Pavel Samuilovich Urysohn (in Russian: ; 3 February, 1898 – 17 August, 1924) was a

Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

who is best known for his contributions in dimension theory, and for developing Urysohn's metrization theorem and Urysohn's lemma, both of which are fundamental results in

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

. He also constructed what is now called the Urysohn universal space and his name is also commemorated in the terms Fréchet–Urysohn space, Menger–Urysohn dimension and Urysohn integral equation. He and

Pavel Alexandrov Pavel Sergeyevich Alexandrov (), sometimes romanized ''Paul Alexandroff'' (7 May 1896 – 16 November 1982), was a Soviet mathematician. He wrote roughly three hundred papers, making important contributions to set theory and topology. In topol ...

formulated the modern definition of

compactness In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it ...

in 1923.

Biography

Pavel Urysohn was born in

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 1898. His mother died when he was little, and he entered the care of his father and sister. The family moved to

Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

in 1912, where Urysohn completed his secondary education. While still at school, he worked at Shanyavsky University on an experimental project on X-ray radiation and was supervised by Petr Lazarev. At that time, Urysohn’s interests lay predominantly in physics. Urysohn enrolled at the Moscow State University in 1915 and earned his Bachelor of science in 1919. There he attended the lectures of Nikolai Luzin and Dimitri Egorov, which made him turn his attention to mathematics. Between 1919 and 1921, Urysohn completed a doctorate on integral equations under the supervision of Luzin. He then became an assistant professor at Moscow University, and Egorov prompted him to start working in topology. By 1922, Urysohn had given topological definitions to curve, surface, and dimension, and his work attracted the attention of many prominent European mathematicians. In the summers of 1923 and 1924, Urysohn and his friend and fellow mathematician, Pavel Aleksandrov, traveled through France, Holland, and Germany, where they met David Hilbert, Felix Hausdorff, and L. E. J. Brouwer. The three European mathematicians were impressed by Urysohn’s work and expressed their hopes that he would visit them again in subsequent years. Urysohn and Aleksandrov were staying in a cottage in

Brittany Brittany ( ) is a peninsula, historical country and cultural area in the north-west of modern France, covering the western part of what was known as Armorica in Roman Gaul. It became an Kingdom of Brittany, independent kingdom and then a Duch ...

France France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...

, when Urysohn drowned at the age of 26 while swimming off the coast nearby Batz-sur-Mer. Urysohn's sister, Lina Neiman, wrote a memoir about his life and childhood. Not being a mathematician, she included in the book memorial articles about his mathematical works by

, Vadim Efremovich, Andrei Kolmogorov, Lazar Lyusternik, and Mark Krasnosel'skii.

References

20th-century Russian mathematicians Moscow State University alumni Academic staff of Moscow State University Topologists 1898 births 1924 deaths Scientists from Odesa Russian scientists Deaths by drowning in France {{Russia-mathematician-stub