I am interested in mathematics only as a creative art.
Young men should prove theorems, old men should write books.
Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not.
It is not worth an intelligent man's time to be in the majority. By definition, there are already enough people to do that.
A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.
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.
...a science is said to be useful if its development tends to accentuate the existing inequalities in the destribution of wealth, or more directly promotes the destruction of human life.
There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.