By the utilitarian test even great mathematicians wasted their lives

Evidence

If useful knowledge is, as we agreed provisionally to say, knowledge which is likely, now or in the comparatively near future, to contribute to the material comfort of mankind, so that mere intellectual satisfaction is irrelevant, then the great bulk of higher mathematics is useless. Modern geometry and algebra, the theory of numbers, the theory of aggregates and functions, relativity, quantum mechanics—no one of them stands the test much better than another, and there is no real mathematician whose life can be justified on this ground. If this be the test, then Abel, Riemann, and Poincaré wasted their lives; their contribution to human comfort was negligible, and the world would have been as happy a place without them. — G. H. Hardy, A Mathematician’s Apology, 271

Categorization

• SEED: Angles toward a defense-of-useless-knowledge essay: the utilitarian standard indicts not just modern mathematics but the giants of the field, so anyone invoking usefulness must revise the standard.
• corroborated: 2 independent passages support this claim — G. H. Hardy, A Mathematician’s Apology, 271
• XREF: connects to: Mathematicians value uselessness because science serves evil in war — G. H. Hardy, A Mathematician’s Apology, 247; Useful mathematics tends to be aesthetically dull — G. H. Hardy, A Mathematician’s Apology, 246; Applied mathematicians must discard their finest ideas for failing to match reality — G. H. Hardy, A Mathematician’s Apology, 270

Broader Connections

• Applied mathematicians must discard their finest ideas for failing to match reality #expands (0.65) — G. H. Hardy, A Mathematician’s Apology, 270