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The Case of Academician Nikolai Nikolaevich Luzin

Sergei S. Demidov and Boris V. Lëvshin, editors
American Mathematical Society
Publication Date: 
Number of Pages: 
History of Mathematics 43
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
P. N. Ruane
, on

In the Soviet Union of the mid-1930s, an internal dispute within a public institution, or even a neighbourly disagreement in a remote rural village, could result in persons being accused of anti-Soviet activities. The official agency for ‘political policing’ was the NKVD, which was empowered to impose sentences without trial. The practice of the NKVD was such that, when a ‘case’ was brought to their notice, the accused was more or less certain to be consigned to a state labour camp (gulag). Millions of Soviet citizens (including artists, dramatists, academics and party members) disappeared from public life due to these political purges.

One particular mathematician who was removed from academic life and died in a remote prison was D. F. Egorov (1869–1931). Egorov was partly known for his work on triply orthogonal systems and potential surfaces, and he made major contributions to differential geometry. But his mathematical eminence didn’t shield him from the Bolshevik zeal and spiteful collusion of some of his colleagues. In fact, the charges against him were based on the claim that he was a ‘reactionary supporter of religious beliefs, a dangerous influence on students, and a person who mixes mathematics and mysticism’. Nikolai Luzin, one of his ablest students, apparently took no part in this plot and eventually succeeded Egorov as head of the Moscow school of mathematics.

Events like this took place at a time when public institutions were being reorganized with the aim of removing all traces of their Imperial origins. Consequently, the Russian Academy of Sciences became the USSR Academy of Sciences, and universities were amalgamated and re-named. In particular, the mathematics school of St Petersburg (led by P. L. Chebyshev) was merged with the Moscow school that had developed under leadership of Egorov and Luzin. The resulting amalgam then became known as the Soviet Mathematical School. This took place within the intimidating ethos of the Stalinist era, and the combination of these circumstances intensified institutional micropolitics. From this setting arose the trauma endured in 1936 by the Russian mathematician Nikolai Luzin (1883–1950)

The account of Luzin’s life-threatening experience of 1936 is central to this book by Demidov and Lëvshin; so a description of his formative and later years is not one of its aims. In fact, the story begins in the late 1920s when Luzin was already co-leader of the Moscow school of Mathematics. He, along with Egorov, had overseen the growth of a notable research group at Moscow University. Among his students were P. S. Aleksandrov, Pavel Urysohn and A. N. Kolmogorov. Most of the research came under the banner of ‘the theory of functions of a real variable’. By all accounts, Luzin became a charismatic personality whose dominance was such that the Moscow school became known as ‘Luzitania’.

While Luzin was leader of the Soviet Mathematical School, powerful young mathematicians (like Aleksandrov) came to regard him as a barrier to the advancement of their academic careers. Representing the old guard, and resentful of Luzin’s status, was E. Y. Kol’man — a Czech immigrant steeped in Bolshevik political dogma.

The attack on Luzin began with an anonymously printed article in Pravda accusing him of anti-Soviet activities. It asserted that his major publications appeared in foreign journals, and that he claimed for himself the results of his own students (Novikov and Suslin, for example). It was also said that Luzin schemed to exclude ‘truly talented scholars’ from the Academy of Sciences and that he was a ‘scion of the supposedly tsarist Moscow Mathematical School whose philosophy was said to be that of the Black Hundreds. The arch conspirator in this tale of deceit and betrayal was Kol’man who, compared to the other players in this dramatic tale, was a mathematical nonentity. His power emanated from his contacts at senior levels of the communist party, who regarded Kol’man as being endowed with true Bolshevik zeal and loyalty.

This book, very well translated from Russian by Roger Cooke, provides convincing evidence of the fact that it was Kol’man who was the unnamed author of several scurrilous newspaper articles labelling Luzin as an anti-Soviet conspirator. The case against Luzin was brought before the USSR Academy of Sciences, which had the power to refer the matter to the NKVD. Mathematicians of high calibre (notably P. S. Aleksandrov) colluded with the principal accusers and took part in the grilling of Luzin over the five full-day hearing.

The historical context for these events is provided in this book by Demidov and Lëvshin, the first edition of which appeared in St Petersburg in 1999. Included within its 363 pages is an outline of the innovatory nature of Russian mathematics in the first 30 years of the 20th century. The core of the book consists of the minutes of the meetings of the five-day hearing during which Luzin was virtually fighting for his life. Indeed, the wealth of documentary evidence provided by the authors creates the impression that they have left no stone unturned in their quest to reveal the awful machinations that beset Nikolai Luzin in 1936. Read all about it in this gripping account of a wrongly persecuted mathematician.


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Peter Ruane is retired from the field of mathematics education, which involved the training of primary and secondary school teachers. His postgraduate study included of algebraic topology and differential geometry, with applications to superconductivity.