Aleksandr Danilovich Aleksandrov
Encyclopedia
Aleksandr Danilovich Aleksandrov ' onMouseout='HidePop("86873")' href="/topics/Transliteration">transliteration
s: Alexandr or Alexander (first name), and Alexandrov (last name)) (August 4, 1912–July 27, 1999), was a Soviet
/Russia
n mathematician
, physicist
, philosopher and mountaineer
.
. His advisors there
were Vladimir Fok, a physicist, and Boris Delaunay
, a mathematician. In 1933 Aleksandrov worked at the State Optical Institute (GOI) and at the same time gave lecture
s 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 entered to 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.
Since 1964 and until 1986 Aleksandrov lived in Novosibirsk
, heading the Laboratory of Geometry
of the Institute of Mathematics of the Siberia
n 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.
s, and prizes of Aleksandrov:
One of many order
s that he was awarded was given to him in 1990 for his active defense of genetics
during the period when it was declared a pseudoscience
in the Soviet union
and fought against (see Lysenkoism
).
s for various levels (schools to universities). He also wrote non-mathematical papers, memoir
s about famous scientists, and philosophical essay
s dealing with the moral values of science.
A full bibliography is available in[1] . Selected works are available in English:
Both in St. Petersburg and in Novosobirsk Aleksandrov was doing joint research also with some of his students' students. Several of them became his co-authors: V. Berestovskii, A. Verner, V. Gol'dshtein, S. Krushkal', S. Kutateladze, N. Necvetaev, I. Nikolaev, V. Ryzhik.
His last Ph.D. student was Grigori Perelman
, who in 2002 made a breakthrough in the proof of Thurston's geometrization conjecture, which contains the Poincaré conjecture
as a special case.
. In the summer of 1937, after defending his D.Sc.,
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
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…
Transliteration
Transliteration is a subset of the science of hermeneutics. It is a form of translation, and is the practice of converting a text from one script into another...
s: Alexandr or Alexander (first name), and Alexandrov (last name)) (August 4, 1912–July 27, 1999), was a Soviet
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
/Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
, philosopher and mountaineer
Mountaineering
Mountaineering or mountain climbing is the sport, hobby or profession of hiking, skiing, and climbing mountains. While mountaineering began as attempts to reach the highest point of unclimbed mountains it has branched into specialisations that address different aspects of the mountain and consists...
.
Scientific career
Aleksandrov graduated from the Department of Physics of Leningrad State UniversitySaint Petersburg State University
Saint Petersburg State University is a Russian federal state-owned higher education institution based in Saint Petersburg and one of the oldest and largest universities in Russia....
. His advisors there
were Vladimir Fok, a physicist, and Boris Delaunay
Boris Delaunay
Boris Nikolaevich Delaunay or Delone was one of the first Russian mountain climbers and a Soviet/Russian mathematician, and the father of physicist Nikolai Borisovich Delone....
, a mathematician. In 1933 Aleksandrov worked at the State Optical Institute (GOI) and at the same time gave lecture
Lecture
thumb|A lecture on [[linear algebra]] at the [[Helsinki University of Technology]]A lecture is an oral presentation intended to present information or teach people about a particular subject, for example by a university or college teacher. Lectures are used to convey critical information, history,...
s at the Department of Mathematics and Mechanics of the University. He completed his Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
in 1935 at the University and later in 1937 — a D.Sc. dissertation. He became a professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
at the University, while also working at LOMI
Lomi
Lomi or Pancit Lomi is a Filipino-Chinese dish made with a variety of thick fresh egg noodles of about a quarter of an inch in diameter. Because of its popularity at least in the eastern part of Batangas, there are as many styles of cooking lomi as there are eateries, panciterias or restaurants...
, the Leningrad Department of the Steklov Mathematical Institute (now PDMI, Petersburg Department of the Mathematical Institute
St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences
The St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences for "Петербургское отделение Математического института", Petersburg Department of the Mathematical Institute) is a mathematical research institute in St. Petersburg, part of the Russian Academy of...
). In 1951 He entered to Communist Party
Communist Party of the Soviet Union
The Communist Party of the Soviet Union was the only legal, ruling political party in the Soviet Union and one of the largest communist organizations in the world...
. Appointed the rector
Rector
The word rector has a number of different meanings; it is widely used to refer to an academic, religious or political administrator...
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
Academician
The title Academician denotes a Full Member of an art, literary, or scientific academy.In many countries, it is an honorary title. There also exists a lower-rank title, variously translated Corresponding Member or Associate Member, .-Eastern Europe and China:"Academician" may also be a functional...
of the USSR Academy of Sciences
Russian Academy of Sciences
The Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....
. 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.
