“I have never done anything ‘useful,’ ” is how he would put it years later. “No discovery of mine has made or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.” He would never say so, perhaps he did not even see it, but he had taken Moore’s sensibilities and applied them to mathematics. “Hardyism,” someone would later dignify this doctrine, so hostile to practical applications; and Hardy’s Mathematician’s Apology, written almost half a century later, would embody it on every page.
