A technique is a trick that works. Image

Are mathematical ideas invented or discovered? The question has been repeatedly posed by philosophers through the ages and will probably be with us forever. Image

If we have no idea why a statement is true, we can still prove it by induction. Image

How did he do it?

He must be a genius! Image

It is a common public relations gimmick to give the entire credit for the solution of famous problems to the one mathematician who is responsible for the last step. Image

Making mathematics accessible to the educated layman, while keeping high scientific standards, has always been considered a treacherous navigation between the Scylla of professional contempt and the Charybdis of public misunderstanding. Image

Mathematicians - for what they do - are really poorly rewarded. And it's a very competitive field, almost as bad as being a concert pianist. Image

Mathematicians also make terrible salesmen. Physicists can discover the same thing as a mathematician and say "We've discovered a great new law of nature. Give us a billion dollars." And if it doesn't change the world, then they say, "There's an even deeper thing. Give us another billion dollars." Image

Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don't look alike are really the same. That is one of their innermost Freudian motivations. In fact, this is what we mean by understanding. Image

Our faith in Mathematics is not likely to be wane if we openly acknowledge that the personalities of even the greatest mathematicians may be as flawed as those of anyone else. Image

The advice we give others is the advice that we ourselves need. Image

The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely interwined. Mathematicians have never decided whether they should feel excited or upset by such events. Image

The lack of real contact between mathematics and biology is either a tragedy, a scandal or a challenge, it is hard to decide which. Image

The progess of mathematics can be viewed as progress from the infinite to the finite. Image

The one contribution of mine that I hope will be remembered has consisted in just pointing out that all sorts of problems of combinatorics can be viewed as problems of location of the zeros of certain polynomials and in giving these zeros a combinatorial interpretation. Image

Theorems are not to mathematics what successful courses are to a meal. Image

[In mathematics] There are two kinds of mistakes. There are fatal mistakes that destroy a theory. But there are also contingent ones. Which are useful in testing the stability of a theory. Image

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

We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?" Image