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This Mathematical Month - March: 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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March 2016

See information on the 2016 Calendar of Mathematical Imagery

Featured Item for March

March 2003: On the 10th of that month, Grigory (also known as Grisha) Perelman posted on the arXiv preprint server a paper that substantiated the tantalizing hints in an earlier posting that he had proved the Poincar´ Conjecture and even Thurston's Geometrization Conjecture. The paper, "Ricci flow with surgery on three-manifolds", absorbed the attention of several experts for about three years before its results were understood and verified. For this work, Perelman was awarded, and declined, the Fields Medal in 2006. This is the only time since the medal was first given in 1936 that the honor was declined. In 2010, the Clay Mathematics Institute awarded Perelman its Millennium Prize of US$1-million, which Perelman also declined. The CMI later announced that the funds would be used to establish the Poincaré Chair, a postdoctoral position for mathematicians at the Institut Henri Poincaré in Paris. Perelman does not have an academic position and has separated himself from contact with other mathematicians.

March 1997: The AMS held its first-ever Congressional Briefing. Organized by the AMS Washington Office, these briefings have become an annual event. They provide a venue for Members of Congress and their staffs to learn about mathematics and its uses. The first briefing, entitled "Mathematical Transcriptions of the Real World," featured as the main speaker Ronald Coifman of Yale University, who described how mathematics is used in data transmission, analysis, and interpretation. One of the most striking stories he told related to music. The composer Brahms, who died in 1897, made a wax cylinder recording of himself playing the piano. That recording was transferred to 78 rpm black disks, which by the time Coifman listened to them were completely garbled. He explained how, after digitizing the recording, he used mathematical tools to extract the music from the noise. Coifman's talk was followed by brief remarks by Andrew Wiles, who was introduced as "the most famous mathematician in the world." Wiles's eloquent speech unified the twin reasons humankind has always pursued mathematical knowledge: for the intrinsic value of the knowledge itself, and for its uses. "Mathematical Transcriptions of the Real World," was published in the May 1997 issue of the Notices of the AMS.

March 1982: The AMS Council passed a resolution to put the Society on the list of supporters of the International Campaign-Massera. José Luis Massera (1915-2002) was a distinguished Uruguayan mathematician known for his work on stability of solutions of differential equations and for his leadership in developing mathematics in Uruguay. A Communist, he was elected to the Uruguayan parliament in 1971. After a military crackdown, Massera was arrested in 1975 and held in solitary confinement for a year. During this time he was tortured and sustained debilitating injuries. He was then tried and convicted of "subversive association" and sentenced to 24 years in prison. The International Campaign-Massera was formed to press for his release; among the key figures in the campaign were mathematicians Henri Cartan and Israel Halperin. It was Halperin who brought the matter before the AMS Council and asked for the Society's support of the campaign. In addition, the chair of the AMS Committee on Human Rights at that time, Eduardo Sontag, proposed the Society circulate a petition about Massera's imprisonment and forward the petition to the relevant authorities in Uruguay. The weight of international pressure was eventually felt by the Uruguayan government, which released Massera in 1984.

March 1980: On the 14th of this month, the National Science Foundation issued a news release about the construction by Robert Griess of "the Monster" group. The Monster is one of the finite simple groups, which are among the most basic objects in mathematics. The classification of finite simple groups was an important goal in mathematics during the 20th century and today has largely been completed. Griess's construction was an important milestone in this effort. "A scientist has taken a major step toward the solution of a long-standing problem in mathematics---an accomplishment that involved a structure with so many elements that he had to develop new ways of doing the computations because even high speed computers could have taken many years of full-time continuous operation to do the job," the NSF news release said. The Monster is one of 26 "sporadic" groups that don't fit neatly into any existing categories in the classification. It is called the Monster because it has so many elements---the number runs to 54 digits. The news release noted that it was in 1965 that the mathematical community was "startled by the discovery of a new sporadic group, the first since 1860". Today all 26 sporadic groups are known, but the Monster still stands out among them. "The Monster remains the single most tantalizing simple group" wrote Ronald Solomon in his article "On Finite Simple Groups and their Classification" in the February 1995 issue of the Notices of the AMS. Additional details about the classification may be found in "The Status of the Classification of the Finite Simple Groups", by Michael Aschbacher, in the August 2004 issue of the Notices of the AMS.

March 1928: On the 13th of that month, Paulo Ribenboim was born in Recife, Brazil. After initial studies in Brazil, Ribenboim went to Nancy, France, in 1950, where he came into contact with some of the top French mathematicians of the day, such as Laurent Schwartz and Jean Dieudonné. Ribenboim also became a close friend of a fellow student who was to become a major figure in the field, Alexander Grothendieck. After two years in France Ribenboim returned to Brazil and got a position in Rio de Janeiro. The following year he returned to Europe, this time to Germany, to study with Wolfgang Krull. Ribenboim's research, in valuations and valuation rings, blossomed at this time, and he wrote several papers in the subject. He returned to Brazil in 1956 and joined the faculty of IMPA (Instituto de Matemática Pura e Aplicada) in Rio. He did not have a doctorate at this point, but he was awarded one the following year by the University of São Paulo. In the early 1960s he moved to Queen's University in Kingston, Ontario, Canada, where he spent the remainder of his career. A warm and witty personality, Ribenboim is especially known for his enthusiasm for number theory, which comes through in his books, such as The Little Book of Big Primes (1991) and My Numbers, My Friends (2000). In 1999, the Canadian Number Theory Association established the Ribenboim Prize for distinguished research in number theory to be awarded to a mathematician who is Canadian or has connections to Canadian mathematics. For more about the life of Paulo Ribenboim, see the biography on the MacTutor History of Mathematics web site.

