Hermann Weyl Quotes

It is almost as hard to define mathematics as it is to define economics, and one is tempted to fall back on the famous old definition attributed to Jacob Viner, "Economics is what economists do," and say that mathematics is what mathematicians do. A large part of mathematics deals with the formal relations of quantities or numbers.

I have found a very great number of exceedingly beautiful theorems.

Mathematics is written for mathematicians.

Math is sometimes called the science of patterns.

Algebra is the metaphysics of arithmetic.

My interest in science started quite early. My earliest school recollection, from age 6, is actually of mathematics, realizing that one could fill an entire page with digits and never come to the largest possible number, so I saw what was meant by infinity.

Mathematics is the queen of the sciences.

Primes are the atoms of the arithmetic - the hydrogen and oxygen of the world of numbers

There are infinite numbers between 0 and 1.

One would be hard put to find a set of whole numbers with a more fascinating history and more elegant properties surrounded by greater depths of mystery--and more totally useless--than the perfect numbers.

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.

Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.

I count Maxwell and Einstein, Eddington and Dirac, among "real" mathematicians. The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are at present at any rate, almost as "useless" as the theory of numbers.

Only Numbers. Pure math. You have to accustom yourself to thinking that way.

I can show you that the art of calculation has to do with odd and even numbers in their numerical relations to themselves and to each other.

The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in the case of entities that are based upon whole and part; then and only then is it an undeniable consequence of the concepts "totum" and "pars". Unfortunately, however, this "axiom" is used innumerably often without any basis and in neglect of the necessary distinction between "reality" and "quantity", on the one hand, and "number" and "set", on the other, precisely in the sense in which it is generally false.

Nature does not count nor do integers occur in nature. Man made them all, integers and all the rest, Kronecker to the contrary notwithstanding.

The study of mathematics is the indispensable basis for all intellectual and spiritual progress.

The primes are the raw material out of which we have to build arithmetic, and Euclid's theorem assures us that we have plenty of material for the task.

If equations are trains threading the landscape of numbers, then no train stops at pi.

Mathematics is as little a science as grammar is a language.

All the mathematical sciences are founded on relations between physical laws and laws of numbers.

The important thing to remember about mathematics is not to be frightened

Numbers are really fascinating things, and they do play a big part in our lives. They are a language of their own.

Now the denominator ... why don't they just call it the bottom number? The denominator ... that sounds like a Schwarzenegger movie doesn't it? [impersonating Arnold Schwarzenegger] I am the Denominator. I'll give your leg a compound fraction!