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

Polish American Polish Americans ( pl, Polonia amerykańska) are Americans who either have total or partial Polish ancestry, or are citizens of the Republic of Poland. There are an estimated 9.15 million self-identified Polish Americans, representing about 2.83 ...

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, structure, space, models, and change. History On ...

. 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 (m ...

, where he systematically developed the concept of

reproducing kernel Hilbert space In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions in which point evaluation is a continuous linear functional. Roughly speaking, this means that if two functions f and g in ...

. He also contributed to

mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...

Life

An Ashkenazi Jew, Aronszajn received his Ph.D. from the

University of Warsaw The University of Warsaw ( pl, Uniwersytet Warszawski, la, Universitas Varsoviensis) is a public university in Warsaw, Poland. Established in 1816, it is the largest institution of higher learning in the country offering 37 different fields o ...

, in 1930, in

Poland Poland, officially the Republic of Poland, is a country in Central Europe. It is divided into 16 administrative provinces called voivodeships, covering an area of . Poland has a population of over 38 million and is the fifth-most populou ...

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

Paris University , image_name = Coat of arms of the University of Paris.svg , image_size = 150px , caption = Coat of Arms , latin_name = Universitas magistrorum et scholarium Parisiensis , motto = ''Hic et ubique terrarum'' (Latin) , mottoeng = Here and a ...

, in 1935; this time

Maurice Fréchet Maurice may refer to: People *Saint Maurice (died 287), Roman legionary and Christian martyr *Maurice (emperor) or Flavius Mauricius Tiberius Augustus (539–602), Byzantine emperor * Maurice (bishop of London) (died 1107), Lord Chancellor and L ...

was his thesis advisor. He joined the

Oklahoma State University Oklahoma (; Choctaw: ; chr, ᎣᎧᎳᎰᎹ, ''Okalahoma'' ) is a state in the South Central region of the United States, bordered by Texas on the south and west, Kansas on the north, Missouri on the northeast, Arkansas on the east, New ...

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, and several satellite campuses, research and educational centers, medical centers, and classes across the state of Kansas. T ...

in 1951 with his colleague Ainsley Diamond after Diamond, a Quaker, 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,

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 ca ...

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 was proven by Aronszajn; Aronszajn lines, 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 ...

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 People from Warsaw University of Paris alumni