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Igor Rostislavovich Shafarevich (; 3 June 1923 – 19 February 2017) was a Soviet Union and Russian mathematician who contributed to algebraic number theory and algebraic geometry. Outside mathematics, he wrote books and articles that criticised socialism and other books which were described as Antisemitism.
Shafarevich was the first mathematician to give a completely self-contained formula for the Hilbert pairing, thus initiating an important branch of the study of explicit formulas in number theory. Another famous (and slightly incomplete) result is Shafarevich's theorem on solvable Galois groups, giving the realization of every finite solvable group as a Galois group over the rational number.
Another development is the Golod–Shafarevich theorem on towers of unramified extensions of .
Shafarevich and his school greatly contributed to the study of algebraic geometry of surfaces. He started a famous Moscow seminar on classification of algebraic surfaces that updated the treatment of birational geometry around 1960 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 led him, independently of John Tate, to the introduction of the group related to elliptic curves over number fields, the Tate–Shafarevich group (usually called 'Sha', and denoted as 'Ш', the first Cyrillic letter of his surname).
He contributed the Grothendieck–Ogg–Shafarevich formula and to the Néron–Ogg–Shafarevich criterion.
With former student Ilya Piatetski-Shapiro, he proved a version of the Torelli theorem for K3 surfaces.
He 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. The conjecture was proved by Gerd Faltings as a partial step in his proof of the Mordell conjecture.
Shafarevich's students included Yuri Manin, Alexey Parshin, Igor Dolgachev, Evgeny Golod, Alexei Kostrikin, Suren Arakelov, G. V. Belyi, Victor Abrashkin, Andrey Todorov, Andrey N. Tyurin, and Victor Kolyvagin.
He was a member of the Serbian Academy of Sciences and Arts in the department of Mathematics, Physics and Earth Sciences. In 1960, he was elected a Member of the German Academy of Sciences Leopoldina. In 1981, he was elected as a foreign member of the Royal Society.
In 2017, Shafarevich was awarded the Leonhard Euler Gold Medal by the Russian Academy of Sciences.
In the 1970s, Shafarevich, with Valery Chalidze, Grigori Podyapolski and Andrei Tverdokhlebov, became one of Andrei Sakharov's human rights investigators and so was dismissed from Moscow University. Shafarevich opposed political interference in universities.
Shafarevich argued that ancient socialism (such as Mesopotamia and Egypt) was not ideological, as an ideology socialism was a reaction to the emergence of individualism in the Axial Age. He compared Thomas More's ( Utopia) and Tommaso Campanella's ( City of the Sun) visions with what is known about the Inca Empire and concluded that there are striking similarities. He claimed that we become persons through our relationship with God and argued that socialism is essentially nihilism and is unconsciously motivated by a death instinct. He concluded that we have the choice of pursuing death or life.
In his talk to the Göttingen Academy of Sciences upon receiving a prize, Shafarevich presented his view of the relationship between mathematics and religion. He noted the multiple discoveries in mathematics, such as that of non-Euclidean geometry, to suggest that pure mathematics reflects an objective reality, not a set of conventional definitions or a formalism. He claimed that the growth of mathematics itself is not directed or organic. To have a unity and direction, mathematics needs a goal. It can be practical applications or God as the source for the direction of development. Shafarevich opted for the latter, as pure mathematics is not in itself driven by practical applications.Ueber einige Tendenzen in der Entwicklung der Mathematik, Jarhrbuch der Akademie der Wissenschaften in Goettingen. (1973) pp. 31–42
Shafarevich was a member of the editorial board of the magazine Nash Sovremennik and in 1991–1992 of the editorial board of Den of Alexander Prokhanov, which was banned in October 1993 following the 1993 Russian constitutional crisis and later reopened under the title Zavtra. In 1994, he joined the "All-Russian National Right Wing Centre", led by Mikhail Astafyev.
In Russophobia, he argued in the essay that great nations experience periods in their history of reformist elitist groups ('small nations') having values that differ fundamentally from the values of the majority of the people but gaining the upper hand in the society. In Shafarevich's opinion, the role of such a 'small nation' in Russia was played by a small group of intelligentsiya, dominated by Jews, "who were full of hatred against traditional Russian way of life and played an active role in the terrorist regimes of Vladimir Lenin and Joseph Stalin".
Its publication led to a request by the United States National Academy of Sciences (NAS) to Shafarevich to resign his membership,Warren E. Leary, "Alleging Bias, Science Group Urges Russian to Quit," The New York Times, July 29, 1992. 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 explained that Russophobia is not antisemitic. Shafarevich also noted that since NAS enlisted him without his request or knowledge, delisting him was its internal matter. Nevertheless, when the United States invaded Iraq, Shafarevich faxed his resignation. "The Steklov Legacy", Ulf Persson, Baltic Worlds'', Pages 34–38, Vol 1, 2011
Accusations of antisemitism continued and involved Shafarevich's other publications. Semyon Reznik targets the Russophobia essay for factual inaccuracies: Shafarevich misassigned Jewish ethnicity to a number of non-Jews involved in the execution of Nicholas II, repeated the false assertion of graffiti in Yiddish at the murder site and suggested that Shafarevich's phrase "Nicholas II was shot specifically as the Tsar, and this ritual act drew a line under an epoch in Russian history" – is read by some as a blood libel. (An accusation which ignores the remainder of Shafarevich's sentence: "so it can only be compared with the execution of Charles I in England or of Louis XVI in France".) Aron Katsenelinboigen wrote that Shafarevish's work "lives up to the best traditions of antisemitic propaganda".Aron J. Katsenelinboigen, The Soviet Union: Empire, Nation, and System (New Brunswick, New Jersey: 1990), page 176. http://aronkatsenelinboigen.net/Downloads/SovietUnion_empire_nation_system.htm
Later, Shafarevich expanded on his views in his book Three Thousand-Year-Old Mystery in which he further claimed that Jews effectively marginalise and exclude non-Jews in all types of intellectual endeavors. The work was published in Russian in 2002; an introductory section explains the relationship with the Russophobia essay, explaining that the essay developed from an appendix to an intended work of wider scope, which he started writing in samizdat. http://shafarevich.voskres.ru/02.htm
In 2005, Shafarevich was amongst the signatories of the Letter of 5000.
The issue of Shafarevich's alleged antisemitism has been the subject of a 2009 doctoral thesis at the University of Helsinki, which was later turned into a book in which the author, Krista Berglund, stated that Shafarevich's views have been misconstrued as antisemitic.Reviews of The Vexing Case of Igor Shafarevich: Bjørn Ditlef Nistad (2010), Nordisk Østforum (in Norwegian), ; Roman Murawski, ; John J. Watkins (2012),
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