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William Schieffelin Claytor
William Schieffelin Claytor William Schieffelin Claytor


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In 1929-30 William Waldron Schieffelin Claytor (1908-1967) was the most promising student in the inaugural year of Professor Dudley Weldon Woodard's new graduate mathematics program at Howard University Professor Woodard, fresh from earning his PhD at Penn, recommended Claytor for admission to Penn's Graduate School of Arts and Sciences Woodard's teacher at Penn, Professor John R Kline, agreed to advise Claytor Claytor was a brilliant student He enrolled at Penn in the 1930-31 academic year, won a Harrison Scholarship in Mathematics in his second year, and took the most prestigious award offered at Penn at that time, a Harrison Fellowship in Mathematics, in his third and final year of graduate studies Claytor's dissertation delighted the Penn faculty, for it provided a significant advance in the theory of Peano continua - a branch of point-set topology in which Kline was an expert On Wednesday, 21 June 1933, Penn conferred its PhD on Claytor, who thereby became the third African American in the nation to earn the degree in mathematics When Claytor published his dissertation, he had every reason to expect competing offers from America's leading research universities But in that era of pervasive racial discrimination only a predominantly African American institution, West Virginia State College, welcomed him to its faculty.

In 1934, Dr Claytor published his embedding theorem, which stated, "a Peano continuum K is homeomorphic to a subset of the surface of a sphere if and only if it contains neither a primitive skew curve nor a topological image of either of the Figures 7 or 8" (see illustration at the top of this page: Proceedings of the Eleventh Annual Meeting of the National Association of Mathematicians (1980) Photograph courtesy of the National Association of Mathematicians) The Polish mathematician Casmir Kuratowski had introduced Figures 7 and 8, but Claytor advanced the theory and incorporated it into an effective whole Professional mathematicians began to refer to these Figures as 'Claytor curves' John R Kline continued to mentor Claytor and on his recommendation Claytor obtained a Rosenwald Fellowship in 1937 He spent a year at the University of Michigan, working with Professor RL Wilder and a group of talented topologists.

Claytor developed further his theory on imbeddability, working with Wilder on questions concerning homogeneous continua Despite the support of his colleagues, Michigan failed to offer him a faculty position Friends intervened and opened the possibility of a position at the Institute for Advanced Study in Princeton But something had changed within him and he declined the offer After service in the United States Army during World War II, Claytor renewed his teaching, but ceased his research In 1947, a year after Woodard's retirement, Claytor joined the Howard University faculty, where he remained until taking early retirement in 1965 William Claytor's best years may well have been those he spent in Philadelphia, but his unfulfilled promise was a great disappointment for John R Kline and his generation of colleagues at Penn.



 
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