705 Quotes About Mathematics

Last time I asked: 'What does mathematics mean to you?', and some people answered: "The manipulation of numbers, the manipulation of structures.' And if I had asked what music means to you, would you have answered: 'The manipulation of notes?

It is a funny paradox of design: utility breeds beauty. There is elegance in efficiency, a visual pleasure in things that just barely work.

Some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. [Fermat's] Last Theorem is the most beautiful example of this.

Rosier flung himself off his horse and ran towards then, already shouting. 'What a landing! What skill! The Prince and Princess of the Air!' 'And me?' said Armand, tossing Rosier a rope. 'Don't I warrant a mention?''Bah, you're not in this story!' Rosier pulled back on the line, holding it tight. 'My story is full of passion! Poetry! Danger and Thrills! But, if I ever write something in praise of tiny little numbers in a row - then Armand, you will be the hero.

Le Verrier—without leaving his study, without even looking at the sky—had found the unknown planet [Neptune] solely by mathematical calculation, and, as it were, touched it with the tip of his pen!

All the truths of mathematics are linked to each other, and all means of discovering them are equally admissible.

The deep study of nature is the most fruitful source of mathematical discoveries. By offering to research a definite end, this study has the advantage of excluding vague questions and useless calculations; besides it is a sure means of forming analysis itself and of discovering the elements which it most concerns us to know, and which natural science ought always to conserve.

Lagrange, in one of the later years of his life, imagined that he had overcome the difficulty (of the parallel axiom). He went so far as to write a paper, which he took with him to the Institute, and began to read it. But in the first paragraph something struck him that he had not observed: he muttered: 'Il faut que j'y songe encore', and put the paper in his pocket.' [I must think about it again].

Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates.