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**Chess and Mathematics Part 1 Part 2
Max Euwe (1901 - 1981)**

The Dutchman Euwe's first name was Machgielis but he is better known as Max. He studied mathematics at the University of Amsterdam and obtained a Ph.D. degree in 1926. Until 1940, he worked as a high school teacher. After the war, Euwe started research in the young field of informatics which at that time was regarded as a branch of mathematics. In 1954, Euwe became professor for cybernetics, and in 1959, director of the Dutch research center for automatic data processing. In 1964, he got a chair for informatics, first at the University of Rotterdam, later at the University of Tilburg.

Max Euwe became famous as chess world champion from 1935 to 1937. The 1935 match with title holder Alexander Alekhine took place in several Dutch cities and was one of the longest in the history of chess. Euwe won 9 games, Alekhine 8 games; 13 games were drawn.

There is a connection of the region where I live to Max Euwe. 70 years ago, in 1937, the spa town of Bad Nauheim in Hesse, Germany staged an international tournament with Euwe, Alekhine, Bogoliubov and Saemisch. This tournament (which was continued in Stuttgart and Garmisch) was won by Euwe.

Euwe was FIDE president from 1970 to 1978. During his presidency, the title match between Fischer and Spassky took place in Reykjavik. As it is well known, the negotiations between Fischer, Spassky and the FIDE were difficult and Euwe's diplomatic skills were very helpful before and during the match.

Euwe provided an interesting link between mathematics and chess. For that reason, I singled him out for part 1 of "Chess and Mathematics" (part 2 portrays six other mathematicians who became famous in chess and who were honoured with stamps).

Now to the problem in which Euwe took interest as a mathematician as well as a chess master.

is repeated three times consecutively.

This rule is called by Euwe the

In the German rule, the length of the sequence is insignificant. The rule may have seemed to make sense because there was evidence for repeated move sequences from numerous very long games in which neither player would resign or agree in a draw.

At this point mathematics enter. In a 1929 article, Euwe defined a sequence d(n) of 0s and 1s recursively:

The asterisk means x

0

0 1

01 10

0110 1001

01101001 10010110

...

It should be mentioned that there is also a direct, non-recursive definition of d(n) :

d(n) = q(n

n

This sequence is analyzed on a

Max Euwe was not the first mathematician who used the sequence d(n) . It seems to have been defined several times independently. E. Prouhet, A. Thue, H.C.M. Morse and G.A. Hedlund applied it in different mathematical fields (cf. Thue-Morse sequence).

1 : g1 - f3 g8 - f6 f3 - g1 f6 - g8

Combining these moves according to Euwe's sequence obviously leads to an

last update 2008-01-23

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