Veniamin Fyodorovich Kagan (; 9 March 1869 – 8 May 1953) was a Russian and Soviet mathematician and expert in non-Euclidean

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

. He is the maternal grandfather of mathematicians

Yakov Sinai Yakov Grigorevich Sinai (; born September 21, 1935) is a Russian–American mathematician known for his work on dynamical systems. He contributed to the modern metric theory of dynamical systems and connected the world of deterministic (dynam ...

and

Grigory Barenblatt Grigory Isaakovich Barenblatt (; 10 July 1927 – 22 June 2018) was a Russian mathematician. Education Barenblatt graduated in 1950 from Moscow State University, Department of Mechanics and Mathematics. He received his Ph.D. in 1953 from Moscow S ...

Biography

Kagan was born in Shavli, in the

Kovno Governorate Kovno Governorate was an administrative-territorial unit (''guberniya'') of the Russian Empire, with its capital in Kovno (Kaunas). It was formed on 18 December 1842 by Tsar Nicholas I of Russia, Nicholas I from the western part of Vilna Govern ...

of the

Russian Empire The Russian Empire was an empire that spanned most of northern Eurasia from its establishment in November 1721 until the proclamation of the Russian Republic in September 1917. At its height in the late 19th century, it covered about , roughl ...

(now

Šiauliai Šiauliai ( ; ) is a city in northern Lithuania, the List of cities in Lithuania, country's fourth largest city and the List of cities in the Baltic states by population, sixth largest city in the Baltic States, with a population of 112 581 in 202 ...

Lithuania Lithuania, officially the Republic of Lithuania, 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, bordered by Latvia to the north, Belarus to the east and south, P ...

) in 1869, to a poor

Lithuanian Jewish {{Infobox ethnic group , group = Litvaks , image = , caption = , poptime = , region1 = {{flag, Lithuania , pop1 = 2,800 , region2 = {{flag, South Africa , pop2 = 6 ...

family. In 1871 his family moved to Yekaterinoslav (now

Dnipro Dnipro 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 River, Dnipro River, from which it takes its name. Dnipro is t ...

), where he grew up. Kagan entered the

Imperial Novorossiya University The Odesa I.I.Mechnykov National University (), often referred to as Odesa National University ( ONU, ), located in Odesa, Ukraine, is one of that country's major state-sponsored universities, named after the scientist Élie Metchnikoff (1845- ...

Odesa Odesa, also spelled Odessa, is the third most populous List of cities in Ukraine, city and List of hromadas of Ukraine, municipality in Ukraine and a major seaport and transport hub located in the south-west of the country, on the northwestern ...

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 offence (law), offender, ordered by the court often in lieu of incarceration. In some jurisdictions, the term ''probation'' applies only to community sentences (alternatives to incar ...

and sent back to

Yekaterinoslav Dnipro 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 River, Dnipro River, from which it takes its name. Dnipro is t ...

. He studied mathematics on his own and in 1892 passed the state exam at

Kyiv University The Taras Shevchenko National University of Kyiv (; also known as Kyiv University, Shevchenko University, or KNU) is a public university in Kyiv, Ukraine. The university is the third-oldest university in Ukraine after the University of Lviv and ...

. In 1894 Kagan moved to

Saint Petersburg Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland ...

where he continued his studies with

Andrey Markov Andrey Andreyevich Markov (14 June 1856 – 20 July 1922) was a Russian mathematician best known for his work on stochastic processes. A primary subject of his research later became known as the Markov chain. He was also a strong, close to mas ...

and

Konstantin Posse __notoc__ Konstantin Alexandrovich Posse (; September 29, 1847 – August 24, 1928) was a Russian mathematician known for contributions to analysis and in particular approximation theory In mathematics, approximation theory is concerned with ho ...

. 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 term "docent" is derived from the Latin word , which is the third-person plural present active indicative of ('to teach, to lecture'). Becoming a docent is often referred to as habilitation or doctor of science and is an academic qualifica ...

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 physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical ph ...

class he taught in 1921-22 included

Nikolai Papaleksi Nikolai Dmitrievich Papaleksi (, 20 November 1880 – 3 February 1947) was a physicist who pioneered radio technology and radio astronomy in the Soviet Union. He was involved in the discovery of radio wave emission by solar coronae in 1947. Ear ...

Alexander Frumkin Alexander Naumovich Frumkin (; 24 October 1895 – 27 May 1976) was a Soviet Russian electrochemist, member of the Russian Academy of Sciences since 1932, founder of the Russian Journal of Electrochemistry '' Elektrokhimiya'' and receiver o ...

and

Igor Tamm Igor Yevgenyevich Tamm (; 8 July 1895 – 12 April 1971) was a Soviet Union, Soviet physicist who received the 1958 Nobel Prize in Physics, jointly with Pavel Alekseyevich Cherenkov and Ilya Mikhailovich Frank, for their 1934 discovery and demon ...

. Kagan worked at

Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

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

Otto Schmidt Otto Yulyevich Shmidt (born Otto Friedrich Julius Schmidt; – 7 September 1956), better known as Otto Schmidt, was a Soviet scientist, mathematician, astronomer, geophysicist, statesman, and academician. Biography He was born in the town of ...

in drawing up plans for the

Great Soviet Encyclopedia The ''Great Soviet Encyclopedia'' (GSE; , ''BSE'') 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 ''Great Russian Enc ...

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 János Bolyai, Bolyai–Nikolai Lobachevsky, Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For a ...

and on

Riemannian geometry Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as manifold, smooth manifolds with a ''Riemannian metric'' (an inner product on the tangent space at each point that varies smooth function, smo ...

. He received the Stalin Prize 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 (; , ; – ) was a Russian mathematician and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry, and also for his fundamental study on Dirichlet integrals, kno ...

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

Viktor Wagner Viktor Vladimirovich Wagner, also Vagner () (4 November 1908 – 15 August 1981) was a Russian mathematician, best known for his work in differential geometry and on semigroups. Wagner was born in Saratov and studied at Moscow State University, w ...

and

Isaak Yaglom Isaak Moiseevich Yaglom (; 6 March 1921 – 17 April 1988) was a Soviet mathematician and author of popular mathematics books, some with his twin Akiva Yaglom. Yaglom received a Ph.D. from Moscow State University in 1945 as student of Veniami ...

Trivia

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

Osip Mandelstam Osip Emilyevich Mandelstam (, ; – 27 December 1938) was a Russian and Soviet poet. He was one of the foremost members of the Acmeist school. Osip Mandelstam was arrested during the repressions of the 1930s and sent into internal exile wi ...

References

External links

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