G.H. Hardy

G.H. Hardy wrote the sentence that accidentally defined machine learning. “A mathematician, like a painter or a poet, is a maker of patterns,” he declared in A Mathematician's Apology in 1940. He meant it as a defense of pure mathematics as a human art; he could not have known that within a century the most powerful technology on earth would be, in the most literal sense, a machine for making patterns. Hardy's definition now fits a class of systems he never imagined, and the fit exposes the deepest unsettled question of the AI age: whether the patterns the machines make are made with ideas, as Hardy required, or merely with weights—whether the output is mathematics or its convincing shadow. He is essential to the cycle not because he was right but because he was precisely, instructively wrong about the most concrete claim he ever made: that his beloved number theory, chosen for its uselessness, could never be applied. It became