Since 1964 and until 1986 Aleksandrov lived in Novosibirsk
Novosibirsk
Novosibirsk is the third-largest city in Russia, after Moscow and Saint Petersburg, and the largest city of Siberia, with a population of 1,473,737 . It is the administrative center of Novosibirsk Oblast as well as of the Siberian Federal District...
, heading the Laboratory of Geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
of the Institute of Mathematics of the Siberia
Siberia
Siberia is an extensive region constituting almost all of Northern Asia. Comprising the central and eastern portion of the Russian Federation, it was part of the Soviet Union from its beginning, as its predecessor states, the Tsardom of Russia and the Russian Empire, conquered it during the 16th...
n Division of the USSR Academy of Sciences, teaching at Novosibirsk State University
Novosibirsk State University
Novosibirsk State University was founded in May 1959 in the USSR by Soviet academicians Mikhail Alekseevich Lavrentiev, Sergei Lvovich Sobolev and Sergey Alekseyevich Khristianovich in a program of establishing a Siberian branch of the USSR Academy of Sciences...
. In 1986 he returned to Leningrad (now Saint Petersburg
Saint Petersburg
Saint Petersburg is a city and a federal subject of Russia located on the Neva River at the head of the Gulf of Finland on the Baltic Sea...
), to head the geometry laboratory at LOMI.
Awards
Partial list of the awards, medalMedal
A medal, or medallion, is generally a circular object that has been sculpted, molded, cast, struck, stamped, or some way rendered with an insignia, portrait, or other artistic rendering. A medal may be awarded to a person or organization as a form of recognition for athletic, military, scientific,...
s, and prizes of Aleksandrov:
- Stalin Prize (1942)
- Lobachevsky International PrizeLobachevsky MedalThe Lobachevsky Prize, awarded by the Russian Academy of Sciences, and the Lobachevsky Medal, awarded by the Kazan State University, are mathematical awards in honor of Nikolai Ivanovich Lobachevsky.-History:...
(1951) - Euler Gold Medal of the Russian Academy of SciencesRussian Academy of SciencesThe Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....
(1992)
One of many order
Order (decoration)
An order or order of merit is a visible honour, awarded by a government, dynastic house or international organization to an individual, usually in recognition of distinguished service to a nation or to humanity. The distinction between orders and decorations is somewhat vague, except that most...
s that he was awarded was given to him in 1990 for his active defense of genetics
Genetics
Genetics , a discipline of biology, is the science of genes, heredity, and variation in living organisms....
during the period when it was declared a pseudoscience
Pseudoscience
Pseudoscience is a claim, belief, or practice which is presented as scientific, but which does not adhere to a valid scientific method, lacks supporting evidence or plausibility, cannot be reliably tested, or otherwise lacks scientific status...
in the Soviet union
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
and fought against (see Lysenkoism
Lysenkoism
Lysenkoism, or Lysenko-Michurinism, also denotes the biological inheritance principle which Trofim Lysenko subscribed to and which derive from theories of the heritability of acquired characteristics, a body of biological inheritance theory which departs from Mendelism and that Lysenko named...
).
Works by Aleksandrov
Aleksandrov wrote a multitude of books, scientific papers, textbookTextbook
A textbook or coursebook is a manual of instruction in any branch of study. Textbooks are produced according to the demands of educational institutions...
s for various levels (schools to universities). He also wrote non-mathematical papers, memoir
Memoir
A memoir , is a literary genre, forming a subclass of autobiography – although the terms 'memoir' and 'autobiography' are almost interchangeable. Memoir is autobiographical writing, but not all autobiographical writing follows the criteria for memoir set out below...
s about famous scientists, and philosophical essay
Essay
An essay is a piece of writing which is often written from an author's personal point of view. Essays can consist of a number of elements, including: literary criticism, political manifestos, learned arguments, observations of daily life, recollections, and reflections of the author. The definition...
s dealing with the moral values of science.
A full bibliography is available in
- 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 German-Soviet War
- A. PogorelovAleksei PogorelovAleksei Vasil'evich Pogorelov , was a Soviet and Ukrainian mathematician. He was most famous for his contributions to convex and differential geometry...
— from Kharkov - A. Yusupov — from BukharaBukharaBukhara , from the Soghdian βuxārak , is the capital of the Bukhara Province of Uzbekistan. The nation's fifth-largest city, it has a population of 263,400 . The region around Bukhara has been inhabited for at least five millennia, and the city has existed for half that time...
- Students from the Aleksandrov Leningrad period (ordered by the time of joining the seminarSeminarSeminar is, generally, a form of academic instruction, either at an academic institution or offered by a commercial or professional organization. It has the function of bringing together small groups for recurring meetings, focusing each time on some particular subject, in which everyone present is...
s): Yu. Borisov, V. ZalgallerVictor ZalgallerVictor Abramovich Zalgaller is a mathematician in the fields of geometry and optimization. He is best known for his results on convex polyhedra, linear and dynamic programming, isoperimetry, and differential geometry....
