Igor Shafarevich

Igor Rostislavovich Shafarevich (, born June 3, 1923 in Zhytomyr) is an outstanding Soviet and Russian mathematician, founder of a school of algebraic number theory and algebraic geometry in the USSR, and a political writer. He was also an important dissident figure under the Soviet regime, a public supporter of Andrei Sakharov's Human Rights Committee from 1970. He supported the criticisms of Aleksandr Solzhenitsyn of both Soviet communism and liberal proposals for the future of Russia. 
==Work in mathematics==
Shafarevich made fundamental contributions to several parts of mathematics 
including algebraic number theory, algebraic geometry and arithmetic algebraic geometry.
In algebraic number theory the Shafarevich-Weil theorem extends the commutative
reciprocity map to the case of Galois groups which are extensions of abelian groups by finite groups.
Shafarevich was the first to give a completely self-contained formula for the pairing 
which coincides with the wild Hilbert symbol on local fields, thus initiating an important branch
of the study of explicit formulas in number theory.
Another famous result is the realization of every finite solvable group 
as the Galois group over rationals. Another fundamental result is 
the Golod-Shafarevich theorem on towers of unramified extensions of number fields. 
Shafarevich and his school greatly contributed to the study of algebraic geometry of surfaces. 
He initiated a Moscow seminar on classification of algebraic surfaces that updated around 1960 the treatment of birational geometry, and was largely responsible for the early introduction of the scheme theory approach to algebraic geometry in the Soviet school. His investigation in arithmetic of elliptic curves led him independently of John Tate 
to the introduction of the most mysterious group related
to elliptic curves over number fields, the Tate-Shafarevich group (usually called 'Sha', written 'Ш', his Cyrillic initial). He also formulated the Shafarevich conjecture which stated the finiteness of the set of Abelian varieties over a number field having fixed dimension and prescribed set of primes of bad reduction. This conjecture was proved by Gerd Faltings as a step in his proof of the Mordell conjecture. 
Shafarevich was a student of Boris Delone, and his students included Yuri Manin, A. N. Parshin,
I. Dolgachev, Evgeny Golod, I.A. Kostrikin, S.Y. Arakelov, G.V. Belyi, A. Tyurin, 
V. A. Kolyvagin. 
In view of later accusations of anti-Semitism on his part, it can be noted that his research students included some identified as Jewish, and that later, during his most serious troubles in the 1970s with the Soviet authorities, he did major work in collaboration with Ilya Piatetski-Shapiro on K3 surfaces. He is a member of the Serbian Academy of Sciences and Arts in department of Mathematics, Physics and Geo Sciences.
On his 80th birthday, Russian President Vladimir Putin hailed his "fundamental research" in mathematics and his creation of "a large scientific school that is known both in Russia and abroad."Putin congratulates prominent academician on 80th birthday TASS June 3, 2003
==Political activities==
According to a statement he released in the mid-1970s, he had had troubles with the Soviet powers in the early 1950s, but was then for a time protected by Ivan Petrovsky, then Rector of the Moscow University. He belonged to the wing of the dissident movement that identified itself with the Orthodox Christian tradition in Russia; what is sometimes called the 'romantic nationalist' or Slavophile tendency. The position criticised the Communist Party as part of a broader condemnation of socialism; Shafarevich published a much-noticed book Socialism (French edition around 1975) of destructive analysis, which was cited centrally by Solzhenitsyn in his 1978 address to Harvard University. From 1970 Shafarevich with Valery Chalidze, Grigori Podyapolski and Andrei Tverdokhlebov was one of Sakharov's human rights investigators. All this was a direct affront to the Soviet system, and Shafarevich was dismissed from Moscow University. Shafarevich continued to challenge the distortions of the academic system: as reported at the time by the algebraic geometer Miles Reid, he intervened in a doctoral defence of a communist party functionary, bringing up questions of plagiarism and inadequate work which were simply ignored (Shafarevich as an Academician in the Soviet Academy of Sciences could expect to be heard).
Shafarevich's 1970s book The Socialist Phenomenon was widely circulated in the West.A look at anti-Semitism in Russia The Washington Times September 18, 1996 After the Cold War, he started attacking Jews whom he called "small people who deny the historical achievements of Russia",The Evil Empire, Continued The New York Times, June 13, 1993 saying his homeland must have "sound democratic statehood, based on the will of the people."Russia Has Future Russian Press Digest January 5, 1993 His critics call him a radical, anti-Semitic, Orthodox nationalist.Russia's future. Into the abyss? The Economist June 15, 1996Egos Mark Battle Of The 'Sofa Parties' The Guardian (London) November 6, 1993
He wrote from this period a number of essays, on topics such as the nationalities issues, Russophobia, and Shostakovich's treatment. These were very prominent, some being included in Solzhenitsyn's collection From Under the Boulders.
