Source: Robert Leonard, Von Neumann, Morgenstern and the Creation of Game Theory, p. 9

Often, chess is credited with rather interesting developments in other fields. This is sometimes done by people who are not particularly good at chess, but it is interesting to note that it is also done by serious researchers, as in this case, about the history of von Neumann, the well-known mathematician. The author dedicates an entire chapter to the effect of chess on the intellectual scene of von Neumann's youth - 1920s Hungary - and credits it with much intellectual stimulation of Jews in Hungary in general and von Neumann in particular. 

It is claimed that Emmanuel Lasker's Kampf (Struggle) - his philosophical thesis - was highly influential, indirectly, in developing game theory. Lasker attempted to generalize the struggles in the game of chess to decision-making in life, and used terms later used by game theorists - "domination" and "equilibrium" for example - to argue that, like chess, in life too the seemingly near-infinite number of possible strategies does not preclude finding out, by logical thinking, the best or at least the few reasonable strategies (Leonard, p. 13).

This, claims Leonard, raising the possibility - later examined by Zermelo, who knew Lasker - of a completely objective analysis of chess, for example, mathematically defining a "winning position" by looking at the existence of a set of future moves that allow the player to mate no matter what the opponent does (Leonard, p. 17). Zermelo's paper was the first time (1912) that winning in chess was defined purely formally. From there, claims Leonard, it is not surprising that the idea of a general game theory along similar formal, purely mathematical principles for life, not just for chess, would occur to von Neumann.

I am somewhat skeptical, not of Zermelo's pioneering work, which very likely influenced von Neumann, but whether Lasker's Kampf was of such great influence on Zermelo. After all, one need not read Lasker's philosophical works to know Lasker, be interested in chess, and attempt to describe it mathematically. I am not convinced that it was Lasker's Kampf that gave to Zermelo, or von Neumann, the idea of the possible analogy between chess and life that led to game theory.

Sylvester and Chess

 

James Joseph Sylvester. Credit: Wikipedia.

It is interesting to note that the famed mathematician Sylvester (1814-1897) was, first, Jewish, and - what is less known - a chess fan. In Eric Temple Bell's article, "Invariant Twins, Cayley and Sylvester" (The World of Mathematics, by James R. Newman (ed.), New York, Simon & Schuster: 1956, vol. 1, pp. 341-365), we read:

After his retirement from Woolwich Sylvester lived in London, versifying, reading the classics, playing chess, and enjoying himself generally, but not doing much mathematics.

Bell's comment does not imply Sylvester was a strong player, but at least it is known publicly that he played chess. Does anybody know more about this? It should be noted that a quick internet search found Sylvester's own address to the British Association for the Advancement of Science (1869) noting:

a very clever writer in a recent magazine article, expresses his doubts whether it is, in itself, a more serious pursuit, or more worthy of interesting an intellectual human being, than the study of chess problems or Chinese puzzles.

The rest of the lecture shows that Sylvester, unsurprisingly, consider mathematics much more important - as his audience also undoubtably did - but it is not clear whether he expects them to consider chess problems unimportant.  

Game Theory

From posters of a conference on game theory in Bar Ilan University. Chess is as always fascinating to game theorists:

Chess, Math, and Taxes

The flag of the Israeli tax authority (Image credit: CRW Flags Inc.)

A translation from Amnon Dankner's article, today (23/4/2010), p. 26 of Maariv's (a large Israeli daily) weekend supplement, about how was forced to pass the matriculation exam in mathematics:

Nothing worked, until he [Danker's father] noted that, since there's a connection between chess and mathematics, perhaps he should look in the back room of the "Orient" coffee house. This was the place where our city's chess players would sit and play and shout and insult each other, and of all of them, Leon Tefilinski caught his eye. A rough man, with a red nose and thick glasses, a gravel-like voice, smoking cigarettes and with an eternal wool shawl around his neck.

My father noted two qualities. First: the man was a natural pedagogue. Every time his opponent made some monumental mistake, Tefilinski would strike him in the arm, shouting 'gurnisht! Schmuck!' and explain to him how he went wrong. Second: when he would wait for his opponent to move -- which sometimes took a while -- he would read Zbivannia Mathematica -- mathematical riddles.

Dankner's father employed him as his son's math teacher, and he succeeded in what no other teacher did -- scare him to death with tales of how he killed Germans in Stalingrad, and how doing the same to him if he makes mistakes would not be difficult (Dankner obviously didn't take this threat literally, but fearing the teacher doesn't necessarily come from literal acceptance of the teacher's threats.)

But this was not the end of the story. When Dankner's father died three years later, he was asked to pay a large amount of property tax. To his surprise, he met Tefilinski in the tax office by chance:

To tell the truth, at the moment, needing a comforting hand, Mr. Tefilinski was not the first, or for that matter the last, man I would choose to meet. But he insisted, looked at the papers in my hand and looked at them... He went into a small room and came out with a small ruler. He went into the [taxman's] office without knocking... went to the table of the fearsome manager of property tax in Jerusalem... shouting 'you did it all wrong here, yob tvou mat! ... 'stupid Russian peasants do better math than you!' ... erasing the numbers from the form, writing other numbers, and telling [the manager] to sign.

Which he did; since, as it turns out, Teflinksi was the living soul, the human computer of the property tax office in Jerusalem.

Dankner concludes that employing Teflinski as a math teacher

[W]as the best investment the Dankner family ever made. It was a good, indeed excellent thing, to study mathematics, Q.E.D.

And they say chess players aren't practical!