a common point the centre of gravity of the whole body of aesthetic; but what that centre is or must be I have not had time to think out.
In 'Proof of the Hitherto Undemonstrated Fundamental Theorem of Invariants', Collected Mathematical Papers (1909), Vol. 3, 123.
Science quotes on:  |  Advance (280)  |  Aesthetic (46)  |  Algebra (113)  |  Apex (6)  |  Art (657)  |  Body (537)  |  Calculus (65)  |  Centre Of Gravity (4)  |  Certain (550)  |  Claim (146)  |  Common (436)  |  Employ (113)  |  Epic (12)  |  Fancy (50)  |  Free (232)  |  Geometry (255)  |  Good (889)  |  Gravity (132)  |  Integral (26)  |  Integral Calculus (6)  |  Intersect (5)  |  Joining (11)  |  Liberal Arts (5)  |  Lie (364)  |  Look (582)  |  Material (353)  |  Mathematics (1328)  |  Mathematics As A Fine Art (23)  |  Modern (385)  |  Music (129)  |  Must (1526)  |  Opposite (104)  |  Other (2236)  |  Outside (141)  |  Passing (76)  |  Place (177)  |  Plane (20)  |  Plastic (28)  |  Point (580)  |  Possible (552)  |  Present (619)  |  Regard (305)  |  Reveal (148)  |  Revealed (60)  |  Scheme (57)  |  Scope (45)  |  Set (394)  |  Surely (101)  |  Tetrahedron (4)  |  Think (1086)  |  Through (849)  |  Time (1877)  |  Two (937)  |  Unlimited (22)  |  Whole (738)  |  Will (2355)

The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.
Aristotle
As translated in Book 13, 1078.a3, Aristotle’s Metaphysics, a Revised Text with Introduction and Commentary by W. D. Ross (1924), Vol. 2, 416.
Science quotes on:  |  Beauty (299)  |  Chief (97)  |  Definiteness (3)  |  Degree (276)  |  Form (959)  |  Mathematics (1328)  |  Order (632)  |  Science (3879)  |  Special (184)  |  Symmetry (43)

The discovery in 1846 of the planet Neptune was a dramatic and spectacular achievement of mathematical astronomy. The very existence of this new member of the solar system, and its exact location, were demonstrated with pencil and paper; there was left to observers only the routine task of pointing their telescopes at the spot the mathematicians had marked.
In J.R. Newman (ed.), 'Commentary on John Couch Adams', The World of Mathematics (1956), 820.
Science quotes on:  |  Achievement (179)  |  Astronomy (229)  |  Discovery (780)  |  Dramatic (17)  |  Exact (68)  |  Existence (456)  |  Location (15)  |  Mark (43)  |  Marked (55)  |  Mathematician (387)  |  Mathematics (1328)  |  Neptune (13)  |  New (1216)  |  Observer (43)  |  Paper (182)  |  Pencil (20)  |  Planet (356)  |  Point (580)  |  Routine (25)  |  Solar System (77)  |  Spectacular (18)  |  Spot (17)  |  System (537)  |  Task (147)  |  Telescope (98)

The Excellence of Modern Geometry is in nothing more evident, than in those full and adequate Solutions it gives to Problems; representing all possible Cases in one view, and in one general Theorem many times comprehending whole Sciences; which deduced at length into Propositions, and demonstrated after the manner of the Ancients, might well become the subjects of large Treatises: For whatsoever Theorem solves the most complicated Problem of the kind, does with a due Reduction reach all the subordinate Cases.
In 'An Instance of the Excellence of Modern Algebra, etc', Philosophical Transactions, 1694, 960.
Science quotes on:  |  Adequate (46)  |  All (4108)  |  Ancient (189)  |  Become (815)  |  Case (99)  |  Complicated (115)  |  Comprehend (40)  |  Deduce (25)  |  Due (141)  |  Evident (91)  |  Excellence (39)  |  Full (66)  |  General (511)  |  Geometry (255)  |  Give (202)  |  Kind (557)  |  Large (394)  |  Length (23)  |  Manner (58)  |  Modern (385)  |  Modern Mathematics (50)  |  More (2559)  |  Most (1731)  |  Nothing (966)  |  Possible (552)  |  Problem (676)  |  Proposition (123)  |  Reach (281)  |  Reduction (51)  |  Represent (155)  |  Science (3879)  |  Solution (267)  |  Solution. (53)  |  Solve (130)  |  Subject (521)  |  Subordinate (9)  |  Theorem (112)  |  Time (1877)  |  Treatise (44)  |  View (488)  |  Whatsoever (41)  |  Whole (738)

