Igor Shafarevich

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From his early years, Shafarevich made fundamental contributions to several parts of mathematics including algebraic number theory, algebraic geometry and arithmetic algebraic geometry. In particular, in algebraic number theory, the Shafarevich–Weil theorem extends the commutative reciprocity map to the case of Galois groups, which are central extensions of abelian groups by finite groups. 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 rationals. Another development 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 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 elliptic curves 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).

Imagem: Konrad Jacobs, Erlangen, Copyright is MFO · BY-SA · Openverse

Shafarevich came into conflict with the Soviet authorities in the early 1950s but was protected by Ivan Petrovsky, the Rector of Moscow University. He belonged to a group of Pochvennichestvo-influenced dissidents who endorsed the Eastern Orthodox tradition. Shafarevich published a book, The Socialist Phenomenon (French edition 1975, English edition 1980), which was cited by Aleksandr Solzhenitsyn in his 1978 address to Harvard University. 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's book The Socialist Phenomenon, which was published in the US by Harper & Row in 1980, analyzed numerous examples of socialism from ancient times to various medieval heresies and a variety of modern thinkers and socialist states. From those examples, he claimed that all the basic principles of socialist ideology derive from the urge to suppress individualism. The Socialist Phenomenon consists of three major parts: 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 nihilistic and is unconsciously motivated by a death instinct. He concluded that we have the choice of pursuing death or life.

Shafarevich adhered to Russian Orthodox Christianity and incorporated the neo-Platonic views of Eastern Orthodoxy into his understanding of the relation of mathematics and religion. 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.

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 a member of the founding committee of the National Salvation Front. In 1993, he was an unsuccessful candidate for the State Duma with Mikhail Astafyev's Constitutional Democratic Party - Party of Popular Freedom. 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.

Shafarevich's essay Russophobia was expanded into his book Three Thousand-Year-Old Mystery (Трехтысячелетняя загадка) and resulted in accusations of antisemitism. He completed the Russophobia essay in 1982 and it was initially circulated as samizdat. In the Soviet Union, it was first officially published in 1989. At the same time, Shafarevich condemned the methods that were used to screen out applicants of Jewish origin when entering prestigious Moscow universities in the 1970s and early 1980s. 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".