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# Schnirelmann, Lev

(1905–1938), Soviet mathematician who contributed to the calculus of variations, topology, and number theory. Lev Schnirelmann went to Moscow in 1921, aged 16, and immediately enrolled at Moscow University. He was admitted without a formal high school diploma because mathematics professor Nikolai Luzin was impressed by his potential. Soon Schnirelmann became an active member of Luzitania, a group of young and talented mathematicians that formed around their professor. Later this group gave rise to the powerful Moscow mathematical school.

In 1929 Schnirelmann (in collaboration with Lazar Lusternik) began to apply topological methods to the study of closed geodesics. Historically, these problems first appeared in the works of Henri Poincaré on celestial mechanics and were regarded as notoriously difficult. In a series of works, Schnirelmann and Lusternik proved that on every convex surface there always exist three different closed geodesics—in some cases even a continuous family of them. Their conclusion was based on the new topological notion of the “category” of a metric space. Since this pioneering work was first performed, the study of the category has remained at the center of modern algebraic topology.

In 1930, Schnirelmann turned to additive number theory, attacking the Goldbach problem of 1742, which had stated that every integer number is the sum of no more than three prime numbers. Schnirelmann achieved the first breakthrough in this problem, proving that every integer is the sum of a *bounded* number of primes. This result was based on the notion of density of sequence first introduced by Schnirelmann. Later, Ivan Vinogradov proved the Goldbach conjecture for all *sufficiently large* integers. However, there remains a huge gap where only Schnirelmann’s result is known. Schnirelmann’s ideas completely revolutionized additive number theory, and “Schnirelmann’s density” remains the fundamental notion.

Schnirelmann’s other works concern various problems of analysis and topology. In 1929, he was appointed to the chair of mathematics at the Novocherkassk Industrial Institute. Returning to Moscow in 1930, from 1934 on he worked at the Steklov Mathematical Institute of the USSR Academy of Sciences. Schnirelmann committed suicide in September 1938. Sparse evidence indicates that he was an indirect victim of Stalin’s repressions.

## Suggested Reading

Octav Cornea et al., eds., *Lusternik-Schnirelmann Category* (Providence, 2003); Smilka Zdravkovska and Peter Duren, eds., *Golden Years of Moscow Mathematics* (Providence and London, 1993).