The extensive literature addressed to the definition or characterization of science is filled with inconsistent points of view and demonstrates that an adequate definition is not easy to attain. Part of the difficulty arises from the fact that the meaning of science is not fixed, but is dynamic. As science has evolved, so has its meaning. It takes on a new meaning and significance with successive ages.
Opening statement on 'The Meaning of “Science”', in Scientific Method: Optimizing Applied Research Decisions (1962), 1.
Science quotes on:  |  Adequate (46)  |  Age (499)  |  Arise (158)  |  Attain (125)  |  Characterization (8)  |  Definition (221)  |  Difficulty (196)  |  Easy (204)  |  Evolution (590)  |  Extensive (33)  |  Fact (1210)  |  Inconsistent (9)  |  Literature (103)  |  Meaning (233)  |  New (1216)  |  Point (580)  |  Point Of View (80)  |  Science (3879)  |  Significance (113)  |  Successive (73)  |  View (488)

The great CREATOR of all things has infinitely diversified the works of his hands, but has at the same time stamped a certain similitude on the features of nature, that demonstrates to us, that the whole is one family of one parent.
Zoonomia (1794), Vol. 1, 1.
Science quotes on:  |  All (4108)  |  Certain (550)  |  Creator (91)  |  Evolution (590)  |  Family (94)  |  Great (1574)  |  Nature (1926)  |  Parent (76)  |  Stamp (36)  |  Thing (1915)  |  Time (1877)  |  Whole (738)  |  Work (1351)

The Greeks in the first vigour of their pursuit of mathematical truth, at the time of Plato and soon after, had by no means confined themselves to those propositions which had a visible bearing on the phenomena of nature; but had followed out many beautiful trains of research concerning various kinds of figures, for the sake of their beauty alone; as for instance in their doctrine of Conic Sections, of which curves they had discovered all the principal properties. But it is curious to remark, that these investigations, thus pursued at first as mere matters of curiosity and intellectual gratification, were destined, two thousand years later, to play a very important part in establishing that system of celestial motions which succeeded the Platonic scheme of cycles and epicycles. If the properties of conic sections had not been demonstrated by the Greeks and thus rendered familiar to the mathematicians of succeeding ages, Kepler would probably not have been able to discover those laws respecting the orbits and motions of planets which were the occasion of the greatest revolution that ever happened in the history of science.
In History of Scientific Ideas, Bk. 9, chap. 14, sect. 3.
Science quotes on:  |  Age (499)  |  All (4108)  |  Alone (311)  |  Bear (159)  |  Beautiful (258)  |  Beauty (299)  |  Celestial (53)  |  Concern (228)  |  Confine (26)  |  Conic Section (8)  |  Curiosity (128)  |  Curious (91)  |  Curve (49)  |  Cycle (40)  |  Destined (42)  |  Discover (553)  |  Doctrine (75)  |  Epicycle (4)  |  Establish (57)  |  Familiar (43)  |  Figure (160)  |  First (1283)  |  Follow (378)  |  Gratification (20)  |  Great (1574)  |  Greatest (328)  |  Greek (107)  |  Happen (274)  |  Happened (88)  |  History (673)  |  History Of Science (63)  |  Important (209)  |  Instance (33)  |  Intellectual (255)  |  Investigation (230)  |  Kepler (4)  |  Kind (557)  |  Late (118)  |  Law (894)  |  Mathematician (387)  |  Mathematics (1328)  |  Matter (798)  |  Mean (809)  |  Means (579)  |  Mere (84)  |  Motion (310)  |  Nature (1926)  |  Occasion (85)  |  Orbit (81)  |  Part (222)  |  Phenomenon (318)  |  Planet (356)  |  Plato (76)  |  Platonic (3)  |  Play (112)  |  Principal (63)  |  Probably (49)  |  Property (168)  |  Proposition (123)  |  Pursue (58)  |  Pursuit (121)  |  Remark (28)  |  Render (93)  |  Research (664)  |  Respect (207)  |  Revolution (129)  |  Sake (58)  |  Scheme (57)  |  Science (3879)  |  Soon (186)  |  Study And Research In Mathematics (61)  |  Succeed (109)  |  Succeeding (14)  |  System (537)  |  Themselves (433)  |  Thousand (331)  |  Time (1877)  |  Train (114)  |  Truth (1057)  |  Two (937)  |  Various (200)  |  Vigour (18)  |  Visible (84)  |  Year (933)

The man of science dissects the statement, verifies the facts, and demonstrates connection even where he cannot its purpose.
From 'The Great Lawsuit. Man versus Men. Woman versus Women,' in the Boston Dial (Jul 1843), 4, No. 1, 3, which she expanded (padded) to publish as Woman in the Nineteenth Century (1844).
Science quotes on:  |  Connection (162)  |  Demonstration (113)  |  Dissection (32)  |  Fact (1210)  |  Facts (553)  |  Man (2251)  |  Men Of Science (143)  |  Purpose (317)  |  Science (3879)  |  Statement (142)  |  Verify (23)

