The great number theorist GH Hardy would probably have disagreed with the label “great”. In his book A Mathematician’s Apology, he admitted: “I have never done anything ‘useful’. 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 added that he had trained other mathematicians “of the same kind as myself, and their work has been . . . as useless as my own”.
Since Hardy was writing in 1940, there was a touch of the humblebrag about this claim. Chemist Fritz Haber had created chemical weapons for use in the first world war. Engineers had produced artillery, tanks and strategic bombers. Oppenheimer and the other physicists would soon create the atomic bomb. There was a comfort in Hardy’s protestations of uselessness — but perhaps a false comfort.
In the 1970s, some basic ideas in supposedly useless number theory were deployed by Ron Rivest, Adi Shamir and Leonard Adleman. They developed the RSA algorithm, which enables public key cryptography, without which there would be no ecommerce. Cryptography is hardly valueless to the military, either. One never knows when useless knowledge will be useful after all.