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This Mathematical Month - May: A Brief Look at Past Events and Episodes in the Mathematical CommunityMonthly postings of vignettes on people, publications, and mathematics to inform and entertain.
May 2000: The Millennium Prize Problems of the Clay Mathematics Institute (CMI) were publicly unveiled at an event at the Collège de France in Paris on the 24th of that month. The event took place exactly 100 years after David Hilbert presented his renowned 23 problems at the Paris International Congress of Mathematicians in 1900. The CMI is offering a prize of US$1 million apiece for the solution of the problems. With the leading lights of Paris mathematics in attendance, Sir Michael Atiyah of the University of Edinburgh and John Tate of the University of Texas at Austin presented descriptions of the prize problems. One of the problems is the Poincaré Conjecture, which to the surprise of many was resolved by Grigori Perelman just a few years after the Millennium Prize Problems were announced (at the time of this writing, the prize had not been awarded because the 2-year waiting period stipulated in the prize rules had not yet passed). Exactly what impact the prizes have had on mathematics is unclear, but they have proved a public relations boon for the field: The announcement of the million-dollar prizes set off a flurry of publicity worldwide, and in the years since the prizes have often been referred to in popular articles about mathematics. Not all mathematicians agree that the prizes are a good thing; see for example "What is Useful for Mathematics?: Thoughts on the Clay Millennium Prizes", by Anatoly Vershik, in the January 2007 issue of the AMS Notices. For an account of the Paris event, see "Million-dollar Mathematics Prizes Announced", by Allyn Jackson, in the September 2000 issue of the Notices. May 1999: The first Paul Erdös Memorial Lecture is delivered by Ronald Graham. The title of Graham's talk was "Paul Erdös and his favorite problems in number theory," and it was presented at the fourth joint meeting of the AMS and the Mexican Mathematical Society at the University of North Texas on May 19, 1999. The Erdös Memorial Lecture is delivered every year by an outstanding mathematician and presented at an AMS sectional meeting. Funding for the lecture series is made possible by Andrew Beal, a Dallas banker with an interest in mathematics. Beal proposed a number theory conundrum that is now called the Beal Conjecture and he has pledged US$100,000 as a prize for its solution. The prize fund is held by the AMS, and Beal requested that income from the fund be used to support the Erdös Memorial Lectures. More information on the lecture series is available on the AMS web site. May 1988: Alexander Grothendieck, one of the most influential mathematicians of the 20th century and a 1966 Fields Medalist, explained in the newspaper Le Monde his reasons for declining the Crafoord Prize of the Royal Swedish Academy of Sciences. The prize, which carried a monetary award of US$270,000, was conferred on Grothendieck and his former collaborator, Pierre Deligne. Why did Grothendieck decline the prize? He explained in a May 4, 1988, letter to Le Monde that he did not need the money and that he had left the world of mathematics in 1970. He also wrote that "the only decisive proof of the fertility of ideas or of a new vision is that of time. Fertility is recognizable by offspring, not by honors." Grothendieck, who was born in 1928 and lives as a recluse, has continued to fascinate many inside and outside of mathematics. In the September 2008 issue of the Notices, two articles about him appeared: "Who is Alexander Grothendieck?", by Winfried Scharlau, and "Grothendieck at 80, IHES at 50", by Allyn Jackson. In addition, an interview with Grothendieck's former PhD student Luc Illusie, "Reminiscences of Grothendieck and his School", appeared in the October 2010 issue. May 1957: Scientific American magazine publishes an article introducing the general public to polyominoes, which are generalizations of dominoes. In fact, the term "polyomino" had been coined three years earlier by Solomon Golomb, who created puzzles based on polyominoes and wrote about them in the American Mathematical Monthly. But the fame of polyominoes increased enormously when Martin Gardner wrote about them in the May 1957 installment of his "Mathematical Games" columns. Eight years after that, Scribner's published a book by Golomb called Polyominoes, which has become a classic in recreational mathematics and was reprinted in a new edition by Princeton University Press in 1994. Polyominoes are the basis for the popular computer game "Tetris" and are often used in precollege mathematics classes. May 1924: Isadore Manuel Singer was born on May 3, 1924 in Detroit, MI. He received his B.S. in Physics at the University of Michigan in 1944, and then spent three years in the U.S. Army Signal Corps. While studying to prepare for an advanced degree in physics at the University of Chicago, he developed a strong background in mathematics, focusing on group theory and differential geometry. He then received his Master's degree in Mathematics 1948 and decided to continue with research in that topic, and was awarded a Ph.D. in Mathematics 1950 for his thesis, "Lie Algebras of Unbounded Operators." Among his many honors are the AMS Bôcher Prize in 1969, being an Invited Speaker at the 1974 International Congress of Mathematicians, AMS Steele Prize in 2000, election