mathematics

I entered Princeton University as a graduate student in 1959, when the Department of Mathematics was housed in the old Fine Hall. This legendary facility was marvellous in stimulating interaction among the graduate students and between the graduate students and the faculty. The faculty offered few formal courses, and essentially none of them were at the beginning graduate level. Instead the students were expected to learn the necessary background material by reading books and papers and by organising seminars among themselves. It was a stimulating environment but not an easy one for a student like me, who had come with only a spotty background. Fortunately I had an excellent group of classmates, and in retrospect I think the "Princeton method" of that period was quite effective.

It (proof by contradiction) is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

Mathematics is the science which draws necessary conclusions.

Mathematicians deal with large numbers sometimes, but never in their income.

...I guess I can put two and two together.""Sometimes the answer's four," I said, "and sometimes it's twenty-two...

Newton was asked as a mathematician, not as a moralist. He replied 'Gentlemen, in applied mathematics, you must describe your unit.

...The pages and pages of complex, impenetrable calculations might have contained the secrets of the universe, copied out of God's notebook. In my imagination, I saw the creator of the universe sitting in some distant corner of the sky, weaving a pattern of delicate lace so fine that that even the faintest light would shine through it. The lace stretches out infinitely in every direction, billowing gently in the cosmic breeze. You want desperately to touch it, hold it up to the light, rub it against your cheek. And all we ask is to be able to re-create the pattern, weave it again with numbers, somehow, in our own language; to make the tiniest fragment our own, to bring it back to eart.

A mathematician says that an electromagnetic wave travels from Andromeda to your eye and that it also extends from Andromeda to your eye.

The spirit of mathematics is not captured by spending 3 hours solving 20 look-alike homework problems. Mathematics is thinking, comparing, analyzing, inventing, and understanding. The main point is not quantity or speed__he main point is quality of thought.The spirit of mathematics is not captured by spending 3 hours solving 20 look-alike homework problems. Mathematics is thinking, comparing, analyzing, inventing, and understanding. The main point is not quantity or speed__he main point is quality of thought.

Some people believe in imaginary friends. I believe in imaginary numbers.

What did we know? This was early days. We had no idea what was out there. How dangerous it might be. It was just a school maths problem. They never asked that in the exams, did they? Like, __f John walks at three miles an hour from London to Brighton, and he's attacked by rabid grown-ups four times, and they bite his right leg off, how long will it take him to bleed to death?

Mathematical knowledge is unlike any other knowledge. While our perception of the physical world can always be distorted, our perception of mathematical truths can__ be. They are objective, persistent, necessary truths. A mathematical formula or theorem means the same thing to anyone anywhere _ no matter what gender, religion, or skin color; it will mean the same thing to anyone a thousand years from now. And what__ also amazing is that we own all of them. No one can patent a mathematical formula, it__ ours to share. There is nothing in this world that is so deep and exquisite and yet so readily available to all. That such a reservoir of knowledge really exists is nearly unbelievable. It__ too precious to be given away to the __nitiated few._ It belongs to all of us.

The number of God is Pi and Euler number is evil.

In his school, Bertrand Russell thought it was better if they had the sex, so they could give their undivided attention to mathematics, which was the main thing.

I am not qualified to say whether or not God exists. I kind of doubt He does. Nevertheless I'm always saying that the SF( The SF is the supreme Fascist, the Number-One guy up there) has this transfinite book-transfinite being a concept in mathematics that is larger than infinite-that contains the best proofs of all mathematical theorems, proofs that are elegant and perfect.

The Ludolphian number is fixed in eternity_ not a digit out of place, all characters in their proper order, an endless sentence written to the end of the world by the division of the circle__ diameter into its circumference.

My beautiful proof lies all in ruins.

Solving a problem for which you know there__ an answer is like climbing a mountain with a guide, along a trail someone else has laid. In mathematics, the truth is somewhere out there in a place no one knows, beyond all the beaten paths. And it__ not always at the top of the mountain. It might be in a crack on the smoothest cliff or somewhere deep in the valley.