- "Mathematics consists of proving the most obvious thing in the least obvious way." --George Polye
- "Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state."
- "Mathematics is not yet capable of coping with the naïveté of the mathematician himself." --Abraham Kaplan
- Mathematics is the only instructional material that can be presented in an entirely undogmatic way.
- "Mathematics is the science of what is clear by itself.
- Mathematics seems to endow one with something like a new sense.
- Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.
- Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
- Bertrand Russell, referring to the axiomatic method, where certain properties of an (otherwise unknown) structure are assumed and consequences thereof are then logically derived.
- "Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere."
- W.S. Anglin, in Mathematics and History, elucidating the symmetry between the creative and logical aspects of mathematics.
- 數學證明如鑽石，既堅硬亦清楚，and will be touched with nothing but strict reasoning.
- I have no faith in political arithmetic.
- "The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and not being.
- "The infinite! No other question has ever moved so profoundly the spirit of man."
- The knowledge of which geometry aims is the knowledge of the eternal.
- The laws of probability, so true in general, so fallacious in particular.
- Edward Gibbon
- I don't believe in Mathematics.
- Do not worry about your problems with mathematics, I assure you mine are far greater.
- Life is only good for doing two things, discovering mathematics and teaching mathematics.
- "Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry."
- Bertrand Russell, in Study of Mathematics, about the beauty of Mathematics.
- If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.
- Alfréd Rényi
- Das Wesen der Mathematik ist ihre Freiheit.
- Although I am not stupid, the mathematical side of my brain is like dumb notes upon a damaged piano.
- Margot Asquith
- He integrates empirically.
- 神不顧我們在數學上遇到的困難。He integrates empirically.
- "From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician." --Sir James Jeans
- "He who can properly define and divide is to be considered a god." --柏拉图
- Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe and not make messes in the house.
- Lazarus Long, "Time Enough for Love", (Robert A. Heinlein)
- "Obvious" is the most dangerous word in mathematics.
- "The art of doing mathematics consists in finding that special case which contains all the germs of generality."
- "No human investigation can be called real science if it cannot be demonstrated mathematically." --Leonardo da Vinci
- "Sex is the mathematics urge sublimated." --M. C. Reed
- "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." --Albert Einstein
- "How dare we speak of the laws of chance? Is not chance the antithesis of all law?" --Bertrand Russell
- "Measure what is measurable, and make measurable what is not so." --Galileo Galilei
- "Medicine makes people ill, mathematics make them sad and theology makes them sinful." --Martin Luther
- "Now I feel as if I should succeed in doing something in mathematics, although I cannot see why it is so very important... The knowledge doesn't make life any sweeter or happier, does it?" --Helen Keller
- "Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore."
- "The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience."
- "The simplest schoolboy is now familiar with facts for which Archimedes would have sacrificed his life." --Ernest Renan
- "There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.
- "I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate." --David Mumford
- There are no creeds in mathematics.