Aleksandr Danilovich Aleksandrov

Aleksandr Danilovich Aleksandrov (Russian: Алекса́ндр Дани́лович Алекса́ндров, alternative transliterations: Alexandr or Alexander (first name), and Alexandrov (last name)) (August 4, 1912 – July 27, 1999), was a Soviet/Russian mathematician, physicist, philosopher and mountaineer.

Scientific career

Aleksandr Aleksandrov was born in 1912 in Volyn village, Ryazan Oblast.^[1] He graduated from the Department of Physics of Leningrad State University. His advisors there were Vladimir Fock, a physicist, and Boris Delaunay, a mathematician. In 1933 Aleksandrov worked at the State Optical Institute (GOI) and at the same time gave lectures at the Department of Mathematics and Mechanics of the University. He completed his Ph.D. in 1935 at the University and later in 1937 — a D.Sc. dissertation. He became a professor at the University, while also working at LOMI, the Leningrad Department of the Steklov Mathematical Institute (now PDMI, Petersburg Department of the Mathematical Institute). In 1951 he became a member of the Communist Party. Appointed the rector of the university in 1952, Aleksandrov remained in this position until 1964. In 1946 he became a corresponding member, and in 1964 — a full member of the USSR Academy of Sciences. Since 1975 he was also a member of the Accademia Nazionale dei Lincei.

Aleksandr Aleksandrov should not be confused with Pavel Alexandrov, another mathematician at the Steklov Institute.

From 1964 to 1986 Aleksandrov lived in Novosibirsk, heading the Laboratory of Geometry of the Institute of Mathematics of the Siberian Division of the USSR Academy of Sciences, teaching at Novosibirsk State University. In 1986 he returned to Leningrad (now Saint Petersburg) to head the geometry laboratory at LOMI.

Awards

Partial list of the awards, medals, and prizes of Aleksandrov:

• Stalin Prize (1942)
• Lobachevsky International Prize (1951)
• Euler Gold Medal of the Russian Academy of Sciences (1992)

One of many orders that he was awarded was given to him in 1990 for his opposition to Lysenkoism, which deviated from standard theories of genetics; it was embraced during Stalin's rule but later considered a pseudoscience.

Works by Aleksandrov

Aleksandrov wrote a multitude of books, scientific papers, textbooks for various levels (schools to universities). He also wrote non-mathematical papers, memoirs about famous scientists, and philosophical essays dealing with the moral values of science.

A full bibliography is available in [1]. Selected works are available in English:

• Alexandrov, A.D. Combinatorial topology. Volumes I-III. 1947 Translated by Horace Komm in 1956. Graylock LCCN 56-13930

• Alexandrov, A.D. Selected works. Part 1: Selected scientific papers. Amsterdam: Gordon and Breach Publishers. x, 322 p. (1996). ISBN 2-88124-984-1

• Alexandrov, A.D. Selected works. Intrinsic geometry of convex surfaces. Vol. 2. Boca Raton, FL: Chapman & Hall/CRC. xiii, 426 p. (2005). ISBN 0-415-29802-4

• Alexandrov, A.D. Convex polyhedra. Springer: Berlin. xi, 539 p. (2005). ISBN 3-540-23158-7

Students of Aleksandrov

• I. Liberman, S. Olovianishnikoff, P. Kostelyanetz — all the three of them died on the battlefields of the World War II
• A. Pogorelov — from Kharkov
• A. Yusupov — from Bukhara
• Students from the Aleksandrov Leningrad period (ordered by the time of joining the seminars): Yu. Borisov, V. Zalgaller, Yu. Reshetnyak, I. Bakelman, Yu. Volkov, A. Zamorzaev, S. Bogacheva (who later married Aleksandrov), Yu. Borovskii, R. Pimenov
• Sobchuk and Starokhozyayev — from Ukraine
• G. Rusiyeshvili — from Georgia (country)
• B. Frank and H. Frank — from Germany
• Yu. Burago, V. Kreinovich; Grigori Perelman
• Moved from Alma-Ata after Aleksandrov's lecture tour there: M. Kvachko, V. Ovchinnikova, E. Sen'kin
• Stayed in Alma-Ata: A. Zilberberg, V. Strel'cov, D. Yusupov
• Novosibirsk students: A. Guts, A. Kuz'minykh, A. Levichev, and A. Shaidenko.