March 1916: Paul R. Halmos was born in Budapest, Hungary, on March 3, 1916. One of the field's outstanding mathematical expositors, Halmos was known for writings and lectures that have a crystal clarity as well as a buoyant sense of enjoyment in doing mathematics. Halmos's father, a physician, emigrated to Chicago, and Paul moved there when he was a teenager. At the age of 15 he enrolled at the University of Illinois to study chemical engineering and later switched to mathematics and philosophy. He received his PhD in 1938, under the direction of Joseph Doob (who served as AMS president 1963-64). After becoming von Neumann's assistant at the Institute for Advanced Study in Princeton, Halmos wrote his first book, based on a lecture course by von Neumann, and his reputation as an excellent writer was immediately established. He was also known for his research in operator theory, ergodic theory, and functional analysis. After faculty positions at the University of Chicago, the University of Michigan, and Indiana University, he went in 1985 to Santa Clara University, where he was a professor emeritus. In 1983 Halmos received the AMS Steele Prize, the citation for which noted that the "felicitous style and content [of his books] has had a vast influence on the teaching of mathematics in North America." In 1993 he received the Distinguished Teaching Award from the Mathematical Association of America. Halmos died in 2006; a memorial article, "Paul Halmos: In His Own Words", prepared by John H. Ewing, appeared in the October 2007 issue of the AMS Notices. Halmos was a tireless picture-taker, and a collection of his photos of mathematicians is being posted on the web site of the Mathematical Association of America. [For more information on Paul Halmos see the biographies section of the MacTutor Web site.]

March 1907: On the 23rd of that month, Hassler Whitney was born in New York. He attended Yale University and received his doctorate from Harvard University in 1932, under the direction of G. D. Birkhoff. Whitney was a professor at Harvard before accepting a permanent position at the Institute for Advanced Study in Princeton in 1952. He was one of the founding fathers of differential topology. Among his best known results is the Whitney Embedding Theorem, which guarantees that a manifold can always be embedded into Euclidean space. Whitney also has a particular distinction in that a trick is named after him, the so-called "Whitney trick," a device used to remove self-intersections of immersed submanifolds. He is the Whitney whose name appears in the term Stiefel-Whitney classes. In his later years, Whitney devoted much time and attention to mathematics education. He was awarded the National Medal of Science (1976), the Wolf Prize (1983), and the AMS Steele Prize for Lifetime Achievement (1985). More about Whitney's life may be found in the obituary that appeared in the July/August 1989 issue of the Notices of the AMS. See also the entry about Whitney on the MacTutor History of Mathematics archive.

March 1882: On the 23rd of that month, Emmy Noether was born in Erlangen, Germany. The daughter of the noted mathematician Max Noether of the University of Erlangen, she studied languages with the intention of becoming a language teacher. But she changed course and decided to study mathematics, a realm then largely closed to women. She obtained special permission to attend courses at the University of Erlangen, and, after spending two years at the University of Göttingen, she received her doctorate from Erlangen. She remained there for a few years before Felix Klein and David Hilbert persuaded her to return to Göttingen, where they fought with the university administration to allow her to earn the Habilitation, which qualifies one to teach in German universities. By 1933 she was one of the outstanding mathematicians in Germany but, because she was Jewish, she was dismissed by the Nazis from her position in Göttingen. She went to the United States and joined the faculty of Bryn Mawr College, where she remained until her death just two years later. Emmy Noether did profound work in mathematics, in particular contributing a new and powerful viewpoint in algebra. "She taught us to think in simple, and thus general, terms ... homomorphic image, the group or ring with operators, the ideal... and not in complicated algebraic calculations," said her colleague P.S. Alexandroff during a memorial service after her death. Read more about Emmy Noether at the MacTutor History of Math web site.

March 1847: On the 22nd of that month, Augustin Cauchy and Gabriel Lamé deposited "secret packets" with the French Academy of Sciences. The depositing of such packets was done when an individual wanted to claim priority for a result without revealing the result itself. Both packets evidently contained purported proofs of Fermat's Last Theorem. Earlier in the month, Lamé had presented to the Academy his ideas for a proof of Fermat. Objections came immediately from Joseph Liouville, who noted that Lamé's proof depended on unique factorization of the complex numbers. Until such a result were proved, Liouville contended, Lamé's work should be regarded skeptically. Cauchy, on the other hand, thought Lamé's approach had merit and jumped on the bandwagon himself with a series of papers. After three weeks of work, Cauchy and Lamé deposited their secret packets. But their efforts were doomed. On May 24th that year, Liouville read out in the Academy a letter from Ernst Kummer, who noted that he had proved the failure of unique factorization of the complex numbers in a paper published three years earlier. This recounting of the story is based on the fuller account in Harold Edwards' book Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory. Edwards received the 2005 AMS Whiteman Prize for his outstanding works in the history of mathematics.

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