The Mathematics, I say, which effectually exercises, not vainly deludes or vexatiously torments studious Minds with obscure Subtilties, perplexed Difficulties, or contentious Disquisitions; which overcomes without Opposition, triumphs without Pomp, compels without Force, and rules absolutely without Loss of Liberty; which does not privately over-reach a weak Faith, but openly assaults an armed Reason, obtains a total Victory, and puts on inevitable Chains; whose Words are so many Oracles, and Works as many Miracles; which blabs out nothing rashly, nor designs anything from the Purpose, but plainly demonstrates and readily performs all Things within its Verge; which obtrudes no false Shadow of Science, but the very Science itself, the Mind firmly adhering to it, as soon as possessed of it, and can never after desert it of its own Accord, or be deprived of it by any Force of others: Lastly the Mathematics, which depends upon Principles clear to the Mind, and agreeable to Experience; which draws certain Conclusions, instructs by profitable Rules, unfolds pleasant Questions; and produces wonderful Effects; which is the fruitful Parent of, I had almost said all, Arts, the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human Affairs.
Address to the University of Cambridge upon being elected Lucasian Professor of Mathematics (14 Mar 1664). In Mathematical Lectures (1734), xxviii.
Science quotes on:  |  Advantage (134)  |  Agreeable (18)  |  All (4108)  |  Arm (81)  |  Art (657)  |  Certain (550)  |  Chain (50)  |  Compel (30)  |  Conclusion (254)  |  Delude (3)  |  Depend (228)  |  Desert (56)  |  Design (195)  |  Difficulty (196)  |  Draw (137)  |  Effect (393)  |  Estimates of Mathematics (30)  |  Exercise (110)  |  Experience (467)  |  Faith (203)  |  False (100)  |  Force (487)  |  Foundation (171)  |  Fountain (16)  |  Fruitful (58)  |  Human (1468)  |  Inevitable (49)  |  Instruction (91)  |  Liberty (25)  |  Loss (110)  |  Mathematics (1328)  |  Mind (1338)  |  Miracle (83)  |  Never (1087)  |  Nothing (966)  |  Obscure (62)  |  Obtain (163)  |  Opposition (48)  |  Oracle (4)  |  Other (2236)  |  Overcome (39)  |  Parent (76)  |  Perform (121)  |  Pomp (2)  |  Possess (156)  |  Principle (507)  |  Profitable (28)  |  Purpose (317)  |  Question (621)  |  Rashly (2)  |  Reach (281)  |  Reason (744)  |  Rule (294)  |  Say (984)  |  Science (3879)  |  Science And Art (184)  |  Shadow (72)  |  Soon (186)  |  Studious (5)  |  Thing (1915)  |  Torment (18)  |  Total (94)  |  Triumph (73)  |  Verge (10)  |  Victory (39)  |  Weak (71)  |  Wonderful (149)  |  Word (619)  |  Work (1351)

The mediocre teacher tells. The good teacher explains. The superior teacher demonstrates. The great teacher inspires.
In Thoughts of a Christian Optimist: The Words of William Arthur Ward (1968), 16
Science quotes on:  |  Explain (322)  |  Good (889)  |  Great (1574)  |  Inspire (52)  |  Mediocre (14)  |  Superior (81)  |  Teacher (143)  |  Tell (340)

The more a science advances, the more will it be possible to understand immediately results which formerly could be demonstrated only by means of lengthy intermediate considerations: a mathematical subject cannot be considered as finally completed until this end has been attained.
In Formensystem binärer Formen (1875), 2.
Science quotes on:  |  Advance (280)  |  Attain (125)  |  Complete (204)  |  Completed (30)  |  Consider (416)  |  Consideration (139)  |  End (590)  |  Finally (26)  |  Formerly (5)  |  Immediately (114)  |  Intermediate (37)  |  Lengthy (3)  |  Mathematics (1328)  |  Mean (809)  |  Means (579)  |  More (2559)  |  Possible (552)  |  Result (677)  |  Science (3879)  |  Study And Research In Mathematics (61)  |  Subject (521)  |  Understand (606)  |  Will (2355)

The stone that Dr. Johnson once kicked to demonstrate the reality of matter has become dissipated in a diffuse distribution of mathematical probabilities. The ladder that Descartes, Galileo, Newton, and Leibniz erected in order to scale the heavens rests upon a continually shifting, unstable foundation.
Mathematics in Western Culture (1953), 382.
Science quotes on:  |  Become (815)  |  René Descartes (81)  |  Distribution (50)  |  Foundation (171)  |  Galileo Galilei (122)  |  Heaven (258)  |  Heavens (125)  |  Samuel Johnson (50)  |  Ladder (16)  |  Gottfried Wilhelm Leibniz (49)  |  Matter (798)  |  Sir Isaac Newton (333)  |  Order (632)  |  Reality (261)  |  Rest (280)  |  Scale (121)  |  Stone (162)

