20th-century Mathematician Quotes

John von Neumann
Kurt Gödel
John Forbes Nash, Jr.
Claude Elwood Shannon
Benoît Mandelbrot
Eugene Wigner
Paul Erdős

Nature might be somehow more powerful than a digital computer.

Aviezri Fraenkel
Aviezri Fraenkel
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
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
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.

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
Equations are the lifeblood of applied mathematics and science.

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

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
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
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...

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

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.

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.

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

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.

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

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
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.

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.

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.

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!

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

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.

Every improvement or innovation begins with an idea. But an idea is only a possibility - a small beginning that must be nurtured, developed, engineer, tinkered with, championed, tested, implemented and checked ideas have no value until they are implemented.

John Alan Robinson
John Alan Robinson