==The Socialist Phenomenon==
Shafarevich's book The Socialist Phenomenon,The Socialist Phenomenon, by Igor Shafarevich. (1980) Translated by William Tjalsma. Foreword by Aleksandr I. Solzhenitsyn. 319 pp. New York: Harper & Row. published in the US in 1980, argued that the leftist-nihilist utopian impulse is a revival of gnostic religion, rooted in rebellion.Capitol Ideas, The American Spectator March 2004 In his view, this is an anti-Christian urge that fights obsessively with the normal state of the world, demanding material equality and the eradication of individual and gender distinctions.Gnostic Urge, The Washington Times March 3, 1999 Shafarevich wrote that "the death of mankind is not only a conceivable result of the triumph of socialism – it constitutes the goal of socialism."'Twixt Heaven and Earth: How the parties play out National Review December 4, 2000 
Shafarevich's views were influenced by Karl Wittfogel's theory of hydraulic society.Russians On Russia, The New York Times November 16, 1980 The mathematician argued that socialism has two archetypes: ancient despotisms (such as Sumeria, Babylonia and Egypt) and millennial sectarian movements of medieval and early modern Europe, along with a Freudian death-instinct. Out of this combination, he said that this ideology works to co-opt the prestige of science and faith in progress. Shafarevich covered in his work what he regarded as socialist tendencies and socialist states that have occurred during the history of mankind. He contrasts Campanella's (City of the Sun) and Thomas More's (Utopia) visions with the facts known of the Inca Empire and concludes there are striking similarities. Also, in Shafarevich's (1980:207) opinion, Marxist ideology has not even the climate of scientific inquiry. Marx's most important postulates are contradicted by the very reality: If a socialist state comes into being only under the conditions created by the development of capitalism, if, as Lenin wrote, "socialism originates in capitalism, develops historically from capitalism, and results from the action of a social force that is engendered by capitalism," then whence did it come and as a result of what social force did it develop in the Inca empire or the states of the ancient Orient? History only reinforces the doubts engendered by the contemporary situation: socialist states have arisen in China, North Korea and Cuba--that is, in the countries where the influence of capitalism can in no way be considered a determining factor.(Shafarevich 1980:202)
==In Russian politics==
During Perestroika, Shafarevich opposed both communism and Western democracy. On 21 December 1991 he took part in the first congress of the Russian All-People's Union headed by Sergei Baburin. In October 1992 he became member of the orgkomitet of the National Salvation Front that united extremist opposition movements.
In 1993 he was a candidate to State Duma from M.Astafyev's Constitutional Democratic Party - Party of Popular Freedom but failed to get elected. In 1994 he joined the All-Russian National Right Centre of M. Astafyev - N. Narotsnitskaya.
Shafarevich was member of the editorial board of the magazine „Nash Sovremennik“, in 1991—1992 the editorial board of „Den“ of Alexander Prokhanov (in was closed in October 1993, and later reopened under the name „Zavtra“).
==Accusations of antisemitism==
Shafarevich's essays titled Russophobia and "Three thousand year old mystery" resulted in accusations of antisemitism.http://www.nytimes.com/1992/07/29/us/alleging-bias-science-group-urges-russian-to-quit.htmlhttp://books.google.com/books?id=9-zvykby20kC&pg=PA30&lpg=PA30&dq=shafarevich+antisemitic&source=bl&ots=nioR-YJdny&sig=I9xbIoJGBLbWLFVnbXiMtBCACNg&hl=uk&ei=YOizSvmAOZKz8Qam3-zDDQ&sa=X&oi=book_result&ct=result&resnum=17Alexei Miller, The Communist Past in Post-Communist Russia, Eurozine, 2002-05-24.Veljko Vujacic, Russian Intellectual Anti-Semitism in the Post-Communist Era, Canadian Slavonic Papers, Mar-Jun 2004. The first was written in 1982 and first published in Germany in 1988.Scientist and Antisemite;The National Academy of Sciences has no business policing its members' attitudes. The Washington Post September 1, 1992 He claimed that his sources were writings by Soviet emigrants of Jewish origin.What Russians Are Saying The Jerusalem Post July 13, 1989. He complained that "Russophobes," who are cunning, hostile, Jewish critics, "dream of transforming Russia into. .. a robot deprived of all elements of human life." Russia and the New Right Newsweek February 12, 1990
This publication led to the request by the US NAS to Shafarevich to resign his membership, because the NAS charter prohibited stripping an existing membership .Joan Birman, AMS Condemns Russophobia, The Scientist, 1993, 7(8):12.Semyon Reznik, On Shafarevich And NAS: Tolerance Vs. Indifference, The Scientist, 1993, 7(8):11. In an open letter to the NAS, Shafarevich denied that Russophobia is antisemitic.Igor R. Shafarevich, Russian Castigates NAS For Making 'Vague Accusations', The Scientist, 1992, 6(24):11. Most recently Shafarevich expanded on the subject in his book "Three thousand year old mystery", which contained further anti-Semitic allegations, as well as attempts at justification of Stalin's repressions directed at Jews (such as executions of the members of the Jewish Anti-Fascist Committee, several writers and poets, etc. in 1947-1953) http://world.lib.ru/r/razumow_g/shafarevich.shtml.
Semyon Reznik criticizes the Russophobia essay for its factual inaccuracies, for example, in Shafarevich's arguments that the murder of Tsar Nicholas II was an example of Jewish ritual murder. Semyon Reznik "Blood Libel in Russia" 
==Notes==
==External links==
* 
*
* Shafarevich's political works (in Russian)
* The Socialist Phenomenon (in English)
Category:1923 births
Category:Living people
Category:People from Zhytomyr
Category:20th-century mathematicians
Category:21st-century mathematicians
Category:Soviet mathematicians
Category:Russian mathematicians
Category:Algebraic geometers
Category:Number theorists
Category:Members of the Russian Academy of Sciences
Category:Members of the Serbian Academy of Sciences and Arts
Category:Foreign Members of the Royal Society
Category:Soviet dissidents
Category:Ukrainians of Russian descent
Category:Russian Orthodox Christians
Category:Antisemitism
Category:Blood libel
be:Ігар Расціслававіч Шафарэвіч
de:Igor Rostislawowitsch Schafarewitsch
fr:Igor Chafarevitch
it:Igor' Rostislavovič Šafarevič
ht:Igor Shafarevich
nl:Igor Sjafarevitsj
ru:Шафаревич, Игорь Ростиславович
sl:Igor Rostislavovič Šafarevič
fi:Igor Šafarevitš