There are three leading objects in the study of truth:—one, to discover it; another, to demonstrate it when discovered; the last, to separate it from all admixture of falsehood.
As translated in Blaise Pascal and M.P. Faugère (trans.), 'On The Geometrical Spirit', collected in The Miscellaneous Writings of Pascal; Consisting of Letters, Essays, Conversations, and Miscellaneous Thoughts (1849), 73. 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'Esprit Géométrique', Pascal: Opuscules Philosophiques (1887), 82. For an alternative translation, see the quote beginning, “We may have three principal objects…” on the Blaise Pascal Quotes page of this website.
Science quotes on:  |  All (4108)  |  Discover (553)  |  Falsehood (28)  |  Last (426)  |  Leading (17)  |  Mixture (41)  |  Object (422)  |  Separate (143)  |  Study (653)  |  Truth (1057)

There is no art so difficult as the art of observation: it requires a skillful, sober spirit and a well-trained experience, which can only be acquired by practice; for he is not an observer who only sees the thing before him with his eyes, but he who sees of what parts the thing consists, and in what connexion the parts stand to the whole. One person overlooks half from inattention; another relates more than he sees while he confounds it with that which he figures to himself; another sees the parts of the whole, but he throws things together that ought to be separated. ... When the observer has ascertained the foundation of a phenomenon, and he is able to associate its conditions, he then proves while he endeavours to produce the phenomena at his will, the correctness of his observations by experiment. To make a series of experiments is often to decompose an opinion into its individual parts, and to prove it by a sensible phenomenon. The naturalist makes experiments in order to exhibit a phenomenon in all its different parts. When he is able to show of a series of phenomena, that they are all operations of the same cause, he arrives at a simple expression of their significance, which, in this case, is called a Law of Nature. We speak of a simple property as a Law of Nature when it serves for the explanation of one or more natural phenomena.
'The Study of the Natural Sciences: An Introductory Lecture to the Course of Experimental Chemistry in the University of Munich, for the Winter Session of 1852-53,' as translated and republished in The Medical Times and Gazette (22 Jan 1853), N.S. Vol. 6, 82.
Science quotes on:  |  Acquired (78)  |  All (4108)  |  Art (657)  |  Ascertain (38)  |  Associate (25)  |  Call (769)  |  Carelessness (6)  |  Cause (541)  |  Component (48)  |  Condition (356)  |  Confound (21)  |  Confuse (19)  |  Consist (223)  |  Correctness (12)  |  Decompose (9)  |  Different (577)  |  Difficult (246)  |  Difficulty (196)  |  Endeavour (63)  |  Experience (467)  |  Experiment (695)  |  Explanation (234)  |  Expression (175)  |  Eye (419)  |  Figure (160)  |  Foundation (171)  |  Himself (461)  |  Imagine (164)  |  Inattention (5)  |  Individual (404)  |  Law (894)  |  Law Of Nature (72)  |  More (2559)  |  Natural (796)  |  Naturalist (70)  |  Nature (1926)  |  Observation (555)  |  Observer (43)  |  Operation (213)  |  Operations (107)  |  Opinion (281)  |  Order (632)  |  Overlook (31)  |  Part (222)  |  Person (363)  |  Phenomenon (318)  |  Practice (204)  |  Produce (104)  |  Proof (287)  |  Property (168)  |  Prove (250)  |  Relationship (104)  |  Report (38)  |  Require (219)  |  Result (677)  |  See (1081)  |  Sensible (27)  |  Separate (143)  |  Series (149)  |  Show (346)  |  Significance (113)  |  Simple (406)  |  Skillful (14)  |  Sober (9)  |  Speak (232)  |  Spirit (265)  |  Stand (274)  |  Test (211)  |  Thing (1915)  |  Together (387)  |  Train (114)  |  Training (80)  |  Truth (1057)  |  Understanding (513)  |  Validity (47)  |  Verify (23)  |  Whole (738)  |  Will (2355)

