Godfrey Harold Hardy
The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.
In these days of conflict between ancient and modern studies, there must surely be something to be said for a study which did not begin with Pythagoras and will not end with Einstein, but is the oldest and youngest of all.
I believe that mathematical reality lies outside of us, and that our function is to discover, or observe it, and that the theorems which we prove, and which we describe grandiloquently as our “creations” are simply notes on our observations.
I am interested in mathematics only as a creative art.
A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.