220 and 284 are called amicable numbers: add up everything that divides 220 except 220 itself and you get 284, and the divisors of 284 add up to 220. The Greeks knew that pair. Fermat put his name to a bigger one, 17,296 and 18,416, Descartes found a pair in the millions, and Euler, a century on, listed dozens more. Then in the 1860s a sixteen-year-old Italian, Nicolò Paganini (not the violinist), pointed out 1,184 and 1,210, the second-smallest pair of all, small enough to check with a pencil in an afternoon. Nobody in Europe seems to have written it down before him, though it may have been known earlier elsewhere. The great mathematicians had methods that made large pairs, and a method only finds what it was built to find. The pair next door was left for someone who simply counted.