Thoughts, no. 204
Around 1918, G. H. Hardy took a taxi to visit Srinivasa Ramanujan, who was ill in a nursing home in Putney, and remarked that the cab’s number, 1729, seemed a rather dull one. Ramanujan said no, it was very interesting: the smallest number that is the sum of two cubes in two different ways, 1³ + 12³ and 9³ + 10³. The story is usually told as a feat of speed. But nearly a century later, Ken Ono and Andrew Granville, going through Ramanujan’s papers at Trinity College, Cambridge, found 1729 there in another form, 9³ + 10³ = 12³ + 1: two cubes adding up to a third cube, and missing by one. He had been hunting near misses to Fermat’s Last Theorem, and had found a way to make infinitely many of them. So the dull number may not have been a stranger he sized up on the spot. It may have been an old acquaintance, one he knew for nearly breaking a rule, and you don’t have to work out who someone is when you recognise them.
Written at the house on .