Veniamin Fyodorovich Kagan (russian: Вениами́н Фёдорович Ка́ган; 10 March 1869 – 8 May 1953) was a Russian and Soviet mathematician and expert in

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

. He is the maternal grandfather of mathematicians

Yakov Sinai Yakov Grigorevich Sinai (russian: link=no, Я́ков Григо́рьевич Сина́й; born September 21, 1935) is a Russian-American mathematician known for his work on dynamical systems. He contributed to the modern metric theory of dy ...

and

Grigory Barenblatt Grigory Isaakovich Barenblatt (russian: Григо́рий Исаа́кович Баренблат; 10 July 1927 – 22 June 2018) was a Russian mathematician. Education Barenblatt graduated in 1950 from Moscow State University, Department of Me ...

Biography

Kagan was born in Shavli, in the

Kovno Governorate Kovno Governorate ( rus, Ковенская губеpния, r=Kovenskaya guberniya; lt, Kauno gubernija) or Governorate of Kaunas was a governorate ('' guberniya'') of the Russian Empire. Its capital was Kaunas (Kovno in Russian). It was form ...

of the

Russian Empire The Russian Empire was an empire and the final period of the Russian monarchy from 1721 to 1917, ruling across large parts of Eurasia. It succeeded the Tsardom of Russia following the Treaty of Nystad, which ended the Great Northern War ...

(now

Šiauliai Šiauliai (; bat-smg, Šiaulē; german: Schaulen, ) is the fourth largest city in Lithuania, with a population of 107,086. From 1994 to 2010 it was the capital of Šiauliai County. Names Šiauliai is referred to by various names in different la ...

Lithuania Lithuania (; lt, Lietuva ), officially the Republic of Lithuania ( lt, Lietuvos Respublika, links=no ), is a country in the Baltic region of Europe. It is one of three Baltic states and lies on the eastern shore of the Baltic Sea. Lithuania ...

) in 1869, to a poor

Lithuanian Jewish Lithuanian Jews or Litvaks () are Jews with roots in the territory of the former Grand Duchy of Lithuania (covering present-day Lithuania, Belarus, Latvia, the northeastern Suwałki and Białystok regions of Poland, as well as adjacent ...

family. In 1871 his family moved to Yekaterinoslav (now

Dnipro Dnipro, previously called Dnipropetrovsk from 1926 until May 2016, is Ukraine's fourth-largest city, with about one million inhabitants. It is located in the eastern part of Ukraine, southeast of the Ukrainian capital Kyiv on the Dnieper Rive ...

), where he grew up. Kagan entered the Imperial Novorossiya University in

Odesa Odesa (also spelled Odessa) is the third most populous city and municipality in Ukraine and a major seaport and transport hub located in the south-west of the country, on the northwestern shore of the Black Sea. The city is also the administrati ...

in 1887, but was expelled for revolutionary activities in 1889. He was put on

probation Probation in criminal law is a period of supervision over an offender, ordered by the court often in lieu of incarceration. In some jurisdictions, the term ''probation'' applies only to community sentences (alternatives to incarceration), such ...

and sent back to Yekaterinoslav. He studied mathematics on his own and in 1892 passed the state exam at

Kyiv University Kyiv University or Shevchenko University or officially the Taras Shevchenko National University of Kyiv ( uk, Київський національний університет імені Тараса Шевченка), colloquially known as KNU ...

