Oswald Veblen

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Oswald Veblen (born June 24, 1880 in Decorah , Iowa , † August 10, 1960 in Brooklin , Maine ) was an American mathematician of Norwegian descent.

Life

In 1903 he received his PhD from the University of Chicago with the thesis A System of Axioms for Geometry . In 1905 he became an employee at Princeton University , from 1910 as a professor of mathematics. In 1917 he joined the army and, as captain and later major, led a team of mathematicians, including Norbert Wiener and the astronomer Forest Ray Moulton , who investigated ballistic problems at the newly founded Aberdeen Proving Ground. Among other things, they calculated shooting tables and developed new calculation methods for external ballistics beyond the classic methods of Francesco Siacci .

In 1926 he became Henry B. Fine Professor of Mathematics at Princeton and in 1928/29 he was in exchange with Godfrey Harold Hardy , who went to Princeton for it, professor at Oxford . In 1932 he was visiting professor at various German universities (Göttingen, Berlin, Hamburg).

From 1932 he was a professor at the newly founded Institute for Advanced Study , which he helped to build. Here he also took care of emigrants who fled Germany from the National Socialists. Albert Einstein , Hermann Weyl and John von Neumann came to the Institute for Advanced Study at that time and contributed significantly to its reputation.

Veblen made valuable contributions in topology , projective geometry and differential geometry , which he turned to in the 1930s under the influence of general relativity. He wrote influential early textbooks on topology and the fundamentals of differential geometry (with Whitehead). He later turned to spinors in the (general) relativity theory (partly with John von Neumann and Abraham H. Taub ) and an extension of the general relativity theory, the projective relativity theory.

The Veblen-Young axiom in projective geometry and the Veblen hierarchy in the theory of large ordinal numbers are named after him . The theorem of Veblen and Young says that projective spaces in three and more dimensions can be constructed as vector spaces over oblique bodies . In a book with JHC Whitehead (1933) he gave the first strict definition of differentiable manifolds.

He criticized Camille Jordan's proof of his curve theorem and gave a new proof.

Veblen was a member of the National Academy of Sciences , Vice President (1915) and President (1923/24) of the American Mathematical Society , whose Colloquium Lecturer he was in 1916 (with lectures on topology). In 1912 he was elected to the American Philosophical Society and in 1923 to the American Academy of Arts and Sciences . In 1928 he was on the council of the London Mathematical Society during his stay in England . He received honorary doctorates from, among others, Oxford (1929), Hamburg, Glasgow, Edinburgh and Oslo. He was a member of the Danish, French, Polish Academies of Science and the Royal Society of Edinburgh and received (like his father) the Norwegian Order of Saint Olav . In 1936 he gave a plenary lecture at the International Congress of Mathematicians in Oslo (Spinors and Projective geometry) and also in Bologna in 1928 (Differential invariants in geometry).

His PhD students include Alonzo Church , James W. Alexander , Harold Hotelling , Robert Lee Moore, and JHC Whitehead .

Veblen, who himself became partially blind in the last few years of his life, also invented some aids for the blind that were expelled by the American blind society. He was married to Elizabeth Richardson, sister of Owen Willans Richardson , since 1908 . The marriage remained childless.

He was a nephew of Thorstein Veblen .

On March 28, 2002 the asteroid (31665) Veblen was named after him.

literature

  • Deane Montgomery : Oswald Veblen , in AMS History of Mathematics, Vol. 1, online here
  • Jim Ritter Geometry as Physics: Oswald Veblen and the Princeton School , in Karl-Heinz Schlote , Martina Schneider (Ed.) Mathematics meets physics: a contribution to their interaction in the 19th and the first half of the 20th century , Harri Deutsch, Frankfurt am Main 2011, pp. 145-180

Fonts

A list of publications is here

  • with WH Bussey: Finite projective geometries, Transactions of the American Mathematical Society, Volume 7, 1906, pp. 241-259
  • Collineations in a finite projective geometry, Transactions of the American Mathematical Society, Volume 8, 1907, pp. 366-368
  • with Joseph Wedderburn : Non-Desarguesian and non-Pascalian geometries, Transactions of the American Mathematical Society, Volume 8, 1907, pp. 379-388
  • with John Wesley Young : Projective geometry, 2 volumes, Ginn a. Co., Boston and London, 1910, 1918
  • Analysis Situs, Colloquium Lectures of the American Mathematical Society 1922, 1931 (topology textbook)
  • The invariants of quadratic differential forms, Cambridge University Press 1927 (Riemannian geometry)
  • with John Henry Constantine Whitehead : The foundations of differential geometry, Cambridge University Press 1933
  • Projective relativity theory, results of mathematics and its border areas, Springer Verlag, 1933
  • with TY Thomas: The geometry of paths , Transactions of the AMS, Volume 25, 1924, pp. 551-608
  • Remarks on the Foundations of Geometry , Bull. Amer. Math. Soc., Vol. 31, 1925, pp. 121-141
  • Hilbert's Foundations of Geometry , The Monist, Volume 13, 1902, pp. 303-309
  • A system of axioms for geometry , Transactions AMS, Volume 5, 1904, pp. 343-384
  • with JHC Whitehead: A Set of Axioms for Differential Geometry , Proc. Nat. Acad. Sci., Vol. 17, 1931, pp. 551-561 (Erratum, p. 660)
  • Geometry of two component spinors , Proc. Nat. Acad. Sci., Vol. 19, 1933, pp. 462, 503
  • with John von Neumann, Taub: The Dirac equation in projective relativity , Proc. Nat. Acad. Sci., Vol. 20, 1934, pp. 383-388

Web links

Individual evidence

  1. ↑ In two dimensions there are non-Desarguesche planes that provide counterexamples for the theorem.
  2. ^ Veblen, Young A Set of Assumptions for Projective Geometry , American Journal of Mathematics, Volume 30, 1908, pp. 347-380, and Veblen / Young Projective Geometry , 1910, 1917
  3. ^ Veblen Theory on Plane Curves in Non-Metrical Analysis Situs , Transactions of the American Mathematical Society, Volume 6, 1905, pp. 83-98
  4. ^ Mathematics Genealogy Project
personal data
SURNAME Veblen, Oswald
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH June 24, 1880
PLACE OF BIRTH Decorah , Iowa , USA
DATE OF DEATH August 10, 1960
Place of death Brooklin , Maine