It is rather astonishing how little practical value scientific knowledge has for ordinary men, how dull and commonplace such of it as has value is, and how its value seems almost to vary inversely to its reputed utility.

No one should ever be bored. … One can be horrified, or disgusted, but one can’t be bored.

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

There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain.

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

A person’s first duty, a young person’s at any rate, is to be ambitious, and the noblest ambition is that of leaving behind something of permanent value.

Pure mathematics is on the whole distinctly more useful than applied... For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.