Igor Shafarevich was born in 1923, the son of Rostislav Stepanovich and Yulia Yacovlevna. He is generally regarded as one of the leading contemporary mathematicians of Russia. He demonstrated mathematical gifts at an early age a gift which was nurtured by his parents. While still in his teens, he read mathematical treatises independently and at the age of 15 he was reading David Hilbert's celebrated report on the theory of Numbers. This was to have a long-lasting influence on his future mathematical activities. While a youth, he read advanced treatises in mathematics. Feeling uncertain of his understanding of the mathematical concepts, he asked senior mathematicians to test his grasp of the more recondite concepts. In addition, as a youth he was fascinated with history and read avidly in this subject. Indeed, it was a toss-up as to which subject he would pursue. His love of mathematics won out.

He was awarded the Doctor of science degree in 1946 at the age of 21 and became an associate at the Stecklov institute of the USSR Academy of Sciences. In addition, he taught at Moscow University.

His life and career however, are inextricably bound with the political upheaval that befell the Former Soviet Union. In 1972, he became an active participant in the group of dissidents of which Solzhenitsyn was a leading member. As a consequence, he was dismissed from the University of Moscow in 1975. In 1980, he published a book entitled The Socialist Phenomenon. This was an elaboration of his essay which first appeared in th collection titled From under the Rubble. He continued his political involvement by publishing the book entitled Russophobia in 1989. This proved offensive to many readers who saw in it elements of racism and it provoked extensive discussion coupled with censure. He wrote a defense of his right to express his ideas freely.

His mathematical research has been universally recognized. He made major contributions to the inverse problem of Galois theory as well as to class field theory, thereby solving some long outstanding conjectures. More recently he made important advances to algebraic geometry. His books and articles are widely read and acclaimed and indeed his work was recognized abroad by his appointment as a foreign member of the National Academy of Sciences of the USA in 1974.

He is outstanding as a lecturer and teacher and his mathematical writings are praised for their clarity and incisiveness. His students report that their association and supervision by Shafarevich were among the happiest of their professional careers.

Article by: Raymond Ayoub, Penn State University.

September 2009

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