Raymond Louis Wilder

Raymond Louis Wilder (born November 3, 1896 in Palmer , Massachusetts , † July 7, 1982 in Santa Barbara , California ) was an American mathematician and mathematics philosopher.

Life

Wilder, who was musically interested in his youth (he played cornet at dance events and the piano in silent film cinemas) studied at Brown University from 1914 , where, after a break in service in the US Navy during World War I , he obtained his master’s degree in actuarial mathematics in 1921. In the same year he married and had four children. In 1923 he received his PhD in Topology (Concerning Continuous Curves) with Robert Lee Moore at the University of Texas at Austin , the first of a long line of PhD students from Moore in Austin. In 1924 he became an assistant professor at Ohio State University and was from 1926 at the University of Michigan at Ann Arbor , where he became a professor in 1947. In 1967 he retired there, but occasionally taught at the University of California at Santa Barbara .

Wilder was Vice President of the American Mathematical Society from 1950 to 1951 , of which he was Gibbs Lecturer in 1969. In 1965/66 he was President of the Mathematical Association of America , whose Distinguished Service Medal he received in 1973. Since 1963 he was a member of the National Academy of Sciences . He received honorary degrees from Brown University and the University of Michigan. In 1950 he gave a plenary lecture at the International Congress of Mathematicians (ICM) in Cambridge (Massachusetts) (The cultural basis of mathematics).

Joseph R. Shoenfield is one of his PhD students .

plant

Wilder initially worked on the topology of point sets (in particular via the Schoenflies program, which revolves around evidence that (n-1) spheres in Euclidean space enclose n balls, and positional invariants of point sets in the plane and on the 2-sphere), but then turned to the algebraic topology. In 1949 his textbook Topology of Manifolds was published . Later he turned to the philosophy of mathematics and its anthropological (Wilder was very interested in Indian culture in the southwest of the USA) and cultural-historical foundations, e.g. B. in his lecture at the ICM 1950 The cultural basis of mathematics and in his book Introduction to the foundations of mathematics (1952). In 1969 his book Evolution of mathematical concepts - an elementary study was published and in 1981 his book Mathematics as a cultural system .

Wilder recognized the importance of generalized manifolds (in the sense of geometric topology) for the expansion of theorems of the Jordan - Schoenflies type from two to higher dimensions. They cannot be generalized directly (counterexample Alexander sphere by J. Alexander in three dimensions). Generalized manifolds form a superordinate framework that allows special properties of topological manifolds (that is, those that are locally homeomorphic to Euclidean spaces) to be discussed, in particular their characterization independently of homeomorphisms. In geometric topology, they are defined as locally compact Hausdorff spaces that are Euclidean neighboring retracts (that is, there is an embedding of the generalized manifold X in one such that X is a retract of an open subset U des ) and also Z homology n -Mannifolds (i.e. the homology groups over in the vicinity of each point are those of where the dimension is). ${\displaystyle \mathbb {R} ^{m}}$ ${\displaystyle \mathbb {R} ^{m}}$ ${\displaystyle \mathbb {Z} }$ ${\displaystyle \mathbb {R} ^{n}}$ ${\displaystyle n}$

Web links

• Literature by and about Raymond Louis Wilder in the catalog of the German National Library
• Literature by and about Raymond Louis Wilder in the WorldCat bibliographic database
• John J. O'Connor, Edmund F. Robertson :  Raymond Louis Wilder. In: MacTutor History of Mathematics archive .
• Wilder Papers at the University of Texas

Individual evidence

1. ↑ D. Repovs, The recognition problem for topological manifolds: a survey, Kodai Math. J., Volume 17, 1994, pp. 538-548