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I'm a mathematician, basically. What I do is look around for problems where I can find useful applications for mathematics. All I do, really, is the math, and other people have the ideas.
You have this world of mathematics, which is very real and which contains all kinds of wonderful stuff. And then we also have the world of nature, which is real, too.
The language that nature speaks is the same language that we invented for mathematics. That's just an amazing piece of luck, which we don't understand.
The "seriousness" of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects.
Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand... So Greek mathematics is 'permanent', more permanent even than Greek literature.
The more reasonable a student was in mathematics, the more unreasonable she was in the affairs of real life, concerning which fewtrustworthy postulates have yet been ascertained.
On the basis of my historical experience, I fully believe that mathematics of the 25th century will be as different from that of today as the latter is from that of the 16th century.
There are three intellectual pursuits, and, so far as I am aware, only three, in which human beings have performed major feats before the age of puberty. They are music, mathematics, and chess.
Our faith in Mathematics is not likely to wane if we openly acknowledge that the personalities of even the greatest mathematicians may be as flawed as those of anyone else.
Mathematics catalogues everything that is not self-contradictory; within that vast inventory, physics is an island of structures rich enough to contain their own beholders.
Mathematics, the non-empirical science par excellence . . . the science of sciences, delivering the key to those laws of nature and the universe which are concealed by appearances.
When we talk about the impact inside mathematics, and applications in the sciences, [Mandelbrot] is one of the most important figures of the last 50 years.
Mathematics is one of the most basic -- and most ancient -- types of knowledge. Yet the details of its historical development remain obscure to all but a few specialists.
Mathematics can remove no prejudices and soften no obduracy. It has no influence in sweetening the bitter strife of parties, and in the moral world generally its action is perfectly null.
This method of deduction ... is often called "combinatory". Its usefulness is not exhausted at this stage, but it does even at the outset lead to some valuable conclusions.
Our thoughts, our language, are always at a distance from whatever they're trying to describe. We have other kinds of languages, like mathematics, like music, like art, but there's always that gap.
Examples ... which might be multiplied ad libitum, show how difficult it often is for an experimenter to interpret his results without the aid of mathematics.
Thinking - in particular abstract thinking, which most of us are introduced to through the study of mathematics and literature - helps us learn that we can become problem solvers.
Given the brief - and generally misleading - exposure most people have to mathematics at school, raising the public awareness of mathematics will always be an uphill battle.