These results demonstrate that there is a new polymerase inside the virions of RNA tumour viruses. It is not present in supernatents of normal cells but is present in virions of avian sarcoma and leukemia RNA tumour viruses. The polymerase seems to catalyse the incorporation of deoxyrinonucleotide triphosphates into DNA from an RNA template. Work is being performed to characterize further the reaction and the product. If the present results and Baltimore's results with Rauscher leukemia virus are upheld, they will constitute strong evidence that the DNA proviruses have a DNA genome when they are in virions. This result would have strong implications for theories of viral carcinogenesis and, possibly, for theories of information transfer in other biological systems. [Co-author with American virologist Satoshi Mizutani]
'RNA-dependent DNA Polymerase in Virions of Rous Sarcoma Virus', Nature (1970), 226, 1213.
Science quotes on:  |   (2863)  |  Author (167)  |  David Baltimore (2)  |  Being (1278)  |  Biological (137)  |  Carcinogenesis (2)  |  Catalysis (7)  |  Cell (138)  |  Characterization (8)  |  Constitute (97)  |  Demonstration (113)  |  DNA (77)  |  Evidence (248)  |  Genome (15)  |  Implication (23)  |  Incorporation (4)  |  Information (166)  |  Leukemia (4)  |  New (1216)  |  Normal (28)  |  Other (2236)  |  Perform (121)  |  Performance (48)  |  Possibly (111)  |  Present (619)  |  Product (160)  |  Reaction (104)  |  Result (677)  |  RNA (4)  |  Strong (174)  |  System (537)  |  Theory (970)  |  Transfer (20)  |  Tumour (2)  |  Virus (27)  |  Will (2355)  |  Work (1351)

This political movement has patently demonstrated that it will not defend the integrity of science in any case in which science runs afoul of its core political constituencies. In so doing, it has ceded any right to govern a technologically advanced and sophisticated nation.
…...
Science quotes on:  |  Advance (280)  |  Case (99)  |  Cede (2)  |  Constituency (2)  |  Core (18)  |  Defend (30)  |  Doing (280)  |  Govern (64)  |  Integrity (17)  |  Movement (155)  |  Nation (193)  |  Patently (4)  |  Political (121)  |  Right (452)  |  Run (174)  |  Science (3879)  |  Sophisticated (15)  |  Technologically (2)  |  Will (2355)

Those who consider James Watt only as a great practical mechanic form a very erroneous idea of his character: he was equally distinguished as a natural philosopher and a chemist, and his inventions demonstrate his profound knowledge of those sciences, and that peculiar characteristic of genius, the union of them for practical application.
As reported in Proceedings of the Public Meeting held at Preemasons' Hall, on the 18th June, 1824, for Erecting a Monument to the Late James Watt (1824), 8.
Science quotes on:  |  Application (242)  |  Character (243)  |  Characteristic (148)  |  Chemist (156)  |  Consider (416)  |  Considered (12)  |  Demonstration (113)  |  Distinguish (160)  |  Distinguished (83)  |  Equal (83)  |  Equally (130)  |  Erroneous (30)  |  Error (321)  |  Form (959)  |  Genius (284)  |  Great (1574)  |  Idea (843)  |  Invention (369)  |  James (3)  |  Knowledge (1529)  |  Mechanic (119)  |  Natural (796)  |  Natural Philosopher (4)  |  Peculiar (113)  |  Philosopher (258)  |  Practical (200)  |  Profound (104)  |  Science (3879)  |  Union (51)  |  James Watt (11)

Those who knew that the judgements of many centuries had reinforced the opinion that the Earth is placed motionless in the middle of heaven, as though at its centre, if I on the contrary asserted that the Earth moves, I hesitated for a long time whether to bring my treatise, written to demonstrate its motion, into the light of day, or whether it would not be better to follow the example of the Pythagoreans and certain others, who used to pass on the mysteries of their philosophy merely to their relatives and friends, not in writing but by personal contact, as the letter of Lysis to Hipparchus bears witness. And indeed they seem to me to have done so, not as some think from a certain jealousy of communicating their doctrines, but so that their greatest splendours, discovered by the devoted research of great men, should not be exposed to the contempt of those who either find it irksome to waste effort on anything learned, unless it is profitable, or if they are stirred by the exhortations and examples of others to a high-minded enthusiasm for philosophy, are nevertheless so dull-witted that among philosophers they are like drones among bees.
'To His Holiness Pope Paul III', in Copernicus: On the Revolutions of the Heavenly Spheres (1543), trans. A. M. Duncan (1976), 24.
Science quotes on:  |  Assert (66)  |  Bear (159)  |  Bee (40)  |  Better (486)  |  Certain (550)  |  Contact (65)  |  Contempt (20)  |  Contrary (141)  |  Devoted (59)  |  Discover (553)  |  Drone (4)  |  Dull (54)  |  Earth (996)  |  Effort (227)  |  Enthusiasm (52)  |  Exposed (33)  |  Find (998)  |  Follow (378)  |  Friend (168)  |  Great (1574)  |  Greatest (328)  |  Heaven (258)  |  High (362)  |  Hipparchus (3)  |  Indeed (324)  |  Jealousy (9)  |  Learn (629)  |  Learned (235)  |  Letter (109)  |  Light (607)  |  Long (790)  |  Lysis (4)  |  Merely (316)  |  Mind (1338)  |  Motion (310)  |  Move (216)  |  Nevertheless (90)  |  Opinion (281)  |  Other (2236)  |  Pass (238)  |  Philosopher (258)  |  Philosophy (380)  |  Profitable (28)  |  Pythagoras (38)  |  Research (664)  |  Splendour (8)  |  Theory (970)  |  Think (1086)  |  Time (1877)  |  Treatise (44)  |  Waste (101)  |  Witness (54)  |  Writing (189)

