Math Quotes - Page 30

Later generations will regard Mengenlehre (set theory) as a disease from which one has recovered.

... if one were to refuse to have direct, geometric, intuitive insights, if one were reduced to pure logic, which does not permit a choice among every thing that is exact, one would hardly think of many questions, and certain notions ... would escape us completely.

Bridges would not be safer if only people who knew the proper definition of a real number were allowed to design them.

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.

Mathematics in general is fundamentally the science of self-evident things.

If you cannot - in the long run - tell everyone what you have been doing, your doing has been worthless.

Without troublesome work, no one can have any concrete, full idea of what pure mathematical research is like or of the profusion of insights that can be obtained from it.

I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate.

Mathematics is concerned with "all possible worlds."

I have tried to avoid long numerical computations, thereby following Riemann's postulate that proofs should be given through ideas and not voluminous computations.

Pseudoscience describes theories that sound like science but are actually just made up, like aromatherapy or biorhythms or love.

I thought I wanted to be a physicist in high school until I learned that there was much more math than philosophy in it. I assumed I would just sit around all day and think.

Nature is an infinite sphere of which the center is everywhere and the circumference nowhere.

All exact science is dominated by the idea of approximation.

Mathematics is the science which draws necessary conclusions.

You live your life between your ears.

From a drop of water a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other.

It is a capital mistake to theorize before one has data.

I changed the course of my life, from the rigidity of mathematics and the corporate rhythm to a more bohemian world.

The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit.

I became more and more convinced that even nature could be understood as a relatively simple mathematical structure.

Mathematics are well and good but Nature keeps dragging us around by the nose.

He who has heard the same thing told by 12,000 eye-witnesses has only 12,000 probabilities, which are equal to one strong probability, which is far from certain.

Mathematics is about making up rules and seeing what happens.