Paul Erdős

He wrote about 1,500 papers with more than 500 co-authors, which is why mathematicians boast about their Erdős number.

He lived out of a suitcase, turning up at colleagues’ doors announcing that his brain was open.

Largely self-taught, he wrote to G. H. Hardy at Cambridge in 1913 with pages of startling formulas. Hardy said some were so strange they had to be true, because nobody could have made them up.

1729 is the Hardy–Ramanujan number: the smallest number that is a sum of two cubes in two ways, 1³ + 12³ = 9³ + 10³. Ramanujan spotted it when Hardy called his taxi number dull.