Nachman Aronszajn (26 July 1907 – 5 February 1980) was a

Polish American Polish Americans () are Americans who either have total or partial Polish ancestry, or are citizens of the Republic of Poland. There are an estimated 8.81 million self-identified Polish Americans, representing about 2.67% of the U.S. population, ...

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 ...

. Aronszajn's main field of study was

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series ( ...

, where he systematically developed the concept of

reproducing kernel Hilbert space In functional analysis, a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional. Specifically, a Hilbert space H of functions from a set X (to \mathbb or \mathbb) is ...

. He also contributed to

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

Life

Ashkenazi Jew Ashkenazi Jews ( ; also known as Ashkenazic Jews or Ashkenazim) form a distinct subgroup of the Jewish diaspora, that Ethnogenesis, emerged in the Holy Roman Empire around the end of the first millennium Common era, CE. They traditionally spe ...

, Aronszajn received his Ph.D. from the

University of Warsaw The University of Warsaw (, ) is a public university, public research university in Warsaw, Poland. Established on November 19, 1816, it is the largest institution of higher learning in the country, offering 37 different fields of study as well ...

, in 1930, in

Poland Poland, officially the Republic of Poland, is a country in Central Europe. It extends from the Baltic Sea in the north to the Sudetes and Carpathian Mountains in the south, bordered by Lithuania and Russia to the northeast, Belarus and Ukrai ...

Stefan Mazurkiewicz Stefan Mazurkiewicz (25 September 1888 – 19 June 1945) was a Polish mathematician who worked in mathematical analysis, topology, and probability. He was a student of Wacław Sierpiński and a member of the Polish Academy of Learning (''PAU''). ...

was his thesis advisor. He also received a Ph.D. from

Paris University The University of Paris (), known metonymically as the Sorbonne (), was the leading university in Paris, France, from 1150 to 1970, except for 1793–1806 during the French Revolution. Emerging around 1150 as a corporation associated with the ca ...

, in 1935; this time

Maurice Fréchet Maurice may refer to: *Maurice (name), a given name and surname, including a list of people with the name Places * or Mauritius, an island country in the Indian Ocean * Maurice, Iowa, a city * Maurice, Louisiana, a village * Maurice River, a t ...

was his thesis advisor. He joined the

Oklahoma State University Oklahoma State University (informally Oklahoma State or OSU) is a public land-grant research university in Stillwater, Oklahoma, United States. The university was established in 1890 under the legislation of the Morrill Act. Originally known ...

faculty, but moved to the

University of Kansas The University of Kansas (KU) is a public research university with its main campus in Lawrence, Kansas, United States. Two branch campuses are in the Kansas City metropolitan area on the Kansas side: the university's medical school and hospital ...

in 1951 with his colleague

Ainsley Diamond Ainsley (also spelt Ainsleigh) is both a unisex given name and a surname and place name. It is derived from words meaning hermitage and clearing (Old English "anne" ("alone, solitary") or ānsetl ("hermitage") + lēah ("woodland, clearing")). ...

after Diamond, a

Quaker Quakers are people who belong to the Religious Society of Friends, a historically Protestant Christian set of denominations. Members refer to each other as Friends after in the Bible, and originally, others referred to them as Quakers ...

, was fired for refusing to sign a newly instituted loyalty oath.. Aronszajn retired in 1977. He was a Summerfield Distinguished Scholar from 1964 to his death.

Work

He introduced, together with

Prom Panitchpakdi A promenade dance or prom is a formal dance party for graduating high school students at the end of the school year. Students participating in the prom will typically vote for a ''prom king'' and ''prom queen''. Other students may be honored ...

injective metric space In metric geometry, an injective metric space, or equivalently a hyperconvex metric space, is a metric space with certain properties generalizing those of the real line and of L∞ distances in higher- dimensional vector spaces. These properties c ...

s under the name of "hyperconvex metric spaces". Together with Kennan T. Smith, Aronszajn offered proof of the Aronszajn–Smith theorem. Also, the existence of

Aronszajn trees In set theory, an Aronszajn tree is a tree of uncountable height with no uncountable branches and no uncountable levels. For example, every Suslin tree is an Aronszajn tree. More generally, for a cardinal ''κ'', a ''κ''-Aronszajn tree is a tree o ...

was proven by Aronszajn;

Aronszajn line In mathematical set theory, an Aronszajn line (named after Nachman Aronszajn) is a linear ordering of cardinality \aleph_1 which contains no subset order-isomorphic to * \omega_1 with the usual ordering * the reverse of \omega_1 * an uncountable s ...

s, also named after him, are the

lexicographic ordering In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a ...

s of Aronszajn trees. He also made a contribution to the theory of

. The Moore–Aronszajn theorem is named after him.

References

External links

Nachman Aronszajn on Scientific Commons

– personal papers of Nachman Aronszajn, 1951–1977 * {{DEFAULTSORT:Aronszajn, Nachman 1907 births 1980 deaths American people of Polish-Jewish descent Mathematical analysts Polish emigrants to the United States Warsaw School of Mathematics 20th-century American mathematicians University of Kansas faculty Oklahoma State University faculty University of Warsaw alumni Academics from Warsaw University of Paris alumni