, Yu. Reshetnyak, I. Bakelman, Yu. Volkov, A. Zamorzaev, S. Bogacheva (who later married Aleksandrov), Yu. Borovskii, R. Pimenov - Sobchuk and Starokhozyayev — from UkraineUkraineUkraine is a country in Eastern Europe. It has an area of 603,628 km², making it the second largest contiguous country on the European continent, after Russia...
- G. Rusiyeshvili — from Georgia (country)Georgia (country)Georgia is a sovereign state in the Caucasus region of Eurasia. Located at the crossroads of Western Asia and Eastern Europe, it is bounded to the west by the Black Sea, to the north by Russia, to the southwest by Turkey, to the south by Armenia, and to the southeast by Azerbaijan. The capital of...
- B. Frank and H. Frank — from GermanyGermanyGermany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
- Yu. BuragoYuri Dmitrievich BuragoYuri Dmitrievich Burago is a Russian mathematician. He works in differential and convex geometry.- Education and career :Burago studied at Leningrad University, where he obtained his Ph.D. and Habilitation degrees. His advisors were Victor Zalgaller and Aleksandr Aleksandrov.Burago is the head...
, V. Kreinovich; Grigori PerelmanGrigori PerelmanGrigori Yakovlevich Perelman is a Russian mathematician who has made landmark contributions to Riemannian geometry and geometric topology.In 1992, Perelman proved the soul conjecture. In 2002, he proved Thurston's geometrization conjecture... - 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. Guc, A. Kuz'minykh, A. Levichev, A. Shaydenko
Both in St. Petersburg and in Novosobirsk Aleksandrov was doing joint research also with some of his students' students. Several of them became his co-authors: V. Berestovskii, A. Verner, V. Gol'dshtein, S. Krushkal', S. Kutateladze, N. Necvetaev, I. Nikolaev, V. Ryzhik.
His last Ph.D. student was Grigori Perelman
Grigori Perelman
Grigori Yakovlevich Perelman is a Russian mathematician who has made landmark contributions to Riemannian geometry and geometric topology.In 1992, Perelman proved the soul conjecture. In 2002, he proved Thurston's geometrization conjecture...
, who in 2002 made a breakthrough in the proof of Thurston's geometrization conjecture, which contains the Poincaré conjecture
Poincaré conjecture
In mathematics, the Poincaré conjecture is a theorem about the characterization of the three-dimensional sphere , which is the hypersphere that bounds the unit ball in four-dimensional space...
as a special case.
Mountaineering
Aleksandrov became attracted to alpinism under the influence of his advisor Boris DelaunayBoris Delaunay
Boris Nikolaevich Delaunay or Delone was one of the first Russian mountain climbers and a Soviet/Russian mathematician, and the father of physicist Nikolai Borisovich Delone....
. 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)
- (See A.D. Aleksandrov in the mountains (an alpinist biography), Savvon S.M.,
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, PamirPamir MountainsThe Pamir Mountains are a mountain range in Central Asia formed by the junction or knot of the Himalayas, Tian Shan, Karakoram, Kunlun, and Hindu Kush ranges. They are among the world’s highest mountains and since Victorian times they have been known as the "Roof of the World" a probable...
), 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
Tian Shan
The Tian Shan , also spelled Tien Shan, is a large mountain system located in Central Asia. The highest peak in the Tian Shan is Victory Peak , ....
his last climb, of the Panfilov Peak…
-
- (same source)
See also
- CAT(k) spaceCAT(k) spaceIn mathematics, a CAT space is a specific type of metric space. Intuitively, triangles in a CAT space are "slimmer" than corresponding "model triangles" in a standard space of constant curvature k. In a CAT space, the curvature is bounded from above by k...
- Cauchy's theoremCauchy's theorem (geometry)Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy. It states thatconvex polytopes in three dimensions with congruent corresponding faces must be congruent to each other...
- Aleksandrov–Rassias problemAleksandrov–Rassias problemThe theory of isometries in the framework of Banach spaces has its beginning in a paper by Stanisław Mazur and Stanisław M. Ulam in 1932. They proved that each isometry of a normed real linear space onto a normed real linear space is a linear mapping up to translation...
- Alexandrov–Fenchel inequality
External links
(with additional photos) (incomplete students listing as of December 2004)- Review of Alexandrov's "Convex Polytopes" – by R. Connelly, published at the Mathematical ReviewsMathematical ReviewsMathematical Reviews is a journal and online database published by the American Mathematical Society that contains brief synopses of many articles in mathematics, statistics and theoretical computer science.- Reviews :...
. - Alexandr Danilovich Alexandrov – biography, reminiscences, references (from St. Petersburg Mathematical Society website)
- Alexandrov Par Excellence - by S.S. Kutateladze