TODAY IN SCIENCE HISTORY ®  •  TODAYINSCI ®
Celebrating 24 Years on the Web
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index P > Category: Preeminence

Preeminence Quotes (3 quotes)

It has been asserted … that the power of observation is not developed by mathematical studies; while the truth is, that; from the most elementary mathematical notion that arises in the mind of a child to the farthest verge to which mathematical investigation has been pushed and applied, this power is in constant exercise. By observation, as here used, can only be meant the fixing of the attention upon objects (physical or mental) so as to note distinctive peculiarities—to recognize resemblances, differences, and other relations. Now the first mental act of the child recognizing the distinction between one and more than one, between one and two, two and three, etc., is exactly this. So, again, the first geometrical notions are as pure an exercise of this power as can be given. To know a straight line, to distinguish it from a curve; to recognize a triangle and distinguish the several forms—what are these, and all perception of form, but a series of observations? Nor is it alone in securing these fundamental conceptions of number and form that observation plays so important a part. The very genius of the common geometry as a method of reasoning—a system of investigation—is, that it is but a series of observations. The figure being before the eye in actual representation, or before the mind in conception, is so closely scrutinized, that all its distinctive features are perceived; auxiliary lines are drawn (the imagination leading in this), and a new series of inspections is made; and thus, by means of direct, simple observations, the investigation proceeds. So characteristic of common geometry is this method of investigation, that Comte, perhaps the ablest of all writers upon the philosophy of mathematics, is disposed to class geometry, as to its method, with the natural sciences, being based upon observation. Moreover, when we consider applied mathematics, we need only to notice that the exercise of this faculty is so essential, that the basis of all such reasoning, the very material with which we build, have received the name observations. Thus we might proceed to consider the whole range of the human faculties, and find for the most of them ample scope for exercise in mathematical studies. Certainly, the memory will not be found to be neglected. The very first steps in number—counting, the multiplication table, etc., make heavy demands on this power; while the higher branches require the memorizing of formulas which are simply appalling to the uninitiated. So the imagination, the creative faculty of the mind, has constant exercise in all original mathematical investigations, from the solution of the simplest problems to the discovery of the most recondite principle; for it is not by sure, consecutive steps, as many suppose, that we advance from the known to the unknown. The imagination, not the logical faculty, leads in this advance. In fact, practical observation is often in advance of logical exposition. Thus, in the discovery of truth, the imagination habitually presents hypotheses, and observation supplies facts, which it may require ages for the tardy reason to connect logically with the known. Of this truth, mathematics, as well as all other sciences, affords abundant illustrations. So remarkably true is this, that today it is seriously questioned by the majority of thinkers, whether the sublimest branch of mathematics,—the infinitesimal calculus—has anything more than an empirical foundation, mathematicians themselves not being agreed as to its logical basis. That the imagination, and not the logical faculty, leads in all original investigation, no one who has ever succeeded in producing an original demonstration of one of the simpler propositions of geometry, can have any doubt. Nor are induction, analogy, the scrutinization of premises or the search for them, or the balancing of probabilities, spheres of mental operations foreign to mathematics. No one, indeed, can claim preeminence for mathematical studies in all these departments of intellectual culture, but it may, perhaps, be claimed that scarcely any department of science affords discipline to so great a number of faculties, and that none presents so complete a gradation in the exercise of these faculties, from the first principles of the science to the farthest extent of its applications, as mathematics.
In 'Mathematics', in Henry Kiddle and Alexander J. Schem, The Cyclopedia of Education, (1877.) As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 27-29.
Science quotes on:  |  Abundant (23)  |  Act (278)  |  Actual (118)  |  Advance (298)  |  Age (509)  |  Alone (324)  |  Analogy (76)  |  Appalling (10)  |  Application (257)  |  Applied (176)  |  Applied Mathematics (15)  |  Arise (162)  |  Assert (69)  |  Attention (196)  |  Auxiliary (11)  |  Basis (180)  |  Being (1276)  |  Branch (155)  |  Build (211)  |  Calculus (65)  |  Certainly (185)  |  Characteristic (154)  |  Child (333)  |  Claim (154)  |  Class (168)  |  Common (447)  |  Complete (209)  |  Auguste Comte (24)  |  Conception (160)  |  Connect (126)  |  Consider (428)  |  Constant (148)  |  Count (107)  |  Counting (26)  |  Creative (144)  |  Culture (157)  |  Curve (49)  |  Demand (131)  |  Demonstration (120)  |  Department (93)  |  Develop (278)  |  Difference (355)  |  Direct (228)  |  Discipline (85)  |  Discovery (837)  |  Distinction (72)  |  Distinctive (25)  |  Distinguish (168)  |  Doubt (314)  |  Elementary (98)  |  Empirical (58)  |  Essential (210)  |  Exercise (113)  |  Extent (142)  |  Eye (440)  |  Fact (1257)  |  Facts (553)  |  Figure (162)  |  Find (1014)  |  First (1302)  |  Foreign (45)  |  Form (976)  |  Formula (102)  |  Foundation (177)  |  Fundamental (264)  |  Genius (301)  |  Geometry (271)  |  Gradation (17)  |  Great (1610)  |  Human (1512)  |  Hypothesis (314)  |  Illustration (51)  |  Imagination (349)  |  Indeed (323)  |  Induction (81)  |  Infinitesimal (30)  |  Infinitesimal Calculus (2)  |  Inspection (7)  |  Intellectual (258)  |  Investigation (250)  |  Know (1538)  |  Known (453)  |  Lead (391)  |  Logic (311)  |  Majority (68)  |  Material (366)  |  Mathematics (1395)  |  Mean (810)  |  Means (587)  |  Memorize (4)  |  Memory (144)  |  Mental (179)  |  Method (531)  |  Mind (1377)  |  More (2558)  |  Most (1728)  |  Multiplication (46)  |  Multiplication Table (16)  |  Name (359)  |  Natural (810)  |  Natural Science (133)  |  Nature Of Mathematics (80)  |  Neglect (63)  |  Neglected (23)  |  New (1273)  |  Notice (81)  |  Notion (120)  |  Number (710)  |  Object (438)  |  Observation (593)  |  Operation (221)  |  Operations (107)  |  Other (2233)  |  Perception (97)  |  Philosophy (409)  |  Physical (518)  |  Power (771)  |  Practical (225)  |  Premise (40)  |  Present (630)  |  Principle (530)  |  Problem (731)  |  Proceed (134)  |  Proposition (126)  |  Pure (299)  |  Push (66)  |  Question (649)  |  Range (104)  |  Reason (766)  |  Reasoning (212)  |  Recognize (136)  |  Recondite (8)  |  Representation (55)  |  Require (229)  |  Resemblance (39)  |  Scarcely (75)  |  Scope (44)  |  Scrutinize (7)  |  Search (175)  |  Series (153)  |  Simple (426)  |  Solution (282)  |  Sphere (118)  |  Step (234)  |  Straight (75)  |  Straight Line (34)  |  Succeed (114)  |  Suppose (158)  |  System (545)  |  Table (105)  |  Themselves (433)  |  Thinker (41)  |  Today (321)  |  Triangle (20)  |  Truth (1109)  |  Two (936)  |  Unknown (195)  |  Verge (10)  |  Whole (756)  |  Will (2350)  |  Writer (90)

