**Mikhail Krawtchouk**'s name, the forms Kravchuk and Krawtschuk also being used. The form used here "Krawtchouk" is the spelling used in the papers which he wrote in French.

Krawtchouk studied at St Vladimir University in Kiev and obtained his first degree in 1914. The First World War broke out shortly after Krawtchouk graduated and because of problems at Kiev University he had to move to Moscow. However, it was a time of severe political problems with one disruption following another for Krawtchouk.

In 1917 the Bolsheviks seized power in St Petersburg and fighting broke out in Moscow. Bolshevik power was soon firmly established and Krawtchouk returned to Kiev. For two years Krawtchouk taught in a number of different institutions until the outbreak of the civil war. This was not an easy period for, in January 1918, an independent Ukrainian state was proclaimed with Kiev as its capital. Red Army troops entered Kiev in the following month.

Later in 1918 an independent Ukraine was again declared in Kiev but there followed a series of struggles between Ukrainian nationalist, White, and Red forces. In November 1919 Kiev was briefly taken by the White armies before being occupied by the Red Army. There was still no peace in Kiev for, in May 1920 the Poles captured Kiev but were driven out in a counterattack. During this stormy period Krawtchouk was headmaster at a country school not far from Kiev.

After working on his doctoral thesis, he was awarded a doctorate for a dissertation *On Quadratic Forms and Linear Transforms* in 1924. In the same year he attended the International Mathematical Congress in Toronto and made contacts with many mathematicians. Four years later he attended the International Mathematical Congress in Bologna.

Krawtchouk's contacts with other mathematicians were extremely valuable, particularly those with Hadamard, Hilbert, Courant and Tricomi. In 1929 Krawtchouk published his most famous work, *Sur une généralisation des polynômes d'Hermite* Ⓣ. 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.

However his mathematical work was very wide and, despite his early death, he was the author of around 180 articles on mathematics. He wrote papers on differential and integral equations, studying both their theory and applications. Other areas he wrote on included algebra (where among other topics he studied the theory of permutation matrices), geometry, mathematical and numerical analysis, probability theory and mathematical statistics. He was also interested in the philosophy of mathematics, the history of mathematics and mathematical education. Krawtchouk edited the first three-volume dictionary of Ukrainian mathematical terminology.

In 1929 Krawtchouk was elected a full member of the Ukrainian Academy of Sciences. He taught at the Kiev Polytechnic Institute (now the National Technical University of Ukraine) where he became professor and was head of the Mathematical

Chair. However, this was a time of new political problems.

At this time political life in the USSR revolved round the exposure and suppression of alleged plotters against the regime. The country was subjected to an vigorous campaign against so-called enemies of the people. There was a series of public trials and in a massive terror campaign against the population as a whole. The worst phase of the terror took place during the period 1937-38 when at least five million people were sent to camps mostly in the Arctic. In 1937 Krawtchouk was accused of being a Polish spy and also a bourgeois nationalist. He was arrested, tried and sentenced to twenty years in prison and five years in exile. 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. He died at the age of 49 in Kolyma, one of the Labour Camps set up by the Gulag.

In March 1992, fifty years after his death, he was restored as a member of the Ukrainian Academy of Sciences. In September 1992 the First International M Krawtchouk Conference was held in the Ukraine. Since then these conferences have been a yearly event.

**Article by:** *J J O'Connor* and *E F Robertson*

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