Both in St. Petersburg and Novosibirsk Aleksandrov participated in joint research also with some of his students' students. Several of them became his co-authors: V. Berestovskii, A. Verner, N. Netsvetaev, I. Nikolaev, and V. Ryzhik.

His last Ph.D. student was Grigori Perelman who proved Thurston's geometrization conjecture in 2002/2003 which contains the Poincaré conjecture as a special case.

Mountaineering

Aleksandrov became attracted to alpinism under the influence of his advisor Boris Delaunay. In the summer of 1937, after defending his D.Sc.,

…together with I. Chashnikov he makes a first climb to the Chotchi summit, and with K. Piskaryov performs a climb of Bu-Ul'gen via the western wall (one of the first wall climbs in the history of the Soviet alpinism).
[…] In 1940  he participates in a record-making traversal[…] He manages, almost by a miracle, to stop the fall of A. Gromov, who had fallen along with a snow shelf. It was with this traversal that Aleksandrov completed the alpinist sports master requirements. The German-Soviet War postponed awarding him this honorary title until 1949.

(See A.D. Aleksandrov in the mountains (an alpinist biography), Savvon S.M., [1], p.182–183)

During his rectorship, Aleksandrov also advanced the mountaineering sport activities in the university, actively participating in the climbs.

The fiftieth birthday was celebrated by Aleksandrov in the mountains with his friends. On that day he made a solo first climb of an

…unnamed peak 6222 m (Shakhdarinsk ridge, Pamir), that as he suggested was then named "The peak of the Leningrad university."

During later years Aleksandrov didn't undertake climbs due to health problems, yet he never ceased dreaming of climbs. Finally, in 1982, the year of his seventieth birthday, he, together with K. Tolstov, performs in Tian Shan his last climb, of the Panfilov Peak…

(same source)

See also

• CAT(k) space
• Cauchy's theorem
• Alexandrov theorem
• Aleksandrov–Rassias problem
• Alexandrov–Fenchel inequality
• Alexandrov's uniqueness theorem

References

1. Академик Александр Данилович Александров. Воспоминания. Публикации. Материалы. (Academician Aleksandr Danilovich Aleksandrov. Recollections. Publications. Biographical materials, in Russian). Editors: G.M. Idlis and O.A. Ladyzhenskaya. Moscow, Nauka publishing house, 2002.
2. Yu. F. Borisov, "On the 90th anniversary of the birth of A.D. Aleksandrov (1912–1999)", Russ. Math. Surv., 2002, 57 (5), 1017–1031.
3. Yu. F. Borisov, V.A. Zalgaller, S.S. Kutateladze, O.A. Ladyzhenskaya, A.V. Pogorelov, Yu. G. Reshetnyak, "К 90-летию со дня рождения А.Д. Александрова (1912–1999)", Uspekhi Mat. Nauk, 2002, 57 (5), 169–181.
4. Liyun Tan and Shuhuang Xiang, On the Aleksandrov-Rassias problem and the Hyers-Ulam-Rassias stability problem, Banach Journal of Mathematical Analysis, 1(1)(2007), 11–22.
5. A.M. Vershik, "Alexander Danilovich as I knew him (in Russian).",St. Petersburg University, No. 3-4 (2004), 36–40.
6. Shuhuang, Xiang, On the Aleksandrov-Rassias problem for isometric mappings, Functional Equations, Inequalities and Applications, Kluwer Acad. Publ., Dordrecht, 2003, pp. 191–221.

External links

• O'Connor, John J.; Robertson, Edmund F., "Aleksandr Danilovich Aleksandrov", MacTutor History of Mathematics archive, University of St Andrews . (with additional photos)
• Aleksandr Danilovich Aleksandrov at the Mathematics Genealogy Project (incomplete students listing as of December 2004)
• Review of Alexandrov's "Convex Polytopes" – by R. Connelly, published at the Mathematical Reviews.
• Alexandr Danilovich Alexandrov – biography, reminiscences, references (from St. Petersburg Mathematical Society website)
• Alexandrov Par Excellence - by S.S. Kutateladze
• Alexandrov of Ancient Hellas - by S.S. Kutateladze
• Author profile in the database zbMATH