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

Today in Science History - Quickie Quiz
Who said: “The path towards sustainable energy sources will be long and sometimes difficult. But America cannot resist this transition, we must lead it... That is how we will preserve our planet, commanded to our care by God. That’s what will lend meaning to the creed our fathers once declared.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index S > Category: Set Theory

Set Theory Quotes (5 quotes)

No one shall expel us from the paradise which Cantor has created for us.
Expressing the importance of Cantor's set theory in the development of mathematics.
In George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 33.
Science quotes on:  |  Georg Cantor (6)  |  Creation (239)  |  Mathematics (1149)  |  Paradise (9)

Since the examination of consistency is a task that cannot be avoided, it appears necessary to axiomatize logic itself and to prove that number theory and set theory are only parts of logic. This method was prepared long ago (not least by Frege’s profound investigations); it has been most successfully explained by the acute mathematician and logician Russell. One could regard the completion of this magnificent Russellian enterprise of the axiomatization of logic as the crowning achievement of the work of axiomatization as a whole.
Address (11 Sep 1917), 'Axiomatisches Denken' delivered before the Swiss Mathematical Society in Zόrich. Translated by Ewald as 'Axiomatic Thought', (1918), in William Bragg Ewald, From Kant to Hilbert (1996), Vol. 2, 1113.
Science quotes on:  |  Achievement (150)  |  Acute (7)  |  Appear (115)  |  Avoid (52)  |  Axiom (52)  |  Completion (17)  |  Consistency (23)  |  Crown (26)  |  Enterprise (32)  |  Examination (65)  |  Explain (105)  |  Gottlob Frege (11)  |  Investigation (175)  |  Least (74)  |  Logic (247)  |  Long Ago (10)  |  Magnificent (19)  |  Mathematician (364)  |  Method (230)  |  Necessary (147)  |  Number Theory (6)  |  Prepared (5)  |  Profound (58)  |  Prove (108)  |  Regard (93)  |  Bertrand Russell (183)  |  Successful (39)  |  Task (83)  |  Whole (189)  |  Work (626)

To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.
In Axiomatic Set Theory (1971), 9-15. In Thomas Tymoczko, New Directions in the Philosophy of Mathematics: an Anthology (), 11-12.
Science quotes on:  |  Appeal (45)  |  Average (41)  |  Choice (79)  |  Consistency (23)  |  Difficulty (144)  |  Enjoyment (29)  |  Formal (29)  |  Formalism (6)  |  Game (61)  |  David Hilbert (46)  |  Mathematician (364)  |  Security (33)  |  Shelter (14)  |  Work (626)

[Cantor’s set theory:] The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.
As quoted in Constance Reid, Hilbert (1970), 176.
Science quotes on:  |  Achievement (150)  |  Activity (128)  |  Fine (33)  |  Genius (243)  |  Human (548)  |  Intellectual (120)  |  Mathematics (1149)  |  Product (82)  |  Purely (28)  |  Supreme (37)

~~[No known source]~~ Later generations will regard Mengenlehre [set theory] as a disease from which one has recovered.
Webmaster finds zero support for the authenticity of this quote. Speculations on how it may have evolved include reference to a beau cas pathologique (a beautiful pathological case) in a very different quote which begins “I think, and I am not the only one…”. (See the Henri Poincarι Quotes web page of this site.) More details readily available with a Google search (for example): Did Poincarι say “set theory is a disease”. The quote is included here to provide this caution.
Science quotes on:  |  Disease (275)  |  Generation (137)  |  Later (17)  |  Recover (11)  |  Regard (93)


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.