## Paul Erdős (1913-1996): “My brain is open”

Coming to the letter E, it is perverse not to write about Leonhard Euler (1707–1783), one of mathematics’ perennial greats. But then Euler did not travel with his mother and sister in tow, did he, so Paul Erdős wins hands down. Though of course if one had for some unfathomable reason to encapsulate the epitome of human achievement as succinctly as possible, nothing Erdős did would qualify, while Euler’s $e^{\pi i}+1=0$ is a contender, with half a chance against a haiku of Bashō or the first eight bars of Bach’s chaconne for violin solo from BWV1004.

Euler is pronounced Oiler and Erdős is pronounced Erdesh. Erdős was born in Budapest into a family of mathematicians. He left Hungary in the 1930s, spent a year in Manchester, then went to Princeton. All he needed and owned was in his suitcase, and he lived mostly travelling from one collaboration to another, living in collaborators’ homes, arriving unexpectedly with his trademark MBIO, and sometimes his mother, or sister, or both, and staying long enough to polish off a couple of papers.  A saying often ascribed to him, and definitely true of him, that “a mathematician is a machine for turning coffee into theorems”, is actually due to Alfréd Rényi and sounds better in German. Needless to say, Rényi was a collaborator of Erdős (32 papers), and so has Erdős number 1; together they created the enormously influential theory of random graphs. 511 people have Erdős number 1, a collaboration record not likely to be beaten soon.

Erdős wrote 1525 papers, and the number of his posthumous papers (about 70) is higher that what most active mathematicians produce in their lifetime. Apparently Euler wrote more pages than Erdős, but Erdős wins easily on the number of papers. He contributed to “number theory, combinatorics, probability, set theory and mathematical analysis”, the above quotation being from his Wolf Prize award letter. The letter classifies his contributions as being “numerous”, which is true, and true damning with faint praise, but his mathematical legacy lives on, as in the work of Terence Tao.

Erdős has been described as “a man who only loved numbers”, and perhaps the fact that he called every type of music “noise” is off-putting, but numbers seem to have loved him back, and let us not forget his mama.

(MG)