## Remembering Paul Erdős, collaborator, eccentric, lover of numbers

Today we celebrate the birthday of one of the most colourful and eccentric characters in the world of mathematics (*a domain not short on eccentrics at the best of times*)- the Hungarian * Paul Erdős* (26 March 1913 – 20 September 1996).

Erdős, a serial collaborator, was one of the most prolific publishers of mathematical papers in history. The volume of his output has been compared with the great Leonhard Euler, but while Euler published more pages (mostly as solo author), Erdős published more articles (more than 1500 in his lifetime), many in collaboration with other mathematicians.

The British mathematician and author Timothy Gowers once wrote an essay entitled *“The Two Cultures of Mathematics”*, in which he classed mathematicians into two groups – the *‘problem solvers’* and the *‘theory developers’*, with the latter often held in higher regard in the history of mathematics. Erdős, however, definitely fell into the former category – he was particularly fond of those problems that appeared simple to understand, yet notoriously difficult to solve. Most of his work focused on number theory, combinatorics, approximation theory, set theory and probability theory. However, thanks in part to his fondness for collaborating with other mathematicians, he also made contributions in completely unrelated fields such as topology.

As mentioned before, Erdős was known to be a bit of an eccentric. He had little interest in earthly possessions, giving most of what he had away to causes he considered worthy. Most of his life fit into a single suitcase, and since he first emigrated from Hungary (moving first to England, and later to America after accepting his first position at Princeton University), he lived a nomadic lifestyle, travelling between different mathematical colleagues and collaborators. It is said that he often arrived without warning, pitching up on a prospective collaborator’s doorstep with the words *“My mind is open!”*, to indicate his readiness to collaborate. After staying for a few weeks, he would move on to the next destination.

In recognition of his prolific collaborations, Erdős’ friends devised the *‘Erdős number’* – an indicator of a person’s degree of separation from Erdős himself (in terms of mathematical collaboration). Thus Erdős had a number of 0, while his immediate collaborators had an Erdős number of 1, his collaborators’ collaborators had an Erdős number of 2, and so on. Due to the extent of his mathematical collaborations, and the collaborations of these individuals with scientists from other fields, many physicists, engineers, biologists etc also have low Erdős numbers.

Despite the extent of his publications and collaborations, Erdős never received mathematics’ highest prize, the Fields Medal, nor did he co-author a paper with a recipient of this award. He similarly missed out on many other of the more illustrious mathematics awards, with the most significant award bestowed on him probably being the Israeli Wolf Prize.

Despite this lack of formal recognition, Erdős’ contribution to a wide range of mathematical topics have been acknowledged by his peers, and he is fondly remembered as someone with an unwavering passion for numbers, and one of the most colourful characters in mathematics.