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

Today in Science History - Quickie Quiz
Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
more quiz questions >>
Home > Dictionary of Science Quotations > Scientist Names Index K > Felix Klein Quotes

Thumbnail of Felix Klein (source)
Felix Klein
(25 Apr 1849 - 22 Jun 1925)

German mathematician.


Science Quotes by Felix Klein (3 quotes)

Every teacher certainly should know something of non-euclidean geometry. Thus, it forms one of the few parts of mathematics which, at least in scattered catch-words, is talked about in wide circles, so that any teacher may be asked about it at any moment. ... Imagine a teacher of physics who is unable to say anything about Röntgen rays, or about radium. A teacher of mathematics who could give no answer to questions about non-euclidean geometry would not make a better impression.
On the other hand, I should like to advise emphatically against bringing non-euclidean into regular school instruction (i.e., beyond occasional suggestions, upon inquiry by interested pupils), as enthusiasts are always recommending. Let us be satisfied if the preceding advice is followed and if the pupils learn to really understand euclidean geometry. After all, it is in order for the teacher to know a little more than the average pupil.
— Felix Klein
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 72.
Science quotes on:  |  Advice (33)  |  Advise (2)  |  Answer (201)  |  Ask (99)  |  Average (31)  |  Better (131)  |  Beyond (65)  |  Bring (53)  |  Certainly (18)  |  Circle (28)  |  Emphatically (2)  |  Enthusiast (4)  |  Euclidean (2)  |  Follow (66)  |  Form (210)  |  Geometry (99)  |  Give (117)  |  Imagine (40)  |  Impression (51)  |  Inquiry (33)  |  Instruction (51)  |  Interest (170)  |  Know (321)  |  Learn (160)  |  Least (43)  |  Let (30)  |  Little (126)  |  Mathematics (587)  |  Moment (61)  |  Non-Euclidean (2)  |  Occasional (10)  |  On The Other Hand (16)  |  Order (167)  |  Part (146)  |  Physics (301)  |  Precede (11)  |  Pupil (16)  |  Question (315)  |  R (2)  |  Radium (19)  |  Ray (32)  |  Really (50)  |  Recommend (4)  |  Regular (8)  |  Satisfied (14)  |  Say (126)  |  Scatter (5)  |  School (87)  |  Suggestion (24)  |  Talk (61)  |  Teacher (90)  |  Unable (12)  |  Understand (189)  |  Wide (14)

The axioms of geometry are—according to my way of thinking—not arbitrary, but sensible. statements, which are, in general, induced by space perception and are determined as to their precise content by expediency.
— Felix Klein
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 142.
Science quotes on:  |  Accord (21)  |  Arbitrary (16)  |  Axiom (26)  |  Content (39)  |  Determine (45)  |  Expediency (4)  |  General (92)  |  Geometry (99)  |  Induce (6)  |  Perception (53)  |  Precise (17)  |  Sensible (22)  |  Space (154)  |  Statement (56)  |  Think (205)

The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.
— Felix Klein
Elementary Mathematics From an Advanced Standpoint (1908). 3rd edition (1924), trans. E. R. Hedrick and C. A. Noble (1932), Vol. 1, 155.
Science quotes on:  |  18th Century (17)  |  Algebra (36)  |  Analysis (123)  |  Calculus (23)  |  Difficulty (113)  |  Imperfection (19)  |  Infinitesimal (8)  |  Teacher (90)



Quotes by others about Felix Klein (2)

These estimates may well be enhanced by one from F. Klein (1849-1925), the leading German mathematician of the last quarter of the nineteenth century. “Mathematics in general is fundamentally the science of self-evident things.” ... If mathematics is indeed the science of self-evident things, mathematicians are a phenomenally stupid lot to waste the tons of good paper they do in proving the fact. Mathematics is abstract and it is hard, and any assertion that it is simple is true only in a severely technical sense—that of the modern postulational method which, as a matter of fact, was exploited by Euclid. The assumptions from which mathematics starts are simple; the rest is not.
Mathematics: Queen and Servant of Science (1952),19-20.
Science quotes on:  |  19th Century (22)  |  Euclid (28)  |  Mathematics (587)

Consciously and systematically Klein sought to enthrall me with the problems of mathematical physics, and to win me over to his conception of these problems as developed it in lecture courses in previous years. I have always regarded Klein as my real teacher only in things mathematical, but also in mathematical physics and in my conception of mechanics.
As quoted in Paul Forman and Armin Hermann, 'Sommerfeld, Arnold (Johannes Wilhelm)', Biography in Dictionary of Scientific Biography (1975), Vol. 12, 526. Cited from 'Autobiographische Skizze', Gesammelte Schriften, Vol 4, 673–682.
Science quotes on:  |  Autobiography (55)  |  Conception (63)  |  Conscious (25)  |  Course (57)  |  Develop (55)  |  Lecture (54)  |  Mathematical Physics (3)  |  Mechanics (44)  |  Problem (362)  |  Real (95)  |  Regard (58)  |  Systematic (25)  |  Teacher (90)  |  Win (25)


See also:
  • 25 Apr - short biography, births, deaths and events on date of Klein's birth.

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 Einstein • Isaac Newton • Lord Kelvin • Charles Darwin • Srinivasa Ramanujan • Carl Sagan • Florence Nightingale • Thomas Edison • Aristotle • Marie Curie • Benjamin Franklin • Winston Churchill • Galileo Galilei • Sigmund Freud • Robert Bunsen • Louis Pasteur • Theodore Roosevelt • Abraham Lincoln • Ronald Reagan • Leonardo DaVinci • Michio Kaku • Karl Popper • Johann Goethe • Robert Oppenheimer • Charles Kettering  ... (more people)

Quotations about: • Atomic  Bomb • Biology • Chemistry • Deforestation • Engineering • Anatomy • Astronomy • Bacteria • Biochemistry • Botany • Conservation • Dinosaur • Environment • Fractal • Genetics • Geology • History of Science • Invention • Jupiter • Knowledge • Love • Mathematics • Measurement • Medicine • Natural Resource • Organic Chemistry • Physics • Physician • Quantum Theory • Research • Science and Art • Teacher • Technology • Universe • Volcano • Virus • Wind Power • Women Scientists • X-Rays • Youth • Zoology  ... (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.