伊曼纽·拉斯克Emanuel Lasker

伊曼纽·拉斯克出生在普鲁士勃兰登堡省的一个犹太家庭。母亲是Rosalie Israelssohn，父亲是Adolf Lasker，一位犹太会堂的领唱，其职责是带领礼拜祈祷和吟唱。拉斯克有一个哥哥Berthold，当拉斯克十一岁被送到柏林上学时，Berthold教他下棋，Berthold当时是那里医学院的学生。他在当地咖啡馆下棋赚了一些钱，但直到大约十五岁才成为认真的棋手。

事实上，拉斯克的父母非常担心他花太多时间下棋而学业不够，于是让Berthold为拉斯克另找一所学校。然而，这所新学校的校长是当地象棋俱乐部的主席，数学老师是当地象棋冠军，因此在这所新中学里，拉斯克继续在数学和象棋两方面展现出非凡才能。1888年，他在格奥尔格·兰茨贝格 an der Warthe获得了高中毕业证书，该地现在是波兰城镇Gorzow Wielkopolski。

拉斯克在柏林、哥廷根和海德堡的大学学习数学和哲学，但他把学习与国际象棋对弈结合在一起。1889年，他在柏林赢得了他的第一次国际象棋锦标赛，一个月后，他在布雷斯劳赢得了主赛，这为他赢得了德国国际象棋大师的称号。这次比赛的一位裁判Leopold Hoffer评论道：-

这位年轻的大师将在未来的比赛中成为一位可怕的对手。

尽管他不久后在阿姆斯特丹的锦标赛中未能获胜，Hoffer强化了他的看法：-

拉斯克只是证实了我们在布雷斯劳观察他时所表达的看法。他只有21岁，但已经具备一流大师的素质——博学、对局面的判断、构思的敏捷、想象力、对棋局的极大热情，最重要的是，他是一个有文化且智力超群的人。

拉斯克在1891-92年长期逗留英国，下了许多精彩的对局，并击败了该国最好的棋手。1893年，他前往美国，继续赢得他所参加的所有比赛。他赢得了纽约国际锦标赛，尽管有一些顶尖棋手参赛，他仍赢得了每一场比赛，并击败了美国国际象棋冠军。然而，他并没有忽视他的数学，1893年，他在新奥尔良的杜兰大学讲授微分方程。他在美国的非凡胜利使拉斯克处于挑战Wilhelm Steinitz（当时58岁）争夺世界冠军头衔的位置。安排了一场比赛，将在纽约、费城和蒙特利尔三个场地举行，首先取得十场胜利的棋手获胜。

比赛于1894年3月15日在纽约开始，前六局相当均衡，每位棋手各赢两局。然而，拉斯克随后在费城连续赢得五局，取得了令人印象深刻的胜利，尽管施泰尼茨在此之后有所恢复，拉斯克在蒙特利尔获胜。他在1894年5月26日在那里取得了他的第十场胜利，此时他已经下了四场平局和五场败局。然而，尽管现在成为了世界冠军，许多人怀疑他是否配得上这一荣誉。Tarrasch说：-

在我看来，与施泰尼茨的这场比赛并不像他们自己赋予的那样重要。因为施泰尼茨已经老了，而年老的施泰尼茨不再是昔日的施泰尼茨。

拉斯克于1894年底回到德国，但他感染了伤寒，病得很重。他的兄弟贝特霍尔德照料他恢复健康，但过程缓慢，1895年他仍在康复中，当时他在英国著名的黑斯廷斯锦标赛中获得第三名，该赛事被描述为：-

……19世纪最重要的锦标赛，汇集了世界国际象棋的全体精英。

在英国期间，他做了一系列关于国际象棋的讲座，并将其整理成Common Sense in Chess出版。该书于1896年以德文出版，英文译本于次年问世。

在接下来的几年里，拉斯克参加了相对较少的国际象棋锦标赛。他在1895-96年的圣彼得堡和1896年夏天的纽伦堡锦标赛中取得了著名的胜利。1896-97年，他再次在世界冠军赛中与施泰尼茨对弈，并再次获胜。这次他取得了十场胜利，仅输了两场，平了五场。1899年在伦敦，拉斯克取得了他最令人印象深刻的锦标赛胜利之一，赢了他所下的28局中的20局，仅输了一局。次年，在巴黎，他同样令人印象深刻，赢了他18局中的14局，同样仅输了一局。