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the logic piano imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.
From 'Les Mathématiques et la Logique', Science et Méthode (1908, 1920), Livre 2, Chap. 3, Sec. 2, 157. English as in Henri Poincaré and George Bruce Halsted (trans.), 'Mathematics and Logic', Science and Method collected in The Foundations of Science: Science and Hypothesis, The Value of Science, Science and Method (1913), 451. From the French, “Ainsi, c’est bien entendu, pour démontrer un théorème, il n’est pas nécessaire ni même utile de savoir ce qu’il veut dire. On pourrait remplacer le géomètre par le piano à raisonner imaginé par Stanley Jevons; ou, si l’on aime mieux, on pourrait imaginer une machine où l’on introduirait les axiomes par un bout pendant qu’on recueillerait les théorèmes à l’autre bout, comme cette machine légendaire de Chicago où les porcs entrent vivants et d’où ils sortent transformés en jambons et en saucisses. Pas plus que ces machines, le mathématicien n’a besoin de comprendre ce qu’il fait”.
Science quotes on:  |  Advantageous (10)  |  Alive (90)  |  Assumption (92)  |  Choose (112)  |  End (590)  |  Geometer (24)  |  Ham (2)  |  Imagine (164)  |  Know (1518)  |  Logic (287)  |  Machine (257)  |  Mathematician (387)  |  Mean (809)  |  Meaning (233)  |  Means (579)  |  More (2559)  |  Necessary (363)  |  Need (290)  |  Other (2236)  |  Piano (12)  |  Pig (8)  |  Prove (250)  |  Replace (31)  |  Sausage (2)  |  Theorem (112)  |  Transform (73)  |  Understand (606)  |  Understood (156)

To demonstrate experimentally that a microscopic organism actually is the cause of a disease and the agent of contagion, I know no other way, in the present state of Science, than to subject the microbe (the new and happy term introduced by M. Sédillot) to the method of cultivation out of the body.
Paper read to the French Academy of Sciences (29 Apr 1878), published in Comptes Rendus de l'Academie des Sciences, 86, 1037-43, as translated by H.C.Ernst. Collected in Charles W. Eliot (ed.) The Harvard Classics, Vol. 38; Scientific Papers: Physiology, Medicine, Surgery, Geology (1910), 364.
Science quotes on:  |  Agent (70)  |  Body (537)  |  Cause (541)  |  Contagion (9)  |  Cultivation (35)  |  Demonstration (113)  |  Disease (328)  |  Experiment (695)  |  Happy (105)  |  Introduce (63)  |  Know (1518)  |  Knowledge (1529)  |  Method (505)  |  Microbe (28)  |  Microscopic (26)  |  New (1216)  |  Nomenclature (146)  |  Organism (220)  |  Other (2236)  |  Present (619)  |  Science (3879)  |  State (491)  |  Subject (521)  |  Term (349)  |  Way (1217)

We are accustomed to say that every human being displays both male and female instinctual impulses, needs, and attributes, but the characteristics of what is male and female can only be demonstrated in anatomy, and not in psychology.
In Sigmund Freud and Joan Riviere (trans.), Civilization and Its Discontents (1930, 1994), 35.
Science quotes on:  |  Accustom (52)  |  Accustomed (46)  |  Anatomy (69)  |  Attribute (61)  |  Being (1278)  |  Both (493)  |  Characteristic (148)  |  Display (56)  |  Female (50)  |  Human (1468)  |  Human Being (175)  |  Impulse (48)  |  Instinct (88)  |  Male (26)  |  Need (290)  |  Psychology (154)  |  Say (984)

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:  |  Discover (553)  |  Discriminate (4)  |  Examine (78)  |  False (100)  |  Object (422)  |  Possess (156)  |  Principal (63)  |  Seek (213)  |  Study (653)  |  Truth (1057)

When you try to explain the behavior of water, remember to demonstrate the experiment first and the cause next.
As quoted in George H. de Thierry, Journal of the Boston Society of Civil Engineers (Jan 1928), 15, No. 1, 2.
Science quotes on:  |  Behavior (84)  |  Cause (541)  |  Experiment (695)  |  Explain (322)  |  First (1283)  |  Hydraulics (2)  |  Next (236)  |  Remember (179)  |  Try (283)  |  Water (481)

