A Quote by David Hilbert

The art of doing mathematics consists in finding that special case which contains all the germs of generality.

David Hilbert

Quote Topics

Art Case Consists Contains Doing Finding Germs Mathematics Special Which

Quote Author

David Hilbert
German - Mathematician
January 23, 1862 - February 14, 1943

...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly generality is, in essence, the same as a small and concrete special case.

Paul Halmos

To criticize mathematics for its abstraction is to miss the point entirely. Abstraction is what makes mathematics work. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools: analogy, generality, and simplicity. Mathematics is the ultimate in technology transfer.

Ian Stewart

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. And that, by some miracle, 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.

Freeman Dyson

Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.

E. T. Bell

Like a stool which needs three legs to be stable, mathematics education needs three components: good problems, with many of them being multi-step ones, a lot of technical skill, and then a broader view which contains the abstract nature of mathematics and proofs. One does not get all of these at once, but a good mathematics program has them as goals and makes incremental steps toward them at all levels.

Richard Askey

Wisdom consists in doing the next think you have to do, doing it with your whole heart, and finding delight in doing it.

Meister Eckhart

There is a striking parallel between the spreading of germs and the spreading of ideas or propaganda. On the one hand we are dealing with a virus which can be transported and transmitted under certain conditions which favor or limit its transportation or transmission: on the other hand with ideas, religions, and doctrines, which can be described as germs, benevolent or malevolent, according to the point of view one takes up. These germs can either remain at their source and be sterile, or emerge in the spreading of infection.

Andre Siegfried

In the USA, we learn "art history" as Western art history, and the history of Asian, or African art is a special case; we learn politics by examining our own government system, and consider other systems special cases, and the same is true of philosophy.

Jay L. Garfield

As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. But we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. But we do not know in what grace consists, which is the object of poetry.

Blaise Pascal

When all is said, its atmosphere [England's] still contains fewer germs of aggression and brutality per cubic foot in a crowded bus, pub or queue than in any other country in which I have lived

Arthur Koestler

One of the chief triumphs of modern mathematics consists in having discovered what mathematics really is.

Bertrand Russell

It is often said that ‘the germ of all Stalinism was in Bolshevism at its beginning’. Well, I have no objection. Only, Bolshevism also contained many other germs – a mass of other germs – and those who lived through the enthusiasm of the first years of the first victorious socialist revolution ought not to forget it. To judge the living man by the death germs which the autopsy reveals in the corpse – and which he may have carried in him since his birth – is that very sensible?

Victor Serge

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then suchand such another proposition is true of that thing.... Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Bertrand Russell

Wisdom consists in doing the next thing that you have to do, doing it with your whole heart and finding delight in it — and the delight is the sense of the sacred.

Helen M. Luke

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.

Freeman Dyson

Euclid avoids it [the treatment of the infinite]; in modern mathematics it is systematically introduced, for only then is generality obtained.