在这些年里，国际象棋当然不是拉斯克唯一的兴趣。事实上，他更专注于数学而非国际象棋，这解释了为什么他参加的锦标赛如此之少。在马克斯·诺特的建议下，拉斯克于1900年向埃尔朗根提交了他的博士论文Über Reihen auf der Convergenzgrenze Ⓣ（论收敛极限的行），并发表在Philosophical Transactions上。

拉斯克于1902年移居美国，并在那里生活到1907年，但这些年间他只参加了一次国际象棋锦标赛，即1904年的剑桥斯普林斯锦标赛。拉斯克在这次锦标赛中并列第二，获胜者Frank Marshall继续挑战拉斯克争夺世界冠军。然而，拉斯克为这样的比赛设定了高额的经济赌注，而Marshall在剑桥斯普林斯锦标赛之前年轻且相对不知名，几乎没有机会找到支持者来支付拉斯克的要价。Marshall不得不接受其他对手，事实上，他确实这样做了。

拉斯克在这一时期很少下棋，他做了一些非凡的数学工作。1905年，他引入了准素理想的概念，它对应于不可约簇，并在整数的素分解中发挥类似于prime幂的作用。他在1905年发表在Mathematische Annalen第60卷上的论文Zur Theorie der Moduln und Ideale Ⓣ（论模和理想的理论）中，用准素理想证明了多项式环理想的准素分解定理。一个交换环$R$现在被称为'拉斯克环'，如果$R$的每个理想都可以表示为有限个准素理想的交集。

1907年，拉斯克回到德国，再次受到马歇尔的挑战，此时他将价格降到了马歇尔能找到支持者出资的数目——这位世界冠军重新大规模地下棋了。在1907年至1910年间，他在六场比赛中捍卫了自己的世界冠军头衔，其中1907年对马歇尔的一场比赛中，拉斯克在所下的15局中从未输过（8胜7和），1908年对塔拉施一场，1909年（两场）和1910年对弗洛伦斯·南丁格尔·大卫雅诺夫斯基三场，以及1910年对卡尔·施莱希特一场。这些年里他只参加了一次锦标赛，在1909年圣彼得堡与阿基巴·鲁宾斯坦并列第一。他还下表演赛，这可以带来丰厚收入，同年他与雅诺夫斯基下了两场这样的比赛。

1911年，拉斯克与埃米尔·科恩的女儿玛莎·科恩结婚，他们住在柏林。安排已经就绪，让拉斯克再次捍卫他的头衔。计划是他与鲁宾斯坦争夺世界冠军，然后胜者与何塞·劳尔·卡帕布兰卡对弈。然而，由于第一次世界大战，比赛无法进行。第一次世界大战结束后，安排再次制定，拉斯克与卡帕布兰卡之间的世界冠军赛被安排出来。然而，拉斯克在比赛即将举行前写信给卡帕布兰卡，辞去世界冠军头衔。然而，他被说服参赛，比赛于次年在古巴哈瓦那举行。十四局后，拉斯克因健康不佳退出，他作为世界国际象棋冠军长达27年的统治结束了。

尽管失去了头衔，拉斯克仍在1924年赢得了纽约国际锦标赛，卡帕布兰卡获得第二，亚历山大·阿廖欣第三。拉斯克现在开始玩桥牌和围棋，后来代表德国参加桥牌比赛。

1933年，由于是犹太人，拉斯克被迫移居，前往英国，在那里一直住到1935年。加雷斯·威廉姆斯在Chess Monthly中撰文，描述了拉斯克的最后几年：-

……拉斯克夫妇被迫离开了舒适的退休生活。当局没收了他们在柏林的公寓、在蒂罗的农场以及毕生积蓄。拉斯克和Martha Lasker在晚年突然发现自己一贫如洗，没有钱、没有家、没有祖国。

他被迫结束退休生活，重新下棋以赚取足够的钱维持生计：-

为了生存，拉斯克不得不再次在棋坛开创一番事业。退休九年后，他受邀参加的第一个比赛是苏黎世。……1936年，拉斯克受邀前往莫斯科参加另一场大型国际比赛。……比赛结束后，拉斯克夫妇被鼓励留在莫斯科，数学家拉斯克博士受邀成为莫斯科科学院的成员。他接受了这一邀请，拉斯克夫妇便在莫斯科永久定居下来。拉斯克在莫斯科科学院潜心从事数学研究。

他参加了1936年8月10日至28日的诺丁汉国际象棋锦标赛。W H Watts在为该锦标赛的书籍撰写的导言中写道：-

拉斯克在整个锦标赛期间给我留下了一个明确无误的印象：他并未竭尽全力。这或许有很充分的理由。他成名于一代人之前，尽管获得高名次会是非常出色的成绩，但对于一个年近七十的人来说，长时间锦标赛中十五盘漫长艰苦的对局所带来的压力是不明智的。

在锦标赛中途的花园聚会上：-

拉斯克那永不枯竭的幽默感表现得淋漓尽致，他显然擅长时钟高尔夫。

事实上，尽管他没有赢得国际象棋锦标赛，但他确实赢得了推杆比赛！据报道，他为了残局而战，换句话说，他确保自己的第二推尽可能短。

1937年，在他们的赞助人克雷连科失势后，拉斯克夫妇再次搬家，这次定居在美国纽约。在那里，Martha Lasker生病了，他们被建议不要旅行；她于当年晚些时候去世。拉斯克在接下来的几年里进行了讲座和表演，但在1939年，在一次讲座中，他感到头晕。这是一种疾病的开始，病情逐渐恶化，直到他去世。

Nathan Divinsky本人是一位杰出的数学家，与拉斯克一样，最著名的是他在环论中的成果，他写道：-

在那份伟大的锦标赛名单中，圣彼得堡1896年、圣彼得堡1914年和纽约1924年，拉斯克总是获胜。1896年，他以两分的优势领先于他的主要同时代人，18年后在决赛中再次以两分的差距获胜，又过了十年（在他将冠军头衔让给卡帕布兰卡三年后），$1\large\frac{1}{2}\normalsize$分领先于强大的对手。这样的成绩无疑表明拉斯克身上有某种真正非凡的东西。

拉斯克除了他的代数成果和国际象棋天才之外，还引入了许多有趣的数学游戏。例如，他设计了拉斯卡，并对尼姆游戏的规则进行了有趣的修改。除了撰写国际象棋方面的著作——其中除了上面提到的经典Common sense in chess之外，我们还可以提到Lasker's manual of chess——拉斯克还撰写了哲学方面的著作。在这个主题上，他出版了Kampf Ⓣ（斗争）（1907年）、Das Begreifen der Welt Ⓣ（对世界的理解）（1913年）、Die Philosophie des Unvollendbar（1919年）、Das verständige Kartenspiel Ⓣ（智能纸牌游戏）（1929年，同年英文翻译）、Brettspiele der Völker Ⓣ（各民族的棋盘游戏）（1931年）和The Community of the Future（1940年）。

米哈伊尔·博特温尼克，于1948年成为世界国际象棋冠军，写道：-

我第一次见到拉斯克时，他已是一位老人。他的外表并不引人注目。他的动作非常缓慢。……他是一个非常睿智的人——他是第一个研究国际象棋比赛所有实际方面的人：如何为锦标赛做准备，何时参赛，如何休息、饮食等等。他完全理解所有这些实际方面。

拉斯克的一段引文显示了他对待棋局的方式。有一次，他在做完讲座后被问到，为什么他几乎总是选择对手声称不满意的开局变着。拉斯克回答说：——

我没有研究任何东西，但所讨论的变着由如此可靠和合理的展开着法组成，以至于它们不可能像我的对手所想的那样糟糕。因此我确信他误判了这些变着，他对它们的理解是有缺陷的。我想利用这种情况。

在[2]中，他的生活哲学和国际象棋哲学被比较：——

拉斯克的生活观，正如在他的著作中所阐述的，是一种战斗或斗争，作为一名棋手，他可能是这项运动所见过的最伟大的斗士。他极其谨慎而顽强，会故意让自己陷入困境以复杂化斗争，并给自己击败对手的机会；一旦他取得优势，他就会以无情的活力和决断将其贯彻到底。

