**Mykhailo Pilipovich Krawtchouk** was a Soviet Ukrainian mathematician who worked on differential and integral equations.

- The form used here "Krawtchouk" is the spelling used in the papers which he wrote in French.
- Krawtchouk then studied at the St Vladimir University in Kyiv and obtained his first degree in 1914.
- The First World War broke out shortly after Krawtchouk graduated and, because of problems at Kyiv University it was evacuated to Saratov.
- Krawtchouk, however, chose to move to Moscow.
- Bolshevik power was soon firmly established and Krawtchouk returned to Kyiv.
- For two years Krawtchouk taught in a number of different institutions until the outbreak of the civil war.
- During this stormy period Krawtchouk was headmaster at a country school not far from Kyiv.
- It was in 1920 that Krawtchouk wrote his 96-page handwritten book Geometry for seven-year labour schools.
- Krawtchouk's contacts with other mathematicians were extremely valuable, particularly those with Jacques Hadamard, David Hilbert, Richard Courant and Francesco Tricomi.
- In 1929 Krawtchouk published his most famous work, Sur une généralisation des polynômes d'Hermite Ⓣ(On a generalisation of Hermite polynomials).
- In this paper he introduced a new system of orthogonal polynomials now known as the Krawtchouk polynomials, which are polynomials associated with the binomial distribution.
- In March 2021, MathSciNet lists 112 papers with 'Krawtchouk' in the title, 88 of these having 'Krawtchouk polynomials' in the title.
- These polynomials belong to the class of orthogonal polynomials with discrete variables and were introduced by the Ukrainian mathematician M Krawtchouk in 1929.
- The content of original works by Krawtchouk devoted to this topic is described in detail here.
- A survey of the further developments and applications of Krawtchouk polynomials is provided.
- Although most references today are to Krawtchouk polynomials, his mathematical work was very wide and, despite his early death, he was the author of around 180 articles on mathematics.
- And the students of Mikhail Filippovich, even after his death, will remember not only the beauty of the ideas that were presented in Krawtchouk's lectures, but also the beauty of his Ukrainian speech.
- In 1929 Krawtchouk was elected a full member of the Ukrainian Academy of Sciences.
- As part of the punishment imposed on him, Krawtchouk was stripped of his membership of the Ukrainian Academy of Sciences and his exile was to be spent at the Kolyma camp in northeastern Siberia, one of the two most notorious of the Corrective Labour Camps.
- As was typical of such events, Krawtchouk was written out of history at this time as if he had never existed.
- In September 1992 the First International M Krawtchouk Conference was held in the Ukraine.
- Inasmuch as the binomial distribution can be considered as a limit of the hypergeometric, this system generalises the Krawtchouk polynomials.

Born 27 September 1892, Chovnitsy, (now Kivertsi) Ukraine. Died 9 March 1942, Kolyma, Siberia, USSR.

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Origin Ukraine

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