This is the second edition of a book first published in 1992, just after the collapse of the Soviet Union. The book collects reflections and memoirs about mathematics in Moscow during the Soviet years, a period that was hardly "golden" for Russians in general. But mathematics in Moscow flourished during this time, particularly in the 1930s and then in the 1950s and 1960s. This was partly due to the fact that mathematics was a "safe" topic, free from political interference, and partly due to the presence of a few great and inspiring mathematicians who created a school and a tradition.
The articles collected here mostly focus on mathematicians. There are articles on Kolmogorov (two of them) and on Markov, and two other articles are basically collections of stories about mathematicians. Many photographs are included. Several articles have an autobiographical thrust. One article, by A. B. Sossinsky, tells the story of his return from the West to Russia, and ends with a discussion of the dangers of the early 1990s. He asks whether perestroika would "destroy what the KGB could not" by allowing a massive "brain drain" to the West. The answer to that seems to have been yes.
In 1992, a group of scholars had just established the Independent University of Moscow, an attempt to preserve, and maybe regenerate, the Moscow mathematical tradition. IUM is mentioned briefly in the original preface, but it was clearly too recent a development to feature in the articles. The mood seemed somber. The past was golden; the future was uncertain.
The new edition adds a new preface and one new article, in addition to a list of errata and an index of names. (One can easily tell the new material, since it is in a slightly different typeface.) The index of names and the errata are certainly very welcome. The new preface notes both the huge number of mathematicians who emigrated and the fact that many of them have preserved some sort of tie to Russia, often by visiting frequently and giving lectures.
The new article, by V. M. Tikhomirov, is something of a disappointment. Rather than focus on the period since 1992, Tikhomirov has written an overview of mathematics in Moscow since the 1920s. That is well and good, but it means that very little space is given to updating the story. The phrase "in the 15 years since the collapse of the USSR" occurs on page 281, and the article ends on page 283. Those two pages contain a little bit of information, but not much. In particular, we learn little about the fortunes of IUM except for a list of those who have spoken at its "Globus" seminar.
One infers from the tone of Tikhomirov's article that these have been hard years for mathematics at Moscow. One cannot read this book without admiring what was achieved during those golden years, nor without a bracing awareness of how easy it was for all that to come to and end.
Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME. He is the editor of MAA Reviews.