最后让我们评论说，拉斯克关于将理想分解为初等理想的结果是埃米·诺特建立抽象理论的基础，该理论将环论发展为一个主要的数学主题，并为现代代数几何提供了基础。埃米·诺特的Idealtheorie in RingbereichenⓉ（除环中的理想论）（1921年）在现代代数的发展中具有根本重要性，通过在任何满足升链条件的交换环中给出理想分解为初等理想的交集，推广了拉斯克的结果。

Emanuel Lasker was born in the Prussian province of Brandenburg into a Jewish family. His mother was Rosalie Israelssohn while his father was Adolf Lasker, a cantor in the synagogue whose role there was to lead the liturgical prayers and chanting. Emanuel had an older brother Berthold and, when sent to attend school in Berlin when he was eleven years old, Emanuel was taught to play chess by Berthold who was a student in the medical faculty there. He made some money playing chess in the local cafés, but he did not become a serious chess player until about the age of fifteen.

In fact 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. In 1888 he obtained his abitur in Landsberg an der Warthe, now a Polish town named Gorzow Wielkopolski.

Lasker studied mathematics and philosophy at the universities in Berlin, Göttingen and Heidelberg but he combined his studies with playing chess. In 1889 he won his first chess tournament in Berlin and, a month later, he won the Hauptturnier in Breslau which earned him the German title of Master of Chess. One of the judges at this event, Leopold Hoffer, commented:-

The young master will be a formidable opponent in future contests.

Although he failed to win the tournament at Amsterdam shortly afterwards, Hoffer reinforced his opinion:-

Young Lasker only confirmed the opinion we expressed about him when we watched him in Breslau. He is only 21 years of age, but possesses already the qualities of a first-class master - erudition, judgement of position, quickness of conception, imagination, great enthusiasm for the game, and above all, he is a man of culture and more than average intelligence.

Lasker had an extended stay in England in 1891-92, playing many fine chess games and beating the best players in that country. In 1893 he went to the United States and continued to win all the matches that he played. He won the New York International tournament, winning every game despite some top players competing, and he defeated the American chess champion. He did not neglect his mathematics however, and in 1893 he lectured on differential equations at Tulane University in New Orleans. 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. A match was arranged which would take place in three venues, New York, Philadelphia and Montreal, with victory going to the first player to record ten victories.

The match began in New York on 15 March 1894 and was fairly even with two victories to each player in the first six games. However, Lasker then won five consecutive games winning impressive victories in Philadelphia, and, despite Steinitz recovering after this, Lasker won in Montreal. He gained his tenth win there on 26 May 1894, having by this time played four draws and having five losses. However despite now being World Champion, many doubted that he deserved the honour. Tarrasch said:-

In my opinion the match with Steinitz does not have the great importance that they themselves attribute to it. For Steinitz has grown old, and the old Steinitz is no longer the Steinitz of old.

Lasker had returned to Germany by the end of 1894 but he contracted typhoid fever and became seriously ill. His brother Berthold nursed him back to health but it was a slow process and he was still recovering in 1895 when he took third place in famous Hastings Tournament in England described as:-

... the most important tournament of the 19th century, which assembled the entire cream of world chess.

While in England he gave a series of lectures on chess which he wrote up for publication as Common Sense in Chess. The book was published in German in 1896 with the English translation appearing in the following year.

Over the next few years Lasker played in relatively few chess tournaments. He had a famous win in St Petersburg in 1895-96 and in a tournament in Nuremberg in the summer of 1896. In 1896-97 he played Steinitz again in a world championship match and was again victorious. This time he reached ten victories having lost only twice and drawn five times. 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. In the following year in Paris he was equally impressive winning 14 of his 18 games, again with only one loss.

Chess was certainly not the only interest for Lasker over these years. In fact he was concentrating more on mathematics than chess which explains why he played in so few tournaments. Advised by Max Noether, Lasker presented his doctoral thesis Über Reihen auf der Convergenzgrenze Ⓣ 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. Marshall had to take on other opponents which, indeed, he did.

