**Lasker** became World Chess Champion in 1894 and held the championship until 1921. In mathematics he introduced the notion of a primary ideal.

- Emanuel's parents were so worried that he was devoting too much time to chess and not enough to his school work that they told Berthold to find another school for Emanuel.
- However, the head of this new school was president of the local chess club and the mathematics master was the local chess champion, so in his new secondary school Emanuel continued to show remarkable talents at both mathematics and at chess.
- Lasker studied mathematics and philosophy at the universities in Berlin, Göttingen and Heidelberg but he combined his studies with playing chess.
- Lasker had an extended stay in England in 1891-92, playing many fine chess games and beating the best players in that country.
- His remarkable wins in the United States put Lasker in a position to challenge Wilhelm Steinitz, who was 58 years old at this time, for the title of World Champion.
- However, Lasker then won five consecutive games winning impressive victories in Philadelphia, and, despite Steinitz recovering after this, Lasker won in Montreal.
- Lasker had returned to Germany by the end of 1894 but he contracted typhoid fever and became seriously ill.
- Over the next few years Lasker played in relatively few chess tournaments.
- In London in 1899 Lasker had one of his most impressive tournament victories, winning 20 of the 28 games he played, losing only one game.
- Chess was certainly not the only interest for Lasker over these years.
- Advised by Max Noether, Lasker presented his doctoral thesis Über Reihen auf der Convergenzgrenze Ⓣ(On rows to the limit of convergence) to Erlangen in 1900 and it was published in the Philosophical Transactions.
- Lasker moved to the United States in 1902 and lived there until 1907 but only played in one chess tournament during these years, namely at Cambridge Springs in 1904.
- Lasker was second equal in this tournament, the winner Frank Marshall went on to challenge Lasker for the world championship.
- However, Lasker set high financial stakes for such a match and Marshall, young and comparatively unknown before the Cambridge Springs tournament, had little chance of finding backers to put up Lasker's asking price.
- Although Lasker played little chess over this period, he did some remarkable mathematics.
- A commutative ring RRR is now called a 'Lasker ring' if every ideal of RRR can be represented as an intersection of a finite number of primary ideals.
- In 1907 Lasker returned to Germany and, challenged again by Marshall, he now dropped the price to a figure that Marshall could find backers to put up - the World Champion was back to playing chess in a big way.
- During the years 1907 to 1910, he defended his World Champion's title in six matches, one against Marshall in 1907 in which Lasker never lost any of the 15 games played (8 wins and 7 draws), one match against Tarrasch in 1908, three matches against David Janowski in 1909 (two matches) and 1910, and one against Carl Schlechter in 1910.
- Arrangements were put in place for Lasker to defend his title again.
- However, Lasker wrote to Capablanca resigning his World Champion title before the match was to be played.
- After fourteen games Lasker retired because of ill health and his reign of 27 years as World Chess Champion was over.
- Despite losing the title, Lasker still won the New York International Tournament in 1924 with Capablanca coming second with Alexander Alehkine in third place.
- Lasker now took up Bridge and Go, going on to represent Germany at Bridge.
- In 1933, being Jewish, Lasker was forced to emigrate and went to England where he lived until 1935.
- the Laskers were forced out of their comfortable retirement.
- The regime confiscated the Laskers' Berlin appartment, their farm at Thyrow and their lifetime savings.
- Emanuel and Martha Lasker, in their old age, suddenly found themselves destitute, without money home or homeland.
- Lasker was invited to Moscow in 1936 to participate in another great international tournament.
- The Laskers were encouraged to stay on in Moscow after the tournament and Dr Emanuel Lasker, mathematician, was invited to become a member of the Moscow Academy of Science.
- The offer was accepted and the Laskers took up permanent residence in Moscow.
- Emanuel became absorbed with his mathematical studies at the Moscow Academy.
- In 1937 the Laskers moved yet again, after their patron Krylenko had been disgraced, this time taking up residence in New York in the United States.
- There Martha Lasker took ill and they were advised not to travel; she died later that year.
- Lasker gave lectures and demonstrations over the next couple of years but, in 1939, during a lecture, he became dizzy.
- Such results surely indicate something truly remarkable about Emanuel Lasker.
- Lasker, in addition to his algebraic results and his chess genius, also introduced a number of interesting mathematical games.
- As well as writing on chess, where we could mention Lasker's manual of chess in addition to the classic Common sense in chess mentioned above, Lasker wrote on philosophy.
- A quotation from Lasker shows how he approached games.
- Finally let us comment that Lasker's results on the decomposition of ideals into primary ideals was the foundation on which Emmy Noether built an abstract theory which developed ring theory into a major mathematical topic and provided the foundations of modern algebraic geometry.
- Emmy Noether's Idealtheorie in Ringbereichen Ⓣ(Ideal theory in division rings) (1921) was of fundamental importance in the development of modern algebra, generalising Lasker's results by giving the decomposition of ideals into intersections of primary ideals in any commutative ring with ascending chain condition.

Born 24 December 1868, Berlinchen, Prussia (now Barlinek, Poland). Died 11 January 1941, New York, USA.

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Algebra, Origin Poland

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive