**Mark G Krein** was a Soviet mathematician who worked in functional analysis, operator theory, classical analysis and representation theory.

- This was also highly significant for Krein's subsequent career, for discrimination against Jews in the Ukraine was bad and, by misfortune for Krein, was particularly bad in Odessa where he lived from the age of 17.
- Krein showed a remarkable talent for mathematics at a young age.
- However, Krein never completed his undergraduate degree for he left his home in Kiev when he was 17 years old and ran away to Odessa.
- Despite the lack of an undergraduate degree, his talents were clearly visible to the mathematicians at Odessa University and, in 1926, Krein was accepted for doctoral studies under Chebotaryov.
- Krein therefore began his doctoral studies well aware of the difficulties of the time.
- Krein completed his doctorate at Odessa in the following year and remained on the staff at the university building up one of the most important centres for functional analysis research in the world.
- Kolmogorov had laid the foundations for the study of extremal problems in 1935 and Krein began to work on extremal problems for the class of differentiable periodic functions.
- In 1941 Krein had to leave Odessa when the university was evacuated as the German armies advanced.
- Not only was Krein dismissed but the whole of the functional analysis school at Odessa was closed down.
- Potapov, who had been one of Krein's non-Jewish students, tried hard to influence the university authorities to reverse their decisions.
- Krein was not reinstated, however, but held the chair of theoretical mechanics at Odessa Marine Engineering Institute from 1944.
- Although the 1940s must have been difficult times for Krein, his mathematical research did not suffer.
- Among other important work, Krein wrote eight papers on harmonic analysis and representation theory in the 1940s.
- From 1954 until his retirement Krein occupied the chair of theoretical mechanics at the Odessa Civil Engineering Institute.
- During the 1940s and 1950s there were many unsuccessful attempts to have Krein and his students reinstated at Odessa University but all attempts failed.
- During the many years of very active research Krein had around him a group of very active mathematicians although this group was based more on an informal arrangement than that of a proper research group.
- This group provided him with strong support, frequently meeting in Krein's own house.
- Livsic, again like Krein, did return to Odessa, teaching at the Hydrometerological Institute until 1957 and forming part of Krein's unofficial research group in Odessa.
- Despite the support of those around him, Krein did have to work at a mathematical disadvantage in one sense, however, for he was not allowed to travel abroad and so was unable to attend international conferences that many mathematicians feel to be almost essential for someone so pre-eminent at an international level.
- International recognition came to Krein despite his inability to visit centres of mathematical research around the world.
- Krein received many other honours, but perhaps the most prestigious award made to him was the Wolf Prize in Mathematics in 1982.
- Krein brought the full force of mathematical analysis to bear on problems of function theory, operator theory, probability and mathematical physics.
- A profound intrinsic unity and close interlacing of general abstract and geometrical ideas with concrete and analytical results and applications and characteristic of Krein's work.
- Despite a life of persecution, in which he often feared arrest, Krein remained enthusiastic, friendly and kind, showing great mathematical generosity towards his students and colleagues.

Born 3 April 1907, Kiev, Russian Empire (now Kyiv, Ukraine). Died 17 October 1989, Odessa, Ukranian SSR.

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Origin Ukraine, Prize Wolf

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive