This is a most unusual book that addresses the discrimination against Jews in Soviet universities during the 1970s and 1980s. It is divided into three parts, preceded by a preface "From the Editor" by M. Shifman, now Professor of Physics at the University of Minnesota.

The first part consists of the answers to all the questions of both the Mekh-Mat (Department of Mechanics and Mathematics) examination at Moscow State University, and, for comparison, the solutions to the Year 2000 International Mathematical Olympiad. These solutions were all done by Ilan Vardi, a mathematician working in France, who does not speak Russian, and has never been in Russia. Vardi has written two essays on the various problems that are included. This material occupies the first 106 pages of a 210 page book.

Part II consists of articles by Kanevsky and Senderov (with mathematical comments by Vardi) and by Vershik and also by Shen documenting the discrimination against Jews in the Mekh-Mat examination in the 1970s and 1980s. In fact, Kanevsky (as a graduate of Moscow University) participated in 1978-1982 in the "Jewish People's University" (see below), was arrested for anti-Soviet slander but released in 1985, and moved to Israel in 1987. Senderov was also arrested in 1982 and his essay *Intellectual Genocide* (included here), about the discrminination, was evidence against him. He was sentenced to seven years in hard labor camps to be followed by a five-year exile, but was released in 1987 and lives in Moscow.

Part III, comprising the last 40 pages of the book, is about Bella Abramovna Subbotovskaya who was the founder, together with Senderov and Kanevsky, of the "Jewish People's University" that existed from 1978 to 1982. The idea was simply to give particularly Jewish students the opportunity to study mathematics and physics at an advanced level.

On September 23, 1982, Subbotovskaya was killed by a "careless driver" around midnight in an abandoned street. There were in fact two cars involved and the suspicion persists that Subbotovskaya (aged 44) was murdered by the KGB because of her persistence in safeguarding the "Jewish People's University". Apparently (according to one version) when asked personally by the KGB the purpose of this "underground university", she answered "to give Jewish children the opportunity to learn math." Her funeral was totally silent (several members of the KGB were in the audience), despite the pleas of her aged mother.

The "university" had begun in Subbotovskaya's apartment, but soon swelled in numbers. She, Senderov, and Kanevsky were the only people who paid a cost for its existence. The "People's University" survived Subbotovskaya's death by about a year, but with *perestroika* and the lifting of restrictions on admission of Jews to Moscow University, the problem itself ceased to exist. Since 1988 it has been possible to speak openly and safely about anti-Semitism, and discrimination in entrance exams has ceased. Yet, the mystery of her death (which exists in several versions) remains.

This book is an interesting examination of an unfortunate period in the Soviet Union. It also contains many interesting mathematical problems requiring not much advanced mathematics. It is ironic that the Soviet anti-Semites' distinction of who was "Jewish" was the same as that of the Nazis: one Jewish grandparent.

S. L. Segal is Professor of Mathematics at the University of Rochester. He is the author of Mathematicians under the Nazis , published by Princeton University Press in 2003.