Question

Some famous quotes often give interesting insights into the vision of mathematics that certain mathematicians have. Which ones are you particularly fond of?

Standard community wiki rules apply: one quote per post.

Answer 1

Il est vrai que M. Fourier avait l'opinion que le but principal des mathématiques était l'utilité publique et l'explication des phénomènes naturels; mais un philosophe comme lui aurait dû savoir que le but unique de la science, c'est l'honneur de l'esprit humain, et que sous ce titre, une question de nombres vaut autant qu'une question du système du monde.

C. G. J. Jacobi writing (in French) to Legendre

Translation as given in Additive number theory: inverse problems and the geometry of sumsets, vol. 2, by M. B. Nathanson: «It is true that Fourier believed that the principal goal of mathematics is the public welfare and the understanding of nature, but as a philosopher he should have understood that the only goal of science is the honor of the human spirit, and, in this regard, a problem in number theory is as important as a problem in physics.» The translation sadly loses much of the tone...

Answer 2

"There are, therefore, no longer some problems solved and others unsolved, there are only problems more or less solved, according as this is accomplished by a series of more or less rapid convergence or regulated by a more or less harmonious law. Nevertheless an imperfect solution may happen to lead us towards a better one."

Henri Poincare

Answer 3

Who can does; who cannot do, teaches; who cannot teach, teaches teachers.

Paul Erdos.

Answer 4

"Mathematics consists of proving the most obvious thing in the least obvious way." - George Polya

Answer 5

Mathema est ars et scientia, discenda

Aquinas?

Answer 6

There are 10 kinds of people in the world, those that understand binary and the other 9.

Answer 7

Without Mathematics Earth is just a Big Zero - Chacko Mash