20th-century Mathematician Quotes

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.

William Kruskal

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

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.

Raymond Lyttleton

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

Andrew M. Gleason

[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.

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.

Shlomo Sternberg

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...

Otto E. Neugebauer

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

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

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

Donald Kingsbury

Equations are the lifeblood of applied mathematics and science.

Thomas L. Saaty

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

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

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

Not only the laws of nature, but also the events occurring in nature, the world itself, must appear the same to all observers, wherever they may be.

Edward Arthur Milne

Misinforming people by use of statistical material might be called statistical manipulation; in a word (though not a very good one), statisticulation.

With even a superficial knowledge of mathematics, it is easy to recognize certain characteristic features: its abstractions, its precision, its logical rigor, the indisputable character of its conclusions, and finally, the exceptionally broad range for its applications.

Aleksandr Danilovich Aleksandrov

The theory of probability as mathematical discipline can and should be developed from axioms in exactly the same way as Geometry and Algebra.

Andrey Kolmogorov

Why do I paint? In my work as a mathematician, form, structure, and economy of expression are important. In music, add tone quality, balance and harmony. And now in painting, these aesthetic values are enhanced by color, contrast, and composition.

Robin Hartshorne

The full beauty of the subject of generating functions emerges only from tuning in on both channels: the discrete and the continuous.

I believe the coordinate-free approach fosters the cultivation of intuition, a scarce commodity in relativity because the phenomena this theory is intended to describe are as yet rather remote from our daily experience.