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# Aleksandr Danilovic Aleksandrov

(4**Aug**

**1912 - 27**

**July**

**1999)**

Aleksandr Danilovic Aleksandrov's father was the headmaster of a secondary school in St Petersburg and his mother was a teacher at the same school. In fact, although he was born in the village of Volyn, he lived in St Petersburg from a very young age. Of course this is not strictly true, since when Aleksandrov was two years old St Petersburg changed its name to Petrograd. Aleksandrov attended school in Petrograd but while he was at school the name of the city in which he lived changed yet again and so by the time he left school in 1928 it was aLeningrad school from which he graduated.

When Aleksandrov left school he did not intend to study mathematics but rather his interests were in physics. Therefore when he entered Leningrad University in 1929 he set out on a theoretical physics course in the Faculty of Physics. In 1930, while still only 18 years of age, he began original work on optics in the Optics Institute. However Aleksandrov was taught mathematics in the Faculty of Physics by B N Delone. Delone's interests in the geometry of numbers and the structure of crystals soon began to attract Aleksandrov at least as much as his work in physics which was supervised by V A Fok.

In 1932 Aleksandrov moved from the Optics Institute to Physics Research Institute of Leningrad University where he worked on the theoretical side of the subject. He graduated with a degree in theoretical physics in 1933 and continued his research, working with two supervisors in Fok and Delone. The influence of these two are clearly seen in Aleksandrov's first few publications which appeared in 1933 and 1934 and represented research largely carried out while he was still an undergraduate.

In 1933 he publishedA theorem on convex polyhedra andAn elementary proof of the existence of a centre of symmetry in a three-dimensional convex polyhedron. Then, in 1934, he published a bookMathematical foundations of the structural analysis of crystals jointly written with Delone and N N Padurov. These first three works were all as a result of his mathematical work with Delone but also in 1934 he published two physics papers on quantum mechanicsOn the calculation of the energy of a bivalent atom by Fok's method and Remark on the commutation rule in Schrödinger's equation. His fourth work in 1934 was on geometry in the area of his first three papers.

While continuing to work at the Physics Research Institute, Aleksandrov began to teach in the Faculty of Mathematics and Mechanics from 1933. Two years later he presented a thesis on geometry for a Master's degree which was on the topic of mixed volumes of convex bodies and he published six papers over the next couple of years on the results of this thesis. This work generalises classical problems in differential geometry. Aleksandrov's doctoral thesis (more of a habilitation thesis) was presented in 1937 and in it he studied the topics of additive set functions and the geometrical theory of weak convergence.

Aleksandrov was appointed as Professor of Geometry at Leningrad University in 1937. He was also appointed to the Steklov Mathematical Institute of the USSR Academy of Sciences which, as a part of the Steklov Institute of Physics and Mathematics had been set up in the early 1920s. In 1934 the Steklov Mathematical Institute had been set up but moved toMoscow and Delone, Aleksandrov's supervisor, had moved with it to head the Algebra Department. In 1940 the Leningrad Branch of the Mathematical Institute was founded and it had among its members Aleksandrov, Kantorovich, Linnik, and Faddeev. However theMoscow part of the Steklov Mathematical Institute was moved toKazan at the beginning of World War II and, in 1942 Aleksandrov went to Kazan to continue his research within the Mathematical Institute.

In 1944 Aleksandrov returned to the University of Leningrad where he was Professor of Geometry. In 1952 he became Rector of the University of Leningrad. It was a period in which he worked hard to recreate the mathematical activity in Leningrad which had been associated with the St Petersburg Mathematical Society.

The St Petersburg Mathematical Society was founded in 1890 and was the third oldest mathematical society inRussia (Moscow founded 1867 and the Kharkov founded 1879 are older). It had ceased to exist in 1917 due to the Revolution, but was recreated after initiatives from Steklov as the Petrograd Physical and Mathematical Society in 1921. Both of Aleksandrov's supervisors, Fok and Delone, played major roles in the Physical and Mathematical Society. However the Society was again closed down due to political pressure. Then Smirnov organised the Leningrad Mathematical Seminar in 1953 which went some way to filling the gap left but both Aleksandrov and Smirnov worked hard to restart the Leningrad Mathematical Society. They succeeded in 1959 when the Leningrad Mathematical Society again began to hold meetings.

In 1964 Aleksandrov leftLeningrad and moved toNovosibirsk where he was appointed as Head of the Department of Geometry of the University of Novosibirsk. He also became Head of the Department of Geometry of the Mathematical Institute of the Siberian Branch of the USSR Academy of Sciences.

In [N V Efimov, V A Zalgaller and A V Pogorelov, Aleksandr Danilovic Aleksandrov (on his fiftieth birthday) (Russian),Uspehi Mat. Nauk**17** (6)(108) (1962), 171-184] and [N V Efimov, V A Zalgaller and A V Pogorelov, Aleksandr Danilovic Aleksandrov (on his fiftieth birthday), ,Russian Math. Surveys**17** (6) (1962), 127-141] Aleksandrov's work in geometry is put into perspective:-[Aleksandrov] approached the differential geometry of surfaces[by extending the notion of the objects studied], extending the class of regular convex surfaces to the class of all convex surfaces ... . In order to solve concrete problems Aleksandrov had to replace the Gaussian geometry of regular surfaces by a much more general theory. In the first place the intrinsic properties(i.e. those properties that appear as a result of measurements carried out on the surface) of an arbitrary convex surface had to be studied, and methods found for the proof of theorems on the connection between intrinsic and exterior properties of convex surfaces. Aleksandrov constructed a theory of intrinsic geometry of convex surfaces on that basis. Because of the depth of this theory, the importance of its applications and the breadth of its generality, Aleksandrov comes second only toGauss in the history of the development of the theory of surfaces.

Aleksandrov's work in physics did not stop in his student days. He published on optics, quantum mechanics, and relativity. He often lectured on the history of mathematical ideas, a topic which greatly fascinated him. In addition he wrote encyclopaedia articles and wrote chapters on methodology.

Finally let us note some of Aleksandrov's interests outside mathematics. He loved mountaineering and in fact it is noted in ([N V Efimov, V A Zalgaller and A V Pogorelov, Aleksandr Danilovic Aleksandrov (on his fiftieth birthday) (Russian), Uspehi Mat. Nauk**17** (6)(108) (1962), 171-184] and [N V Efimov, V A Zalgaller and A V Pogorelov, Aleksandr Danilovic Aleksandrov (on his fiftieth birthday), ,Russian Math. Surveys**17** (6) (1962), 127-141]) that he spent his fiftieth birthday on a mountaineering expedition to Pamir. His other interests, noted in ([P S Aleksandrov, N V Efimov, V A Zalgaller, and A V Pogorelov, Aleksandr Danilovic Aleksandrov (on the occasion of his sixtieth birthday) (Russian),Uspehi Mat. Nauk**28** (2)(170) (1973), 249-253] and [P S Aleksandrov, N V Efimov, V A Zalgaller, and A V Pogorelov, Aleksandr Danilovic Aleksandrov (on the occasion of his sixtieth birthday),Russian Math. Surveys**28** (2) (1973), 225-230]), include questions of education, morals, and other questions of community interest.

Aleksandrov received many awards for his major contributions to geometry. In 1942 he received the State Prize for his work in geometry, and then in 1946 he was elected a Corresponding Member of the USSR Academy of Sciences. In 1951 he received the international Lobachevsky Prize.**Article by: J J O'Connor and E F Robertson**

**Taken from:** http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Aleksandrov_Aleksandr.html