**Yuri Linnik** was a Ukranian-born mathematician who worked on number theory, probability theory and mathematical statistics.

- After studying at secondary school in Leningrad, Yuri Vladimirovich worked as a laboratory assistant for a year in 1931 before starting his university training.
- However, the German armies were approaching Leningrad and Linnik volunteered to serve in the People's Guard to defend the city.
- Linnik was taken ill with dystrophy, almost certainly the result of malnutrition, and discharged from the army.
- Because of the war, the Mathematical Institute of the USSR Academy of Sciences had been moved from Moscow to Kazan, with the Leningrad branch also evacuated there, so Linnik was sent to Kazan.
- Millions of the citizens died of starvation during the siege, so Linnik, given his poor physical condition, would almost certainly have perished.
- After the siege of Leningrad ended in early 1944, Linnik was able to return from Kazan to Leningrad.
- By the "large sieve", which was Linnik's own term, he meant the operation of eliminating some residue classes modulo ppp from a given set of integers where as ppp increased so, possibly, did the number of classes.
- Linnik's large sieve proved highly significant and was further developed by others including Alfréd Rényi in 1950, Klaus Roth in 1965, Enrico Bombieri in 1965 and Harold Davenport and Heini Halberstam in 1966.
- The large sieve method led Linnik to study Dirichlet's LLL-functions.
- After his early concentration on number theory, from 1947 onwards Linnik embarked on a deep study of probability.
- Later Linnik made major contributions to probability with his work on limit theorems and was the first to use powerful techniques from analysis in mathematical statistics.
- Linnik substantially improved and developed the methods of his predecessors and gave an almost definitive solution of the problem for an inhomogeneous chain with an arbitrary finite number of events.
- Linnik also solved the Behrens-Fisher problem and many other difficult problems of mathematical statistics.
- Also in 1967 Linnik published Leçons sur les problèmes de statistique analytique which came about as the result of a series of lectures he had given in the previous year at the Institut de Statistique of the University of Paris.
- Linnik wrote other important texts including Characterisation Problems in Mathematical Statistics (jointly with A M Kagan and S R Rao) which appeared in Russian in 1972 with an English translation appearing in the following year.
- One has to feel that Linnik did not fully appreciate the strength of his own outstanding talents if he though that others following this route would lead to them making similar breakthroughs.
- As a director of studies, Yuri V Linnik was generous in giving both ideas and advice, always having time for working discussions with his disciples and colleagues.
- An relations with his disciples, Yuri V Linnik was solicitous not only as a teacher, but also as a senior colleague, trying to be helpful also in everyday life, when necessary.
- Linnik received many honours, including being elected to the International Statistical Institute, the Academy of Sciences of the USSR in 1964, and to the Swedish Academy of Sciences.

Born 21 January 1915, Belaya Tserkov, Ukraine. Died 30 June 1972, Leningrad, USSR (now St Petersburg, Russia).

View full biography at MacTutor

Origin Ukraine, Statistics

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive