Paul Erdős: a memoir

My memoirs of Paul Erdős will be almost all entirely personal, but I would like to begin with two small incidents illustrating attitudes of the mathematical community and the wider world to Paul. Both took place on trains. After I received my copy of the two-volume work The Mathematics of Paul Erdős [13] (published just after Paul’s death), I was reading it on the train home from work. Sitting opposite me was a non-mathematician, who noticed what I was reading. He was familiar with the concept of Erdős number and, after striking up a conversation, he raised this topic, and was delighted to learn that my Erdős number was 1. A rather different reaction came from an eminent mathematician whom I met by chance on a train in Europe. He was sceptical about Paul Erdős and his mathematics, and was reluctant to believe that someone like, for example, Jean-Pierre Serre could have an Erdős number. On the spot, I was able to construct a path of length 5 from Erdős to Serre passing through me. I learned later [14] that Serre has Erdős number 3; but my pride was restored when I read that Efim Zelmanov had Erdős number 4 and the shortest path passed through me. (But even this is not true: see [14]. So short-lived is fame . . . )