to the National Academy of Sciences and to the American Academy of Arts and Sciences, and the Abel Prize (with Sir Michael Atiyah) in 2004, "for their discovery and proof of the index theorem, bringing together topology, geometry and analysis, and their outstanding role in building new bridges between mathematics and theoretical physics." The Steele Prize citation also notes Singer's other significant contributions to geometry--his work with D B Ray on analytic torsion, the precursor of much modern work on "determinant" invariants in geometry, and an influential textbook joint with J A Thorpe, Lecture Notes on Elementary Topology and Geometry--and his decades dedicated to bringing together mathematicians and theoretical physicists. "This renaissance of serious interaction between mathematicians and physicists, which dates from the mid-1970s, has had a dramatic effect on mathematics, and Singer has played a major role in this development." Singer is currently Professor at Massachusetts Institute of Technology in Cambridge, MA. See and read "'I Do It to Learn' - Isadore Singer proves that age has nothing to do with mathematics," an interview with Singer and science journalist Dana Mackenzie. May 1923: Cathleen Synge Morawetz, the second woman to serve as President of the AMS, was born in Toronto, Canada. Her parents were both Irish and both trained in mathematics. Her father, John Lighton Synge, was on the faculty of the University of Toronto, and, after the family moved back to Ireland, he moved to Dublin University. Morawetz went to the Courant Institute at New York University as a doctoral student and finished her Ph.D. in 1951, under the direction of Kurt O. Friedrichs. She became part of the legendary group that, under the leadership of Richard Courant, made the Courant Institute the premier center for applied mathematics in the United States. She made fundamental contributions to partial differential equations related to shock waves and transonic flow. Her many honors include the National Medal of Science (1998) and the AMS Steele Prize (2003). Morawetz served as AMS President from 1995 to 1997. Read more about her in a Notices of the AMS article on the occasion of her receipt of the Steele Prize. May 1919: On the 12th of that month, Wu Wen-Tsun, one of the outstanding Chinese mathematicians of the twentieth century, was born in Shanghai. His initial university education was made difficult by the war between China and Japan. After the surrender of Japan at the end of World War II in 1945, Wu was able to restart his mathematics studies. The following year he met Shiing-Shen Chern, who was already an established mathematician with an international reputation and who was starting the Intsitute of Mathematics in the Academia Sinica. This was a crucial contact for Wu. The following year he traveled to France, where he studied for his doctorate at the University of Strasbourg, with Charles Ehresmann. Wu's work at this time centered on the topology of manifolds that underpins differential geometry. He discovered a set of invariants parallel to Chern classes, known as the Wu classes, which have proved nearly as important. He returned to China in 1951 and took a position at Peking University; two years later he became a researcher at the Academia Sinica. At this time his research continued to focus on topological problems. In 1966, during the Cultural Revolution, Wu was sent to work in a factory that manufactured computers. His deep interest in ancient Chinese mathematics, combined with the exposure to computers, led him to begin thinking about how to solve geometric problem in a mechanical way, and he wrote two influential monographs on the subject. Wu received various honors during his career, including two invitations to speak at the International Congress of Mathematicians. In 2006, he shared the US$1-million Shaw Prize with David Mumford; Wu was recognized "for his contributions to the new interdisciplinary field of mathematics mechanization". In May 2009, Wu celebrates his 90th birthday. Find out more from the biography of Wu on the MacTutor History of Mathematics web site. May 1899 : The great historian of mathematics in antiquity, Otto Neugebauer, was born in Innsbruck Austria. An obituary that appeared in the journal Mathematical Astronomy (24 (1993) no. 4, 289-299) after his death at the age of 90 said: "It is no exaggeration to say that in our age the study of the early history of mathematical astronomy has largely been defined by the work of one scholar, Otto Neugebauer. He began as a mathematician, then turned to Egyptian mathematics, and after completing a comprehensive edition and analysis of Babylonian mathematics, took up the history of mathematical astronomy, to which he afterward devoted the greatest part of his attention. Through a productive career of sixty-five years, through three generations of colleagues and students, he has to a great extent created our understanding of mathematical astronomy from Babylon and Egypt, through Greco-Roman Antiquity, to India, Islam, and Europe of the Middle Ages and Renaissance." Neugebauer was the founder of the mathematical reviewing journal Zentralblatt für Mathematik. After emigrating from Germany to the United States during World War II, he founded Mathematical Reviews® in 1940. An obituary about Neugebauer appeared in the May/June 1990 issue of the AMS Notices. Read more about him in the entry on the MacTutor History of Mathematics web page.
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