Machgielis Euwe is better known by the name Max Euwe, and he is better known as the world chess champion from 1935 to 1937 than as a mathematician. However, Euwe was indeed a very fine mathematician who concentrated more on his mathematics throughout his life than on his chess.
Max Euwe's parents were Elisabeth and Cornelius Euwe. Cornelius was a teacher and he often played chess with his wife who loved the game. By the time Max was five years old his parents had taught him to play and soon he was able to beat them. Max attended school in Amsterdam where he excelled in mathematics, and he began to play chess at ever more advanced levels. In 1911, when he was ten years old, Max entered his first chess tournament, a one day Christmas congress, and won every game. He became a member of the Amsterdam chess club when he was twelve years old and by the time he was fourteen he was playing in the Dutch Chess Federation tournaments. This was a difficult time in most European countries as World War I was totally disrupting normal life in most places, but The Netherlands remained neutral, so life in Amsterdam was relatively comfortable.
When he was eighteen years old Euwe was awarded his Abitur after attending a six-form High School in Amsterdam. By this time World War I had ended and international travel became possible again. Euwe made his first trip abroad, going to England to play in the famous Hastings Chess Tournament where he took fourth place. There had been little doubt in his mind what subject he should study at university, and he entered Amsterdam University to begin his study of mathematics. It should not be thought that Euwe kept his study of chess distinct from his mathematical studies. On the contrary he saw mathematics as being able to provide him with a logical, precise, even algebraic, approach to the game. We mention below an interesting mathematics paper he wrote which was motivated by chess.
By 1920 he was the leading Dutch player and he won the Dutch Championship for the first time in August 1921. In 1923 he was awarded an Honours Degree in mathematics from Amsterdam University. He then undertook research in mathematics which led to him being awarded a doctorate in 1926 from the University of Amsterdam. His dissertation, Differentiaalinvarianten van twee covariantie-vectorvelden met vier veranderlijken Ⓣ, was supervised by Roland Weitzenböck and Hendrick de Vries (who also supervised van der Waerden around this time). Euwe then lectured on mathematics in Winterswyk and Rotterdam and was appointed to the Lyceum for Girls in Amsterdam, teaching mathematics there from 1926 to 1940.
His doctoral studies behind him, from December 1926 to January 1927 Euwe narrowly lost a match with Alekhine 2 games to 3 won with 5 draws. At this stage Alekhine was not World Chess Champion, but soon after this he won the title and Euwe saw that, having competed so well with Alekhine, he was in with a chance at becoming World Champion himself. In 1928 he beat Bogolyubov twice in matches played in Amsterdam, Rotterdam and Utrecht.
In 1929 he published a mathematics paper in which he constructed an infinite sequence of 0's and 1's with no three identical consecutive subsequences of any length. He then used this to show that, under the rules of chess that then were in force, an infinite game of chess was possible. It had always been the intention of the rules that this should not be possible, but the rule that a game is a draw if the same sequence of moves occurs three times in succession was not, as Euwe showed, sufficient.
In 1930 he won the Hastings tournament ahead of Capablanca. However in an Euwe - Capablanca match which was played later Euwe lost 0 wins to 2 with 8 draws. The year 1932 was a very successful one beating Spielmann, drawing twice with Flohr and taking second place behind Alekhine in a tournament in Berne.
During 1933-34 he played very little chess while he concentrated on mathematics. Then, in the summer of 1935, he challenged Alekhine; the match began on 3 October. It was held at twenty-three different locations in Amsterdam, The Hague, Delft, Rotterdam, Utrecht, Gouda, Groningen, Baarn, Hertogenbosch, Eindhoven, Zeist, Ermelo, and Zandvoort. L Pins and B H Wood write in :-
The dramatic result of his first match against Alekhine is old history. Three points down after seven games, he pulled up to equality, only to see his redoubtable opponent draw away again. Battling gamely, he was still two down at the two-thirds stage, but won the twentieth, twenty-first, twenty-fifth, and twenty-sixth games and retained his grip on a now desperate adversary to the end.
In  there is also a description of Euwe's style of play:-
Euwe's great characteristic is economy of force. He is logic personified, a genius of law and order. His play is accurate and aggressive. One would hardly call him an attacking player, yet when his genius is functioning at its smoothest he strides confidently into some extraordinary complex positions: he is no disciple of simplicity. His greatest weakness is a tendency to blunder.
Euwe played the Nottingham International Chess Tournament from 10 August to 28 August 1936 while he was World Champion. In the Introduction to the Book of the Tournament, W H Watts writes:-
Euwe is the essence of caution. To win the world's championship and to secure a place only half a point behind the winner on caution alone is impossible, there must be depth and imagination, but the outstanding impression to be gained from his games is caution and dogged perseverance.
Despite this overall impression of caution, it is worth noting that Euwe shared the prize for the most wins in his score during the tournament.
While Euwe was World Champion he changed the way that players competed for the title. From that time on the rights to organise World Championship matches was given to FIDE (Fédération Internationale des échecs - the World Chess Federation). The one exception was the return match between Euwe and Alekhine which went ahead according to the conditions already arranged at the time of the first match.
In his return match with Alekhine things went badly for Euwe after winning the first game, and he lost the match by a margin of five points. Various reasons have been put forward as to why he was defeated so heavily, but the main reason was almost certainly the fact that his advisor, Reuben Fine, had taken ill with appendicitis and could not assist him.
After this Euwe went through a rather bad spell as regards his chess. His teaching duties made it difficult for him to concentrate on tournaments and in the Dutch championship which followed his defeat as World Champion he could only play matches in the evening as he had teaching commitments through the day. For other tournaments, although he did receive time off from his teaching duties to play, he had no time to prepare as he would teach up to the last moment.
He played at Hastings at Christmas 1938-39 and won the Dutch Championship again in 1939 but the onset of war made international play difficult over the next few years. During the war Euwe led work to provide food for people through an underground charity organisation.
After the war he won the London Tournament in 1946 and it looked for a while as though he might challenge again for the World Championship. However after some impressive play in the couple of years following the war, he then began to look past his best. Euwe became interested in electronic data processing and was appointed as Professor of Cybernetics in 1954. In 1957 he visited the United States to study computer technology in that country. While in the United States he played two unofficial chess games in New York against Bobby Fischer, winning one and drawing the second. He was appointed director of The Netherlands Automatic Data Processing Research Centre in 1959. He was chairman, from 1961 to 1963, of a committee set up by Euratom to examine the feasibility of programming computers to play chess. Then, in 1964, he was appointed to a chair in an automatic information processing in Rotterdam University and, following that, at Tilburg University. He retired as professor at Tilburg in 1971.
In 1970 Euwe was elected the president of FIDE and held that position until 1978. His role as arbitrator of the Fischer - Spassky World Championship match in Reykjavik, Iceland in 1972 was a very difficult one which he carried out with great tact and skill. He was unfortunate that during his time as president negotiations for the World Championship match between Fischer and Karpov became extremely difficult. Euwe made huge efforts to ensure that the match was played but, unfortunately, despite every effort eventually the match had to be awarded to Karpov by default.
Article by: J J O'Connor and E F Robertson