Children at play are not playing about; their games should be seen as their most serious-minded activity.
Logic and mathematics are nothing but specialized linguistic structures.
Beauty is the first test: there is no permanent place in the world for ugly mathematics.
Mathematics is a place where you can do things which you can't do in the real world.
[Mathematics is] to be recommended as a preventative against frivolous reading and a premature development of the imagination.
The ballet makes us look at those bodies, it makes us listen to that music, it makes us wonder at the geometry, of the way they come together. The way that extraordinary space is controlled and given such emotional force.
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.