Whenever … a controversy arises in mathematics, the issue is not whether a thing is true or not, but whether the proof might not be conducted more simply in some other way, or whether the proposition demonstrated is sufficiently important for the advancement of the science as to deserve especial enunciation and emphasis, or finally, whether the proposition is not a special case of some other and more general truth which is as easily discovered.
In Mathematical Essays and Recreations (1898), 88.
Science quotes on:  |  Advancement (62)  |  Arise (158)  |  Conduct (69)  |  Controversy (29)  |  Deserve (65)  |  Discover (553)  |  Ease (35)  |  Emphasis (17)  |  Enunciation (7)  |  General (511)  |  Important (209)  |  Issue (42)  |  Mathematics (1328)  |  More (2559)  |  Nature Of Mathematics (80)  |  Other (2236)  |  Proof (287)  |  Proposition (123)  |  Science (3879)  |  Simplicity (167)  |  Special (184)  |  Special Case (9)  |  Thing (1915)  |  True (212)  |  Truth (1057)  |  Way (1217)  |  Whenever (81)

Who, by vigor of mind almost divine, the motions and figures of the planets, the paths of comets, and the tides of the seas, his mathematics first demonstrated.
English translation of the epitaph inscribed in Latin on the monument beside his grave in Westminster Abbey. Seen, for example as epigraph, without citation, in Morris Kline, Mathematical Thought from Ancient to Modern Times (1972), 342. The original Latin is, “Qui, animi vi prope divinâ, Planetarum Motus, Figuras, Cometarum semitas, Oceanique Aestus, Suâ Mathesi facem praeferente Primus demonstravit:” as given in Le journal des sçavans, pour l'année MDCCXXXI (Jul 1731), 438. The words “his mathematics” are missing from most quotes of this epitaph, but have been added by Webmaster for the Latin words “Suâ Mathesi” which are present in the verbatim epitaph.
Science quotes on:  |  Comet (54)  |  Divine (112)  |  Figure (160)  |  First (1283)  |  Mathematics (1328)  |  Mind (1338)  |  Motion (310)  |  Path (144)  |  Planet (356)  |  Sea (308)  |  Tide (34)  |  Vigor (9)

Whoever … proves his point and demonstrates the prime truth geometrically should be believed by all the world, for there we are captured.
In J. Heidrich (ed.), 'Von Menschlicher Proportion', Albrecht Dürer’s Schriftlicher Nachlass (1920), 270. From the original German: “Welcher aber … durch die Geometria sein Ding beweist und die gründliche Wahrheit anzeigt, dem soll alle Welt glauben. Denn da ist man gefangen.”
Science quotes on:  |  All (4108)  |  Belief (578)  |  Capture (10)  |  Geometry (255)  |  Point (580)  |  Prime (11)  |  Prove (250)  |  Truth (1057)  |  Whoever (42)  |  World (1774)

Without preparing fluorine, without being able to separate it from the substances with which it is united, chemistry has been able to study and to analyze a great number of its compounds. The body was not isolated, and yet its place was marked in our classifications. This well demonstrates the usefulness of a scientific theory, a theory which is regarded as true during a certain time, which correlates facts and leads the mind to new hypotheses, the first causes of experimentation; which, little by little, destroy the theory itself, in order to replace it by another more in harmony with the progress of science.
[Describing the known history of fluorine compounds before his isolation of the element.]
'Fluorine', lecture at the Royal Institution (28 May 1897), translated from the French, in Proceedings of the Royal Institution (1897). In Annual Report of the Board of Regents of the Smithsonian Institution to July 1897 (1898), 262.
Science quotes on:  |  Being (1278)  |  Body (537)  |  Cause (541)  |  Certain (550)  |  Chemistry (353)  |  Classification (97)  |  Compound (113)  |  Correlation (18)  |  Destroy (180)  |  Destruction (125)  |  Element (310)  |  Experiment (695)  |  Fact (1210)  |  Facts (553)  |  First (1283)  |  Fluorine (5)  |  Great (1574)  |  Harmony (102)  |  History (673)  |  Hypothesis (296)  |  Isolation (31)  |  Known (454)  |  Lead (384)  |  Little (707)  |  Marked (55)  |  Mind (1338)  |  More (2559)  |  New (1216)  |  Number (699)  |  Order (632)  |  Periodic Table (17)  |  Preparing (21)  |  Progress (465)  |  Progress Of Science (34)  |  Regard (305)  |  Replacement (12)  |  Science (3879)  |  Scientific (941)  |  Scientific Method (175)  |  Scientific Theory (24)  |  Separate (143)  |  Separation (57)  |  Study (653)  |  Substance (248)  |  Theory (970)  |  Time (1877)  |  Truth (1057)  |  Usefulness (86)

