JEWISH WORLD CHESS CHAMPIONS
(44% of undisputed world champions)
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The listing of world chess champions of Jewish descent given below is based on the list of so-called "undisputed world chess champions," a category whose definition reflects the fact that the world chess championship was in dispute in the years 1993-2006.  In 1993, the then world champion Garry Kasparov and his challenger Nigel Short broke with
the Fédération Internationale des Échecs (FIDE), which had sponsored the world chess championship matches since 1948, and organized the Professional Chess Association (PCA) to sponsor their 1993 championship match.  As a result, between 1993 and 2006 there were both FIDE and PCA champions.  Kasparov was the PCA champion from 1993 until 2000, when he lost the title to Vladimir Kramnik.  Former world champion Anatoly Karpov was appointed the FIDE champion in 1993 and held that title until he lost it to Alexander Khalifman in 1999.*  In 2006, Kramnik became the first undisputed world chess champion since 1993 and was succeeded shortly thereafter by Viswanathan Anand, who won the title from him in 2007.  Excluding the disputed period 1993-2006, the chess players of Jewish descent listed below held the world chess championship approximately 54% of the time since its inception in 1886:
NOTES
* There is a listing for Alexander Khalifman in the Russian Jewish Encyclopedia, but it should be noted that this work generally doesn't distinguish between Jewish and partly Jewish individuals (see http://www.jewishgen.org/Belarus/rje_k.htm).  Although Anatoly Karpov is generally described as being of purely Russian ethnicity, according to GM Lev Alburt, he is not without "some Jewish grandparents" (see "The Perilous World of Soviet Chess" in the January 1986 issue of The World and I).
1. Jewish mother, non-Jewish father.  It should be noted that there is considerable controversy over this claim.  It should also be noted that in the late 1970s, when Viktor Korchnoi defected from the USSR and leveled charges of rampant anti-Semitism in the Soviet chess establishment, Soviet government newspapers, in an apparent effort to counter those charges, published lists of Soviet Jewish chess luminaries whose successful careers, it was claimed, proved the absence of any such bias.  Those lists of Jewish, or partly Jewish, players included Vasily Smyslov (They did not include Boris Spassky.) 
2. According to recently unsealed FBI files and other independent archival materials, Bobby Fischer's biological father was not the German physicist Hans-Gerhardt Fischer, as previously supposed, but rather the Hungarian-Jewish engineer and fluid dynamicist Paul Nemenyi, making both of his parents Jewish.  See "Life is not a Board Game," by Peter Nicholas and Clea Benson, The Philadelphia Inquirer, 8 February, 2003.  Additional information can be found in Bobby Fischer Goes to War: How the Soviets Lost the Most Extraordinary Chess Match of All Time, by David Edmonds and John Eidinow (HarperCollins, New York, 2004, pp. 313-321).  This reference, incidentally, states (p. 39) that Boris Spassky told its authors that there is "no truth" to the widely reported claim that his mother was Jewish.
3. Jewish father, non-Jewish mother.

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