Zero Sum Game

 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.

John’s strength as a player, not surprisingly, lay in his extraordinary powers of concrete calculation: what he lacked, at the very highest level, was brute competitiveness and the sort of intuitive “feel” for positions exhibited by (for example) Magnus Carlsen. In fact Carlsen has cited Nunn as the embodiment of why “extreme intelligence” might be a hindrance to reaching the highest level in chess: “He has so incredibly much in his head. Simply too much. His enormous powers of understanding and his constant thirst for knowledge distracted him from chess.”

However, it did not prevent John from becoming the world champion at chess problem-solving on three occasions (2004, 2007 and 2010). But then problems, being the closest in chess to pure mathematics, and without the psychological stress of facing an opponent across the same board, are ideally suited to Nunn’s special gifts.

In one respect Nunn’s approach to chess defied pure logic. While theory suggests that White has a very slight advantage which Black must first neutralise before playing for a win, John always preferred from the outset to go for a quick knockout with the Black pieces. Of course, this from time to time backfired, but when it came off it was spectacular — as in the following victory against no less an opponent than Viktor Korchnoi, who at the time (1981) was the world’s second-highest-rated player. 1.c4 Nf6 2.Nc3 g6 3.e4 d6 (Nunn plays the enormously double-edged King’s Indian Defence—knowing that his redoubtable opponent had a massive plus score against it) 4.d4 Bg7 5.Be2 0-0 6.Nf3 Nbd7 7.0-0 e5 8.Qc2 a5 9.Rd1 exd4 10.Nxd4 Nc5 11.Ndb5 Re8 12.Bg5 Bd7 13.f3 Ne6 14.Be3 Nh5 15.Bf1 f5! 16.exf5 gxf5 (Korchnoi cannot now play 17.Qxf5 because after 17…Nef4 the discovered attacks on White’s Queen on f5 and Bishop on e3 win a piece) 17.Bf2 Rf8 18.g3 Nf6!? (Nunn once again invites his opponent to grab the pawn on f5. Korchnoi was famed for refuting unsound sacrifices, so this is deliberately provocative) 19.Qxf5? (Korchnoi is duly provoked. A less confident player would have settled for 19.Bg2) Ng4!! (An astonishing follow-up sacrifice, which Korchnoi cannot have anticipated) 20. Qxg4 Ng5 (The idea becomes clear: White’s Queen has been lured to its doom) 21. Qh5 Be8 22. Qxg5 (If 22.Qg4 h5 23.Qh4 Nxf3+ wins her majesty) Qxg5 23.Nxc7 (If Nunn now moves his attacked Rook on a8 Korchnoi will play 24.Ne6 forking Queen on g5 and Rook on f8, after which White has neutralized Black’s attack and has sufficient assorted material for his lost Queen. Nunn instead insists on maintaining the initiative with an inspired double rook sacrifice) Rxf3!! 25.Nxa8 Rxf2! 26.Kxf2 Qc5+ 26.Kg2? (It later emerged that the only defence was 26.Kf3 but Korchnoi can’t be blamed for not pushing his King further into the open) Bxc3 27.Nc7 (After 27.bxc3 Bc6+ 28.Rd5 Bxd5+ 29.cxd5 Qxc3 White cannot save his remaining Rook) Bg6 28.Nd5 Be4+ 29.Kh3 Bxb2 30.Rab1 Qf2 31.Rxb2 Qxb2 32.Nf4 Bf5+ 33.g4 Qf2! Korchnoi resigned. After 34.gxf5 Qf3+ 35.Kh4 Qxf4+ 36.Kh3 Qf3+ the massacre is complete. A game of extreme violence from the cerebral Dr Nunn.

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