As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.

The mathematician's patterns, like the painter's or the poet's, must be beautiful.

In [great mathematics] there is a very high degree of unexpectedness, combined with inevitability and economy.

[I was advised] to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant.

Most people can do nothing at all well

The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been conjectured, sometimes a hundred years or more before they were proved; and they have been suggested by the evidence of a mass of computations.

A mathematician, like a painter or a poet, is a maker of patterns.