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Zero Sum Game
September 2014


Max Euwe, 1963: A world chess champion, and a doctor of mathematics (Harry Pott/ Dutch National Archives)
 
When I have told someone that I am a chess obsessive, the most common response is, "You must have been very good at maths at school." To which the answer is: definitely not. I am, however, a mere club and county player, so even if I had been a highly proficient mathematician, it would prove nothing.

Yet there is no great overlap even between outstanding talent at chess and mathematical ability. The programs which now can beat all humans have reduced the game to a series of algorithms connected to immense computing power. But this is not what humans are doing when we play chess. Numbers have nothing to do with it; it is above all a game of pattern recognition, with intuition (admittedly based on an enormous amount of prior work) at the heart of the creative process. It is also a struggle between two people and therefore, like any sport, there is a strong element of psychology.

The aesthetic joy that the chess-player derives from solving an especially difficult problem is doubtless similar to what is experienced by a mathematician in his field; and both are characterised by their abstractness. Yet here too there is a difference: mathematics can be used to solve problems in the real world — for example in the applied field of engineering. Chess is a gloriously beautiful dead end: sublime for those who can feel its artistry, and even force, but of marginal social utility. This is not an argument against its being taught in schools: children can learn valuable lessons about self-discipline and patience by playing the game. But so they can by playing cricket, if they are fortunate enough to attend a school with access to the necessary space.

It may be that because I was a mediocre mathematician (at best) I am underestimating the connections between the two pursuits. That polymath among great mathematicians, Poincaré, declared in Science and Method: "Every good mathematician should also be a good chess player and vice versa." However, no chess games by Poincaré survive, which suggests that he might have been the refutation of his own theory.

There are examples that lend some credence to Poincaré's general observation, but many fewer than most people would imagine. Dr Machgielis ("Max") Euwe, who held the world chess championship between 1935 and 1937, gained his doctorate in mathematics from the University of Amsterdam and became a maths teacher (during which time he won the world amateur chess championship). He also published a mathematical analysis of chess, in which he apparently proved (though this is quite beyond me) that the then official rules of chess did not exclude the possibility of games of infinite duration.

But Euwe was no mathematical prodigy. Perhaps the only example of someone of extreme talent in both fields is Dr John Nunn, who at his chess peak was ranked ninth in the world but whose greater claim to fame is that he became, at 15, the youngest Oxford undergraduate in almost 500 years. He remained there until 1981, when he gave up his lectureship in maths to become a full-time chess player. I was lucky, when I was an undergraduate at Oxford, to be across the road from John, while he was completing his doctorate (with a thesis on finite H-spaces): he would spare the time to show me some of his chess analyses, which were breathtaking in their depth and rigour.

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