20th-century Mathematician Quotes

I think we need more math majors who don't become mathematicians. More math major doctors, more math major high school teachers, more math major CEOs, more math major senators. But we won't get there unless we dump the stereotype that math is only worthwhile for kid geniuses.

It seems to me highly improper to introduce God to solve our scientific problems.

The dictum that everything that people do is "cultural" licenses the idea that every cultural critic can meaningfully analyze even the most intricate accomplishments of art and science... It is distinctly weird to listen to pronouncements on the nature of mathematics from the lips of someone who cannot tell you what a complex number is!

I disagree with Adler, who wrote (in the New Yorker) that there is no point in being a mathematician unless you can be a great mathematician. That's nonsense. Mathematics is like a Gothic cathedral. If you can build a little part of it, it is there - forever - in some sense. At least I have the illusion that it is so.

Consider the Pitiful Plight Of a runner who wasn't too bright, But sprinted so fast He vanished at last By red-shifting himself out of sight.

It is all too easy to notice the statistical sea that supports our thoughts and actions. If that sea loses its buoyancy, it may take a long time to regain the lost support.

Mathematics, springing from the soil of basic human experience with numbers and data and space and motion, builds up a far-flung architectural structure composed of theorems which reveal insights into the reasons behind appearances and of concepts which relate totally disparate concrete ideas.

Saunders Mac Lane
Saunders Mac Lane
Mathematics is a human activity almost as diverse as the human mind itself.

A new idea may be likened to a new-born babe: it is to be carefully nurtured and given every consideration rather than attacked with the choking diet of a multitude of so-called facts because it cannot prove at once that it will one day grow into a Samson.

Proofs really aren't there to convince you that something is true — they're there to show why it is true.

[It has been] said that the zeros [of the Riemann zeta function] weren't real, nobody measured them. They are as real as anything you will measure in a laboratory — this has to be the way we look at the world.

Peter Sarnak
Peter Sarnak
Mathematics is the science of order and mathematicians seek to identify instances of order and to formulate and understand concepts that enable us to perceive order in complicated situations.

I think that I have always had a basic liking for the natural numbers. To me they are the one real thing. We can conceive of a chemistry that is different from ours, or a biology, but we cannot conceive of a different mathematics of numbers. What is proved about numbers will be a fact in any universe.

Good mathematicians see analogies between theorems or theories, the very best ones see analogies between analogies.

I do not hesitate to assert that I consider astronomy as the most important force in the development of science since its origin sometime around 500 B.C...

The notion that the intellect can create meaningful postulational systems at its whim is a deceptive half-truth. Only under the discipline of responsibility to the organic whole, only guided by intrinsic necessity, can the free mind achieve results of scientific value.

Herbert Robbins
Herbert Robbins
It is a well-known experience that the only truly enjoyable and profitable way of studying mathematics is the method of "filling in details" by one's own efforts.

Cornelius Lanczos
Cornelius Lanczos
Mathematics is the Queen of Science but she isn't very Pure; she keeps having babies by handsome young upstarts and various frog princes.

Equations are the lifeblood of applied mathematics and science.

A mathematician experiments, amasses information, makes a conjecture, finds out that it does not work, gets confused and then tries to recover. A good mathematician eventually does so — and proves a theorem.

Steven G. Krantz
Steven G. Krantz
Beauty is very integrated with rarity.... Beauty is connected so much with innovation and priority.... [In mathematics], it has to be something special to make it beautiful. If it's just ordinary, it's not beautiful.

To me, that the distribution of prime numbers can be so accurately represented in a harmonic analysis is absolutely amazing and incredibly beautiful. It tells of an arcane music and a secret harmony composed by the prime numbers.

Enrico Bombieri
Enrico Bombieri
Reading a paper is a voluntary and demanding task, and a reader needs to be enticed and helped and stimulated by the author.

George Batchelor
George Batchelor
Proof, being the highest level of reproduction activity, has an important interiorization aspect: as Yuri Manin stresses in his book Provable and Unprovable, a proof becomes such only after it is accepted (as the result of a highly rigorous process)... Manin describes the act of acceptance as a social act; however, the importance of its personal, psychological component can hardly be overestimated.

Our brains are just not wired to do probability problems very well.

Persi Diaconis
Persi Diaconis