. In 1894 Kagan moved to

Saint Petersburg Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...

where he continued his studies with

Andrey Markov Andrey Andreyevich Markov, first name also spelled "Andrei", in older works also spelled Markoff) (14 June 1856 – 20 July 1922) was a Russian mathematician best known for his work on stochastic processes. A primary subject of his research lat ...

and Konstantin Posse. They tried to help him to obtain an academic position, but Kagan's Jewish background was an obstacle. Only in 1897 was he allowed to become a

dozent The title of docent is conferred by some European universities to denote a specific academic appointment within a set structure of academic ranks at or below the full professor rank, similar to a British readership, a French " ''maître de conf ...

at the Imperial Novorossiya University, where he continued to work until 1923. His students in the

theory of relativity The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...

class he taught in 1921-22 included Nikolai Papaleksi, Alexander Frumkin and

Igor Tamm Igor Yevgenyevich Tamm ( rus, И́горь Евге́ньевич Тамм , p=ˈiɡərʲ jɪvˈɡʲenʲjɪvitɕ ˈtam , a=Ru-Igor Yevgenyevich Tamm.ogg; 8 July 1895 – 12 April 1971) was a Soviet physicist who received the 1958 Nobel Prize in ...

. Kagan worked at

Moscow State University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

where he held the Geometry Chair from 1923 till 1952. In 1924 he joined

Otto Schmidt Otto Yulyevich Shmidt, be, Ота Юльевіч Шміт, Ota Juljevič Šmit (born Otto Friedrich Julius Schmidt; – 7 September 1956), better known as Otto Schmidt, was a Soviet scientist, mathematician, astronomer, geophysicist, statesm ...

in drawing up plans for the

Great Soviet Encyclopedia The ''Great Soviet Encyclopedia'' (GSE; ) is one of the largest Russian-language encyclopedias, published in the Soviet Union from 1926 to 1990. After 2002, the encyclopedia's data was partially included into the later ''Bolshaya rossiyskaya e ...

Mathematical work

He published over 100 mathematical papers in different parts of

, particularly on

hyperbolic geometry In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P ...

and on

Riemannian geometry Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a ''Riemannian metric'', i.e. with an inner product on the tangent space at each point that varies smoothly from point to point ...

. He received the

Stalin Prize Stalin Prize may refer to: * The State Stalin Prize in science and engineering and in arts, awarded 1941 to 1954, later known as the USSR State Prize The USSR State Prize (russian: links=no, Государственная премия СССР, ...

in 1943. He founded the science publisher ''Mathesis'' in Odesa. He was a director of the mathematics and natural sciences department of the Great Soviet Encyclopedia. He wrote a definitive biography of

Nikolai Lobachevsky Nikolai Ivanovich Lobachevsky ( rus, Никола́й Ива́нович Лобаче́вский, p=nʲikɐˈlaj ɪˈvanəvʲɪtɕ ləbɐˈtɕɛfskʲɪj, a=Ru-Nikolai_Ivanovich_Lobachevsky.ogg; – ) was a Russian mathematician and geometer, ...

and edited his collected works (5 volumes, 1946–1951). Kagan's doctoral students include

Viktor Wagner Viktor Vladimirovich Wagner, also Vagner (russian: Виктор Владимирович Вагнер) (4 November 1908 – 15 August 1981) was a Russian mathematician, best known for his work in differential geometry and on semigroups. Wagner w ...

and Isaak Yaglom.

Trivia

* He's a minor character in ''The Fourth Prose'' (1930) by

Osip Mandelstam Osip Emilyevich Mandelstam ( rus, Осип Эмильевич Мандельштам, p=ˈosʲɪp ɨˈmʲilʲjɪvʲɪtɕ mənʲdʲɪlʲˈʂtam; – 27 December 1938) was a Russian and Soviet poet. He was one of the foremost members of the A ...

External links

* *
Biography
– in the "Kstati" newspaper (in Russian) {{DEFAULTSORT:Kagan, Veniamin 1869 births 1953 deaths 19th-century mathematicians from the Russian Empire 20th-century Russian mathematicians Mathematicians from the Russian Empire People from Šiauliai People from Kovno Governorate Moscow State University faculty Odesa University alumni Taras Shevchenko National University of Kyiv alumni Stalin Prize winners Recipients of the Order of the Red Banner of Labour Lithuanian Jews Soviet Jews Soviet mathematicians Geometers Differential geometers