Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different.

Sometimes a good idea comes to you when you are not looking for it. Through an improbable combination of coincidence, naivete and lucky mistakes ...

The highest form of pure thought is in mathematics.

Don’t try to make life a mathematics problem with yourself in the center and everything coming out equal. When you’re good, bad things can still happen. And if you’re bad, you can still be lucky.

Mathematical demonstrations being built upon the impregnable Foundations of Geometry and Arithmetick are the only truths that can sink into the Mind of Man, void of all Uncertainty; and all other Discourses participate more or less of Truth according as their Subjects are more or less capable of Mathematical Demonstration.

You treat world history as a mathematician does mathematics, in which nothing but laws and formulas exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.

It has become almost a cliche to remark that nobody boasts of ignorance of literature, but it is socially acceptable to boast ignorance of science and proudly claim incompetence in mathematics.

A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

What science can there be more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of mathematics?

Arithmetic is numbers you squeeze from your head to your hand to your pencil to your paper till you get the answer.

Besides it is an error to believe that rigour is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is at the same time the simpler and the more easily comprehended. The very effort for rigor forces us to find out simpler methods of proof.

A mathematician who is not also something of a poet will never be a complete mathematician.

The Good Lord made all the integers; the rest is man's doing.

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.

The purpose of computing is insight, not numbers.

It is easier to square a circle than to get round a mathematician.

If only I had the Theorems! Then I should find the proofs easily enough.

Why are numbers beautiful? It’s like asking why is Beethoven’s Ninth Symphony beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.

One good thing about teaching calculus is that you develop a hardened attitude towards repeating yourself.

The world is continuous, but the mind is discrete.

Arithmetic is where numbers fly like pigeons in and out of your head.

There is something in statistics that makes it very similar to astrology.

If things are nice there is probably a good reason why they are nice: and if you do not know at least one reason for this good fortune, then you still have work to do.

When I give this talk to a physics audience, I remove the quotes from my 'Theorem'.

Counting pairs is the oldest trick in combinatorics... Every time we count pairs, we learn something from it.

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