Mathematics Quotes - Page 11

I believe there are 15, 747, 724, 136, 275, 002, 577, 605, 653, 961, 181, 555, 468, 044, 717, 914, 527, 116, 709, 366, 231, 425, 076, 185, 631, 031, 296 protons in the universe and the same number of electrons.

I think the term "Kantian constructivism" as an oxymoron. Kant was a constructivist about mathematics, but not about ethics.

There is a logic of language and a logic of mathematics.

Proofs exist only in mathematics and logic, not in science.

Some things that satisfy the rules of algebra can be interesting to mathematicians even though they don't always represent a real situation.

This is not very important what I'm doing. I'm just proving something.

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.

The Torus is my enemy!

There is an explicit way to define what explicit is.

The advance and perfecting of mathematics are closely joined to the prosperity of the nation.

... a result once generally accepted by mathematicians is seldom retracted, and then only with great pangs. The Nature of Mathematics

Education is worth little if it teaches only how to make a living rather than how to make a life.

Mathematics is not a separate entity. It owes a great deal of its power and its beauty to other disciplines.

Philosophically, mathematics is not a part of science. Mathematics studies patterns, science studies nature

Yet what are all such gaieties to me whose thoughts are full of indices and surds?

Without computers we will be stuck only proving theorems that have short proofs.

I knew my purpose well and clear: to show how Nature behaves without cluttering its beauty with abtruse mathematics.

One would normally define a "religion" as a system of ideas that contain statements that cannot be logically or observationally demonstrated... Gödels theorem not only demonstrates that meathematics is a religion, but shows that mathematics is the only religion that proves itself to be one!

MacPherson told me that my theorem can be viewed as blah blah blah Grothendieck blah blah blah, which makes it much more respectable.

Great mathematics is achieved by solving difficult problems not by fabricating elaborate theories in search of a problem.

A peculiarity of the higher arithmetic is the great difficulty which has often been experienced in proving simple general theorems which had been suggested quite naturally by numerical evidence.

As for explaining mathematical phenomena it opens the question: explaining to whom? humans?, other computers?

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

Very little mathematics has direct applications - though fortunately most of it has plenty of indirect ones.

The pendulum of mathematics swings back and forth towards abstraction and away from it with a timing that remains to be estimated.