Mathematics, including not merely Arithmetic, Algebra, Geometry, and the higher Calculus, but also the applied Mathematics of Natural Philosophy, has a marked and peculiar method or character; it is by preeminence deductive or demonstrative, and exhibits in a nearly perfect form all the machinery belonging to this mode of obtaining truth. Laying down a very small number of first principles, either self-evident or requiring very little effort to prove them, it evolves a vast number of deductive truths and applications, by a procedure in the highest degree mathematical and systematic.
In Education as a Science (1879), 148.
Science quotes on:  |  Algebra (117)  |  Application (257)  |  Applied (176)  |  Applied Mathematics (15)  |  Arithmetic (144)  |  Belonging (36)  |  Calculus (65)  |  Character (259)  |  Deduction (90)  |  Degree (277)  |  Demonstration (120)  |  Demonstrative (14)  |  Down (455)  |  Effort (243)  |  Evident (92)  |  First (1302)  |  Form (976)  |  Geometry (271)  |  Little (717)  |  Machinery (59)  |  Marked (55)  |  Mathematics (1395)  |  Merely (315)  |  Method (531)  |  Natural (810)  |  Natural Philosophy (52)  |  Nearly (137)  |  Number (710)  |  Peculiar (115)  |  Perfect (223)  |  Philosophy (409)  |  Principle (530)  |  Procedure (48)  |  Prove (261)  |  Self (268)  |  Self-Evident (22)  |  Small (489)  |  Systematic (58)  |  Truth (1109)  |  Vast (188)

We set sail on this new sea because there is new knowledge to be gained, and new rights to be won, and they must be won and used for the progress of all people. For space science, like nuclear science and technology, has no conscience of its own. Whether it will become a force for good or ill depends on man, and only if the United States occupies a position of preeminence can we help decide whether this new ocean will be a sea of peace or a new terrifying theater of war.
Address at Rice University in Houston (12 Sep 1962). On website of John F. Kennedy Presidential Library and Museum. [This go-to-the-moon speech was largely written by presidential advisor and speechwriter Ted Sorensen.]
Science quotes on:  |  Become (821)  |  Conscience (52)  |  Decision (98)  |  Depend (238)  |  Dependence (46)  |  Force (497)  |  Gain (146)  |  Good (906)  |  Help (116)  |  Ill (12)  |  Knowledge (1647)  |  Man (2252)  |  Must (1525)  |  New (1273)  |  Nuclear (110)  |  Nuclear Science (2)  |  Ocean (216)  |  Peace (116)  |  People (1031)  |  Position (83)  |  Progress (492)  |  Right (473)  |  Sail (37)  |  Sailing (14)  |  Science And Technology (46)  |  Sea (326)  |  Set (400)  |  Space (523)  |  State (505)  |  Technology (281)  |  United States (31)  |  Use (771)  |  War (233)  |  Will (2350)  |  Winning (19)


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 |
Thank you for sharing.
- 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


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