Although Lasker played little chess over this period, he did some remarkable mathematics. In 1905 he introduced the notion of a primary ideal, which corresponds to an irreducible variety and plays a role similar to prime powers in the prime decomposition of an integer. He proved the primary decomposition theorem for an ideal of a polynomial ring in terms of primary ideals in a paper Zur Theorie der Moduln und Ideale Ⓣ published in volume 60 of Mathematische Annalen in 1905. A commutative ring $R$ is now called a 'Lasker ring' if every ideal of $R$ 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. He only played in one tournament during these years, coming first equal with Akiba Rubinstein in St Petersburg in 1909. He also played exhibition matches, which could be lucrative, and in the same year he played two such matches against Janowski.

Lasker married Martha Cohn, the daughter of Emil Cohn, in 1911 and they lived in Berlin. Arrangements were put in place for Lasker to defend his title again. The plan was that he play Rubinstein for the World Championship, then that the winner would play José Raúl Capablanca. However, due to World War I, the matches could not be played. After World War I ended, arrangements were again worked out, with a world championship match between Lasker and Capablanca being set up. However, Lasker wrote to Capablanca resigning his World Champion title before the match was to be played. However, he was persuaded to play and the match took place in Havana, Cuba, in the following year. 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. Gareth Williams, writing in Chess Monthly, describes Lasker's last few years:-

... 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.

He was forced to come out of retirement and to play chess again to make enough money to live:-

In order to survive Lasker had once again to build a career in chess. The first tournament he was invited to after nine years retirement was Zürich. ..... 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.

He played in the Nottingham International Chess Tournament from 10th to 28 August 1936. W H Watts, writing an Introduction to the book of the tournament, wrote:-

Lasker, throughout the tournament gave me the unmistakable impression that he was not extending himself. There may be a very good reason for this. He made his name a generation ago and although winning a high place would be a very fine performance, the strain of a long tournament with fifteen long arduous games would be unwise for a man of nearly seventy years.

At the garden party in the middle of the tournament:-

Lasker's never failing fund of humour was much in evidence and he evidently excels at clock golf.

Indeed although he did not win the chess tournament, he did win the putting competition! It was reported that he played for the ending, in other words he made sure his second putt was as short as possible.

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. This was the start of an illness which slowly worsened until his death.

Nathan Divinsky, himself an exceptional mathematician and like Lasker most famous for his results in ring theory, writes:-

In that great roll-call of tournaments, St Petersburg 1896, St Petersburg 1914 and New York 1924, Emanuel Lasker always won. In 1896 it was by a two-point margin over his leading contemporaries, 18 years later again by a two-point gap in the final and ten years further on (three years after he conceded the title to Capablanca) $1\large\frac{1}{2}\normalsize$ points ahead of a mighty field. 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. For example he devised laska, and produced an interesting modification to the rules of nim. 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. On that topic he published Kampf Ⓣ (1907), Das Begreifen der Welt Ⓣ (1913), Die Philosophie des Unvollendbar (1919), Das verständige Kartenspiel Ⓣ(1929, English translation in the same year), Brettspiele der Völker Ⓣ (1931), and The Community of the Future (1940).

Mikhail Botvinnik, who became World Chess Champion in 1948, wrote:-

The first time I saw Lasker, he was an elderly man. His appearance was not impressive. His movements were very slow. ... He was a very wise man - he was the first one who studied all the practical sides of a chess game: how to prepare for a tournament, when to play in it, how to rest, eat, etc. He perfectly understood all these practical aspects.

A quotation from Lasker shows how he approached games. He was once asked after giving a lecture why he almost always chose variations in openings which his opponent had declared unsatisfactory. Lasker replied:-

I did not study anything but the variations in question consisted of developing moves which were so sound and reasonable that they could not be so bad as my opponent thought. I was therefore convinced that he had misjudged these variations, and his understanding of them was faulty. I wanted to take advantage of this state of affairs.

In [2] his philosophy of life and of chess are compared:-

Lasker's conception of life, as expounded in his writings, was that of a fight or struggle and as a chess player he was probably the greatest fighter that the game has seen. Supremely wary and tenacious, he would deliberately involve himself in difficulties to complicate the struggle and give himself chances of outplaying his opponent; and once he had the advantage, he would push it home with relentless vigour and decision.

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 Ⓣ (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.