This Mathematical Month - September: A Brief Look at Past Events and Episodes in the Mathematical Community
Monthly postings of vignettes on people, publications, and mathematics to inform and entertain.
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See information on the 2013 Calendar of Mathematical Imagery
Featured Item - Posted here September 2012
September 1910: September 8, 1910, is the date that wrongly appeared on official documents for the birth of Nathan Jacobson. He was actually born on October 5 that year, in the Jewish ghetto of Warsaw, and emigrated to the United States around the age of seven. He attended high school in Columbus, Mississippi, and received a bachelor's degree in mathematics from the University of Alabama. He went on to graduate school at Princeton University, where he received his PhD in 1934, under the direction of Joseph Wedderburn. Jacobson's job opportunities were lessened by the depression as well as by discrimination against Jews, and he had a succession of temporary positions. In 1947, he moved to Yale University, where he was the first Jew to be appointed to a permanent position at that institution. He remained at Yale for the rest of his career. Jacobson's main research contributions were in ring theory. He served as president of the AMS during 1971-72 and of the International Mathematical Union 1972-1974. He received the AMS Steele Prize for Lifetime Achievement in 1998. An obituary appeared in the October 2000 issue of the Notices of the AMS, and there is a biographical sketch on the MacTutor History of Mathematics web site.
September 1994: Dirk Struik celebrated his 100th birthday by giving a lecture at Brown University entitled "Mathematicians I Have Known." Born in Rotterdam in 1894, Struik received his Ph.D. in 1922 and held positions in Europe before joining the faculty of MIT in 1928, at the urging of Norbert Wiener. In his centenary lecture, Struik presented some personal reminiscences about David Hilbert. So inconspicous was Hilbert's presence that "you might take him for a bank teller," Struik said, but his complete command of the field of mathematics made him a formidable figure. Struik's lecture also painted striking portraits of Norbert Wiener and Emmy Noether. In 2000, Struik passed away at the age of 106. [See "Dirk Struik Celebrates his 100th," Notices of the AMS, January 1995; and "Dirk Jan Struik (1894-2000)," Notices of the AMS, June/July 2001.]
September 1956: John Milnor 's paper "On Manifolds Homeomorphic to the Seven-Sphere" appeared in the Annals of Mathematics. This revolutionary paper showed that a given topological manifold can have more than one differentiable structure and thereby brought into focus the distinction between topological, combinatorial, and differentiable manifolds. Together with the seminal work of Whitney and Thom, Milnor's paper sparked the development of a whole new field of mathematics, called differential topology. Within a few years spectacular progress in this field was made by Milnor himself, as well as by Kervaire, Smale, and many others. In 1962, Milnor received a Fields Medal for this work. Milnor's paper is available on JSTOR (subscription required).
September 1950: The AMS Council passes a resolution asking the Regents of the University of California to reconsider the loyalty oath for university employees. In taking the oath, employees had to affirm that they did not belong to or believe in organizations that advocated the overthrow of the United States government. Coming during the Cold War and around the time of the anti-Communist crusade led by Senator Joseph McCarthy, the loyalty oath was serious business: Thirty-one UC faculty members who refused to sign lost their jobs, including at least two mathematics faculty (Anthony P. Morse and Pauline Sperry). The controversy roiled the university, with faculty seeing the oath as an affront to their rights and the university regents seeing opposition to the oath as a challenge to their authority. Twenty-three learned societies registered their opposition to the oath. The AMS also adopted a resolution barring the Society from holding meetings at UC for a period of three years, if the oath were not scrapped in the meantime. In 1952, the California Supreme Court struck down the oath. A group of the faculty who had been fired sued and won reinstatement.
September 1935: The International Topology Conference was held in Moscow. In reminiscences published in Russian in the journal Uspehi Mat. Nauk in 1966, the Swiss topologist Heinz Hopf called the year of 1935 "an especially important landmark in the evolution of topology" and singled out this meeting as holding particular significance. He wrote that the lectures of J. Aleksandrov, I. Gordon, and A. N. Kolmogorov initiated the theory of cohomology (which goes back to the work of Solomon Lefschetz). "What most impressed me, and of course other topologists, was not the emergence of cohomology groups--after all, these are just groups of characters of ordinary homology groups--but the possibility of defining multiplication of arbitrary complexes and more general spaces, that is, the emergence of chomology rings, which are generalizations of the ring of intersections in the case of manifolds. Before this development we thought that such a situation could arise only because of the local euclideanness of manifolds."
September 1923: René Thom was born in Montbéliard, France. He was a strikingly original thinker whose interests ranged over a wide swath of science and mathematics. His early work contributed to the foundation of differential geometry and singularity theory. He was awarded the Fields Medal in 1958 for his creation of cobordism theory, which provides a way of classifying manifolds. Thom wrote his doctoral thesis at the University of Strasbourg under Henri Cartan and was also influenced by Charles Ehresmann. Thom spent 1951-52 in Princeton and then returned to France, joining the faculty in Grenoble and then in Strasbourg. In 1964, he took a position as a professor at the Institut des Hautes Études Scientifiques in Paris, where he remained for the duration of his career. It was after his move to the IHÉS that Thom began to think deeply about morphogenesis, which led to his creation of catastrophe theory. This theory, which strikes some of the same themes as chaos theory, describes how forms can emerge out of homogeneity and how discontinuities can emerge out of continuous phenomena. Thom's ideas about catastrophe theory are described in his brilliant 1972 book Structural Stability and Morphogenesis. Catastrophe theory fell out of favor to some extent when some researchers overstated the theory's potential for applications to a wide range of phenomena. Thom's work in this area is nevertheless regarded as vital and original. He died in 2002. The MacTutor biography of Thom provides further details about his life, as well as links to unsigned obituaries in British newspapers; this brief account draws in particular on the Times of London obituary.
September 1913: I. M. Gelfand was born on the 2nd of that month in Krasnye Okny, Odessa, Ukraine. He went to Moscow in 1930, at the age of 16, working at various jobs including teaching mathematics, and two years later he began studying under Andrei Kolmogorov. Gelfand's 1938 D.Sc. thesis brought to light the importance of the concept of a maximal ideal, which he used to unite various ideas that had until then seemed unconnected and to create a new theory of commutative normed rings. He has worked in an extraordinarily wide range of areas, including representation theory, differential equations, and Lie algebras. In the late 1950s he developed an interest in biology and medicine and helped to set up the Institute of Biological Physics at the Soviet Academy of Sciences. Starting in 1941, Gelfand was a professor at Moscow State University, where he ran a seminar that was one of the main centers of mathematical life in the Soviet Union; the seminar continued after he joined the faculty of Rutgers University after the fall of the Soviet Union. He maintained a strong interest in teaching and founded a mathematics correspondence school that touched the lives of many young people in the Soviet Union, especially in the country's isolated areas. He also established a correspondence school in the United States. Gelfand received many honors in his lifetime, including the State Prize of the U.S.S.R. (1953), the Lenin Prize (1956), first Wolf Prize in Mathematics (1978), the Kyoto Prize in Mathematical Sciences (1989), a MacArthur Fellowship (1994), and the AMS Steele Prize for Lifetime Achievement (2005). He was a member of the U.S. National Academy of Sciences and holds several honorary doctorates. I.M. Gelfand died in 2009 at the age of 96. Read more about him in the biography at the MacTutor History of Mathematics web site.
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