Oswald Veblen Biography

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World of Mathematics on Oswald Veblen

Oswald Veblen is remembered mainly for his contributions to topology and differential and projective geometry, many of which scientists later found useful in atomic physics and relativity. He taught for many years at Princeton University and helped found the university's Institute for Advanced Study (IAS).

Veblen was born in Decorah, Iowa on June 24, 1880, the son of Norwegian immigrants. His father taught physics at the University of Iowa. Veblen attended school in Iowa City, enrolling at the University of Iowa in 1894. He earned a bachelor's degree in 1898 and then worked as a laboratory assistant at the school for a year before transferring to Harvard University. There he completed another BA in 1900 before going on to the University of Chicago for his doctorate, which he earned in 1903. His doctoral thesis was "A System of Axioms for Geometry."

Veblen started his long career at Princeton University in 1905. In 1910 he compiled much of his research into the two-volume Projective Geometry. Critics highlighted the work's expert explanation of the axiomatic method, which would immediately have a strong influence on other algebra and geometry researchers.

Also in 1905, Albert Einstein made public his special theory of relativity, which had a huge impact on Veblen. He began dedicating most of his research efforts to differential geometry, with results that would later lead to important advances in relativity theory and atomic physics.

Kept busy with his teaching duties, the next book Veblen published did not come out until 1922. Analysis Situs was the product of his 1916 Colloquium Lectures to the American Mathematical Society. In the lectures he had discussed this branch of geometry, which concerns the algebraic and numerical measures of geometric figures' "connectivity." Analysis Situs elaborated on and clarified the work of Jules-Henri Poincare, which was pioneering, yet difficult. Veblen's book, the first systematic coverage of the main principles of topology, was so effective in discussing the topic that several generations of mathematicians studied it intensively and considered it the premiere work on topology. It was this book that laid the groundwork for the world-renowned Princeton school of topological research.

Based on his continuing study of Einstein's work, Veblen published a systematic treatment of Riemannian geometry, The Invariants of Quadratic Differential Forms, in 1927. In the academic year 1928-1929, Veblen taught at Oxford University. Aside from that short time, however, he remained at Princeton for his entire career. He helped create the IAS in 1932, becoming a professor there the same year, and was integral to the formation of the Institute's School of Mathematics.

In 1933, Veblen produced two important books. The first, written with student John Henry Constantine Whitehead, was The Foundations of Differential Geometry, which provided the first definition of a differentiable manifold. The second was Projective Relativity Theory. In the latter, demonstrating his mathematical influence on the field of physics, Veblen offered a new treatment of "spinors," which physicists use to depict the spin of electrons.

Becoming professor emeritus at the IAS in 1950, Veblen eventually moved to Brooklyn, Maine. He died there on August 10, 1960. Veblen and his wife had married in 1908.