I finally read A Mathematician’s Apology, G.H. Hardy’s classic defense of a lifetime dedicated to the study of pure (“impractical”) mathematics. It’s a remarkably sad book, in which Hardy, near the end of his life, famously describes mathematics as a “young man’s pursuit”¹ in which the elderly have little to contribute. However, it also contains some really well-composed thoughts:

A man who is always asking, “Is what I do worth while?” and “Am I the right person to do it?” will always be ineffective himself and a discouragement to others. He must shut his eyes a little and think a little more of his subject and himself than they deserve.

[…]

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. … It may be very hard to define mathematical beauty, but that is just as true of beauty of any kind—we may not know quite what we mean by a beautiful poem, but that does not prevent us from recognizing one when we read it.