Quotes, Quoting, and Quotations



Some thoughts and comments on various topics



John Bartlett wrote one of the most famous collections of quotations. His book, Bartlett’s Familiar Quotations, was published in 1855 and is still published today, or is available on-line.

Today I thought I would share some quotes about mathematics, theory, and science.



I hope you enjoy them and like some of them. My favorite is

Quotes—Computer Science

Only math nerds would call finite.

—Leonid Levin

When a professor insists computer science is X but not Y, have compassion for his graduate students.

—Alan Perlis

Computers are useless. They can only give you answers.

—Pablo Picasso

All parts should go together without forcing. You must remember that the parts you are reassembling were disassembled by you. Therefore, if you can’t get them together again, there must be a reason. By all means, do not use a hammer.

—IBM Manual, 1925

The biggest difference between time and space is that you can’t reuse time.

—Merrick Furst

Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.

—John von Neumann

The trouble with integers is that we have examined only the very small ones. Maybe all the exciting stuff happens at really big numbers, ones we can’t even begin to think about in any very definite way. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions.

—Ronald Graham

Quotes—Mathematics

The infinite we shall do right away. The finite may take a little longer.

—Stanislaw Ulam

Complete disorder is impossible.

—Theodore Motzkin

A set is a Many that allows itself to be thought of as a One.

—Georg Cantor

The Riemann Hypothesis is the most basic connection between addition and multiplication that there is, so I think of it in the simplest terms as something really basic that we don’t understand about the link between addition and multiplication.

—Brian Conrey

If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?

—David Hilbert

Quotes—Problem Solving

Try a hard problem. You may not solve it, but you will prove something else.

—John Littlewood

If you don’t work on important problems, it’s not likely that you’ll do important work.

—Richard Hamming

A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one.

—Paul Halmos

A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies.

—Stefan Banach

It isn’t that they can’t see the solution. It is that they can’t see the problem.

—Gilbert Chesterton

I have yet to see any problem, however complicated, which, when you looked at it in the right way, did not become still more complicated.

—Poul Anderson

The open secret of real success is to throw your whole personality at a problem.

—George Polya

“Obvious” is the most dangerous word in mathematics.

—Eric Bell

In mathematics the art of proposing a question must be held of higher value than solving it.

—Georg Cantor

We are not very pleased when we are forced to accept a mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context.

—Hermann Weyl

The essence of mathematics is not to make simple things complicated, but to make complicated things simple.

—Stanley Gudder

For every complex problem there is an answer that is clear, simple, and wrong.

—Henry Mencken

Proof is an idol before whom the pure mathematician tortures himself.

—Arthur Eddington

Open Problems

What are your favorites?