Photograph of Oswald Veblen.
Oswald Veblen

Overview

Oswald Veblen (24 June 1880 in Decorah, Iowa - 10 August, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905.

Life

He went to school in Iowa City. He did his undergraduate studies at the University of Iowa, where he received an A.B. in 1898, and Harvard University, where he was awarded a second B.A. in 1900. For his graduate studies, he went to study mathematics at the University of Chicago, where he obtained a Ph.D. in 1903. His dissertation, A System of Axioms for Geometry was written under the supervision of E. H. Moore.

Veblen taught mathematics at Princeton University from 1905 to 1932. In 1926, he was named Henry B. Fine Professor of Mathematics. In 1932, he helped organize the Institute for Advanced Study in Princeton, resigning his professorship to become the first professor at the Institute that same year. He kept his professorship at the Institute until he was made emeritus in 1950.

Veblen died in Brooklin, Maine, in 1960 at age 80. After his death the American Mathematical Society created an award in his name, called the Oswald Veblen Prize in Geometry. It is awarded every three years, and is the most prestigious award in recognition of outstanding research in geometry.

Accomplishments

During his career, Veblen made important contributions in topology and in projective and differential geometries, including results important in modern physics. He was involved in overseeing the World War II work that produced the pioneering ENIAC electronic digital computer.

Books by O. Veblen

* Projective geometry with John Wesley Young (Ginn and co., 1910-1918) * Introduction to infinitesimal analysis; functions of one real variable with N. J. Lennes (John Wiley & Sons, 1907)
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* 1907 Born Philadelphia, PA, USA * 1927 BA, University of Pennsylvania * 1930 PhD, University of Pennsylvania, 1930 under Howard Mitchell, who had studied under Oswald Veblen at Princeton * 1930/31 at Cal Tech with E.T. Bell * 1931 married Clara Skaler * 1931/32 at Cambridge with G.H...

That biography says:

James Waddell Alexander II (September 19, 1888 – September 23, 1971) was an important topologist of the pre-WWII era and part of an influential Princeton topology elite, which included Oswald Veblen, Solomon Lefschetz, and others. He was one of the first members of the Institute for Advanced Study (1933–1951), and also a professor at Princeton University (1920–1951)...

That biography says:

...He remained at Cambridge following his doctorate, then was a Rockefeller Fellow at Princeton University where he worked with Hermann Weyl, Oswald Veblen, and Solomon Lefschetz. In 1936 he moved to the University of Toronto, becoming a professor in 1948...

That biography says:

...In 1915-16, he taught philosophy at Harvard, then worked for General Electric and wrote for the Encyclopedia Americana. When World War I broke out, Oswald Veblen invited him to work on ballistics at the Aberdeen Proving Ground in Maryland. Thus Wiener, an eventual pacifist, wore a uniform 1917-18...

That biography says:

...in 1929 at Princeton University. His thesis, titled The representation of projective spaces, was written under the direction of Oswald Veblen in 1930. While in Princeton, he also worked with Solomon Lefschetz....

That biography says:

...Mauchly's proposal for building an electronic digital computer using vacuum tubes, many times faster and more accurate than the differential analyzer for computing ballistics tables for artillery, caught the interest of the Moore School's Army liaison, Lieutenant Herman Goldstine, and on April 9, 1943 was formally presented in a meeting at Aberdeen Proving Ground to director Colonel Leslie Simon, Oswald Veblen, and others. A contract was awarded for Moore School's construction of the proposed computing machine, which would be named ENIAC, and Eckert was made the project's chief engineer...

That biography says:

...Bliss was a Preceptor at Princeton, 1905-08, joining a strong group of young mathematicians that included Luther P. Eisenhart, Oswald Veblen, and Robert Lee Moore. While at Princeton he was also an associate editor of the Annals of Mathematics...

That biography says:

...H., 1983, "In pursuit of the finite division algebra theorem and beyond: Joseph H M Wedderburn, Leonard Dickson, and Oswald Veblen," Archives of International History of Science 33: 274–99. *--------, 1991, "A study in group theory: Leonard Eugene Dickson's Linear groups," Mathematical Intelligencer 13: 7–11...

This biography says:

...For his graduate studies, he went to study mathematics at the University of Chicago, where he obtained a Ph.D. in 1903. His dissertation, A System of Axioms for Geometry was written under the supervision of E. H. Moore....

That biography says:

...At Chicago, Moore supervised 31 doctoral dissertations, including those of George Birkhoff, Leonard Dickson, Robert Lee Moore (no relation), and Oswald Veblen. Birkhoff and Veblen went on to forge and lead the first-rate departments at Harvard and Princeton, respectively...

That biography says:

...(In 1944 he managed to reduce the dimension of the ambient space by 1, so long as n > 2, by a technique that has come to be known as the "Whitney trick.") This basic result shows that manifolds may be treated intrinsically or extrinsically, as we wish. The intrinsic definition had only been published a few years earlier in the work of Oswald Veblen and J.H.C. Whitehead. These theorems opened the way for much more refined studies: of embedding, immersion and also of smoothing, that is, the possibility of having various smooth structures on a given topological manifold...

That biography says:

...During that time he travelled extensively, visiting Rome and working with Federigo Enriques, then in 1934 Princeton University, where he attended lectures by James W. Alexander, Luther P. Eisenhart, Solomon Lefschetz, Oswald Veblen, Joseph Wedderburn, and Hermann Weyl....

That biography says:

...Moore (no relation), who headed the Department of Mathematics at the University of Chicago, and whose research interests were on the foundations of geometry, heard of Robert's feat, he arranged for a scholarship that would allow Robert to study for a doctorate at Chicago. Oswald Veblen supervised Moore's 1905 thesis, titled Sets of Metrical Hypotheses for Geometry....

That biography says:

...He co-authored a paper with Alexander Aleksandrovich Friedmann of Petersburg and another with Václav Hlavatý. He interacted with Oswald Veblen of Princeton University, and corresponded with Wolfgang Pauli on spin space. (See H. Goenner, Living Review link below.)...
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