You know the formula m over naught equals infinity, m being any positive number? [m/0 = ∞]. Well, why not reduce the equation to a simpler form by multiplying both sides by naught? In which case you have m equals infinity times naught [m = ∞ × 0]. That is to say, a positive number is the product of zero and infinity. Doesn't that demonstrate the creation of the Universe by an infinite power out of nothing? Doesn't it?
In Point Counter Point (1928), 162.
Science quotes on:  |  Being (1278)  |  Both (493)  |  Creation (327)  |  Equal (83)  |  Equation (132)  |  Form (959)  |  Formula (98)  |  Infinite (231)  |  Infinity (90)  |  Know (1518)  |  Multiply (37)  |  Naught (10)  |  Nothing (966)  |  Number (699)  |  Positive (94)  |  Power (746)  |  Product (160)  |  Reduce (94)  |  Say (984)  |  Side (233)  |  Simplify (13)  |  Time (1877)  |  Universe (857)  |  Why (491)  |  Zero (37)

[1158] There is no certainty in sciences where one of the mathematical sciences cannot be applied, or which are not in relation with these mathematics.
Notebook G (c.1515), sheet 95 back. In the original Italian: “Nessuna certezza delle sciētie è, dove no si può applicare vna delle sciētie matematiche e che non son vnight con esse matematiche.” English and Italian in Jean Paul Richter (trans.), 'Philosophical Maxims: Of Mechanics', The Literary Works of Leonardo da Vinci (1883), Vol. 1, Part 2, 289, Aphorism 1158. [Note: da Vinci wrote ē=en; v=u] The following, found on the web, without citation, seems to be a paraphrase: “No human investigation can be called real science if it cannot be demonstrated mathematically.”
Science quotes on:  |  Applied (177)  |  Call (769)  |  Certainty (174)  |  Human (1468)  |  Investigation (230)  |  Mathematics (1328)  |  Real (149)  |  Science (3879)

[There was] in some of the intellectual leaders a great aspiration to demonstrate that the universe ran like a piece of clock-work, but this was was itself initially a religious aspiration. It was felt that there would be something defective in Creation itself—something not quite worthy of God—unless the whole system of the universe could be shown to be interlocking, so that it carried the pattern of reasonableness and orderliness. Kepler, inaugurating the scientist’s quest for a mechanistic universe in the seventeenth century, is significant here—his mysticism, his music of the spheres, his rational deity demand a system which has the beauty of a piece of mathematics.
In The Origins of Modern Science (1950), 105.
Science quotes on:  |   (2863)  |  17th Century (16)  |  Aspiration (32)  |  Beauty (299)  |  Century (310)  |  Clock (47)  |  Clockwork (7)  |  Creation (327)  |  Defective (4)  |  Deity (22)  |  Demand (123)  |  God (757)  |  Great (1574)  |  Intellectual (255)  |  Johannes Kepler (91)  |  Leader (43)  |  Mathematics (1328)  |  Music (129)  |  Music Of The Spheres (3)  |  Mysticism (14)  |  Orderliness (9)  |  Orderly (38)  |  Pattern (110)  |  Quest (39)  |  Rational (90)  |  Reasonable (27)  |  Reasonableness (6)  |  Religious (126)  |  Scientist (820)  |  Significant (74)  |  Something (719)  |  Sphere (116)  |  System (537)  |  Universe (857)  |  Whole (738)  |  Work (1351)

~~[Dubious]~~ I demonstrate by means of philosophy that the earth is round, and is inhabited on all sides; that it is insignificantly small, and is borne through the stars.
Included here to add a caution. As quoted in Paul Lyle, The Abyss of Time: A Study in Geological Time and Earth History (2015), 38, citing Astronomia Nova (1609). Webmaster has not yet been able to find in a primary source, so cannot vouch for this quote. Can you help?
Science quotes on:  |  All (4108)  |  Bear (159)  |  Earth (996)  |  Inhabit (16)  |  Mean (809)  |  Means (579)  |  Philosophy (380)  |  Round (26)  |  Side (233)  |  Small (477)  |  Star (427)  |  Stars (304)  |  Through (849)

…from the same principles, I now demonstrate the frame of the System of the World.
From Principia Mathematica, Book 3, as translated from the Latin by ‎Andrew Motte, revised by ‎William Davis, in The Mathematical Principles of Natural Philosophy (1803), Vol. 2, 159.
Science quotes on:  |  Frame (26)  |  Principle (507)  |  Same (157)  |  System (537)  |  World (1774)


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.