Veblen, Oswald

▪ American mathematician
born June 24, 1880, Decorah, Iowa, U.S.
died August 10, 1960, Brooklin, Maine

      American mathematician who made important contributions to differential geometry and the early development of topology. Many of his contributions found application in atomic physics and the theory of relativity.

      Veblen graduated from the University of Iowa in 1898. He spent a year at Harvard University before moving to the University of Chicago (Ph.D., 1903). He taught mathematics at Princeton University (1905–32) and was appointed a professor at the Institute for Advanced Study, Princeton, New Jersey, when it opened in 1932. Veblen played a key role in the formation and research direction of the school of mathematics at the institute. He became professor emeritus in 1950.

      From the beginning of his research career, Veblen was interested in the foundations of mathematics (mathematics, foundations of). His thesis concerned the axiomatization of Euclidean geometry and had implications in the study of mathematical logic (logic). This began his study of axiom systems in projective geometry, which culminated in the highly acclaimed Projective Geometry, 2 vol. (1910–18), in collaboration with John Wesley Young.

      Veblen's Analysis Situs (1922) was the first book to cover the basic ideas of topology systematically. It was his most influential work and for many years the best available topology text. Veblen also laid the foundations for topological research at Princeton.

      Soon after the discovery of general relativity, Veblen turned to differential geometry and took a leading part in the development of generalized affine and projective geometry. His work The Invariants of Quadratic Differential Forms (1927) is distinguished by precise and systematic treatment of the basic properties of Riemannian geometry. In collaboration with his brilliant student John Henry Whitehead, Veblen extended the knowledge of the Riemann metric for more general cases in The Foundations of Differential Geometry (1932).

      Veblen's belief that “the foundations of geometry must be studied both as a branch of physics and as a branch of mathematics” quite naturally led him to the study of relativity and the search for a geometric structure to form a field theory unifying gravitation and electromagnetism. With respect to the Kaluza-Klein field theory, which involved field equations in five-dimensional space, he provided the first physical interpretation of the fifth coordinate. By regarding the coordinate as a gauge variable (see gauge theory), he was able to interpret the theory as one involving four-dimensional space-time. In connection with this contribution, Veblen provided a new treatment of spinors (expressions used to represent electron spin) that he summarized in Projektive Relativitätstheorie (1933; “Projective Relativity Theory”).

      Veblen was notable in his efforts to aid German mathematicians displaced by the Nazi regime. These activities, combined with his tremendous influence in encouraging and developing young mathematicians, represent a contribution equal to that of his mathematical innovations.

Additional Reading
William Aspray, “Oswald Veblen and the Origins of Mathematical Logic at Princeton,” in Thomas Drucker (ed.), Perspectives on the History of Mathematical Logic (1991), pp. 54–70.

* * *

Universalium. 2010.

Look at other dictionaries:

  • Oswald Veblen — Born June 24, 1880(1880 06 24) Decorah, Iowa, U.S. Died August 10, 1960(1960 08 10) (aged 80) …   Wikipedia

  • Veblen — may refer to* Thorstein Veblen, the economist and sociologist * A Veblen good, named after Thorstein Veblen * Oswald Veblen, the mathematician (and Thorstein s nephew) * Veblen, South Dakota …   Wikipedia

  • Veblen — puede referirse a: Thorstein Veblen, un economista y sociólogo. Bien de Veblen, un concepto ideado por Thorstein Veblen. Oswald Veblen, un matemático, sobrino de Thorstein Veblen (Dakota del Sur), una localidad estadounidense. Esta página de… …   Wikipedia Español

  • VEBLEN (O.) — VEBLEN OSWALD (1880 1960) Mathématicien américain né à Decorah (Iowa) et mort à Brooklin (Maine). Veblen apporta d’importantes contributions en géométrie différentielle et en topologie, et plusieurs de ses travaux eurent des applications en… …   Encyclopédie Universelle

  • Oswald Veblen — Pour les articles homonymes, voir Veblen. Oswald Veblen Naissance 24 juin 1880 Decorah, Iowa (États Unis) Décès 10 août 1960 …   Wikipédia en Français

  • Veblen — Cette page d’homonymie répertorie les différents sujets et articles partageant un même nom. Thorstein Veblen (1857 1929), économiste et sociologue, qui mit en évidence l « effet Veblen » Oswald Veblen (1880 1960), mathématicien… …   Wikipédia en Français

  • Oswald Veblen — (* 24. Juni 1880 in Decorah, Iowa; † 10. August 1960 in Brooklyn, Maine) war ein amerikanischer Mathematiker norwegischer Abstammung. Im Jahr 1903 hat er an der University of Chicago mit der Arbeit A System of Axioms for Geometry promoviert. 1905 …   Deutsch Wikipedia

  • Veblen — bezeichnet Thorstein Veblen (* 30. Juli 1857; † 3. August 1929), US amerikanischer Ökonom und Soziologe Oswald Veblen (* 24. Juni 1880; † 10. August 1960), US amerikanischer Mathematiker Veblen (South Dakota), US amerikanische Stadt Siehe auch:… …   Deutsch Wikipedia

  • Oswald (given name) — Oswald as given name The name Oswald meaning Osmeans god and Weald means rule. The name Oswald means divine ruler Oswald Avery (1877–1955), Canadian American physician, medical researcher and molecular biologist Oswald Achenbach (1827–1905),… …   Wikipedia

  • Veblen —   [ veblən],    1) Oswald, amerikanischer Mathematiker, * Decorah (Iowa) 24. 6. 1880, ✝ Brooklin (Me.) 10. 8. 1960; ab 1910 Professor an der Princeton University; arbeitete 1929 32 in Oxford und Oslo und war danach Professor am Institute for… …   Universal-Lexikon

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.