AMS in the Twentieth Century
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A Century of Mathematics in America, Peter Duren Et Ai., (Eds.), Vol
Garrett Birkhoff has had a lifelong connection with Harvard mathematics. He was an infant when his father, the famous mathematician G. D. Birkhoff, joined the Harvard faculty. He has had a long academic career at Harvard: A.B. in 1932, Society of Fellows in 1933-1936, and a faculty appointmentfrom 1936 until his retirement in 1981. His research has ranged widely through alge bra, lattice theory, hydrodynamics, differential equations, scientific computing, and history of mathematics. Among his many publications are books on lattice theory and hydrodynamics, and the pioneering textbook A Survey of Modern Algebra, written jointly with S. Mac Lane. He has served as president ofSIAM and is a member of the National Academy of Sciences. Mathematics at Harvard, 1836-1944 GARRETT BIRKHOFF O. OUTLINE As my contribution to the history of mathematics in America, I decided to write a connected account of mathematical activity at Harvard from 1836 (Harvard's bicentennial) to the present day. During that time, many mathe maticians at Harvard have tried to respond constructively to the challenges and opportunities confronting them in a rapidly changing world. This essay reviews what might be called the indigenous period, lasting through World War II, during which most members of the Harvard mathe matical faculty had also studied there. Indeed, as will be explained in §§ 1-3 below, mathematical activity at Harvard was dominated by Benjamin Peirce and his students in the first half of this period. Then, from 1890 until around 1920, while our country was becoming a great power economically, basic mathematical research of high quality, mostly in traditional areas of analysis and theoretical celestial mechanics, was carried on by several faculty members. -
2012 Cole Prize in Algebra
2012 Cole Prize in Algebra Alexander S. Merkurjev received the 2012 AMS speaker at the International Congress of Mathema- Frank Nelson Cole Prize in Algebra at the 118th An- ticians (Berkeley, 1986). Twice he has delivered nual Meeting of the AMS in Boston in January 2012. an invited address at the European Congress of Mathematics (1992, 1996), and he was a plenary Citation speaker in 1996 (Budapest). The 2012 Frank Nelson Cole Prize in Algebra is awarded to Alexander S. Merkurjev of the Univer- Response from Alexander S. Merkurjev sity of California, Los Angeles, for his work on the It is a great honor and great pleasure for me to essential dimension of groups. receive the 2012 Frank Nelson Cole Prize in Alge- The essential dimension of a finite or of an alge- bra. I would like to thank the American braic group G is the smallest number of parameters Mathematical Society and the Selection needed to describe G-actions. For instance, if G Committee for awarding the prize to is the symmetric group on n letters, this invari- me. ant counts the number of parameters needed to I am very grateful to my teacher, specify a field extension of degree n, which is the Andrei Suslin (he was awarded the algebraic form of Hilbert’s thirteenth problem. Merkurjev’s papers (“Canonical p-dimension Frank Nelson Cole Prize in Algebra in of algebraic groups”, with N. Karpenko, Adv. 2000). I also want to thank my parents, Math. 205 (2006), no. 2, 410–433; and “Essential family, friends, and colleagues for dimension of finite p-groups”, with N. -
Harish-Chandra 1923–1983
NATIONAL ACADEMY OF SCIENCES HARISH- C HANDRA 1 9 2 3 – 1 9 8 3 A Biographical Memoir by R O G E R H O W E Any opinions expressed in this memoir are those of the author and do not necessarily reflect the views of the National Academy of Sciences. Biographical Memoir COPYRIGHT 2011 NATIONAL ACADEMY OF SCIENCES WASHINGTON, D.C. Photo by Herman Landshoff; Courtesy Archives of the Institute for Advanced Study. HARISH-CHANDRA October 11, 1923–October 12, 1983 BY ROGER HOWE He taught them the Kshatria code of honor: that a warrior may never refuse a challenge…. The Five Sons of Pandu, The Story of the Mahabharata Retold by Elizabeth Seeger ARISH-CHANDRA WAS, if not the exclusive architect, cer- Htainly the chief engineer of harmonic analysis on semisimple Lie groups. This subject, with roots deep in mathematical physics and analysis, is a synthesis of Fou- rier analysis, special functions and invariant theory, and it has become a basic tool in analytic number theory, via the theory of automorphic forms. It essentially did not ex- ist before World War II, but in very large part because of the labors of Harish-Chandra, it became one of the major mathematical edifices of the second half of the twentieth century. Harish-Chandra was born in 1923 in Uttar Pradesh, in northern India. His family belonged to the Kshatria (war- rior) caste. Kshatria traditionally were rulers, landowners, and military leaders, and more recently have commonly been businessmen or civil servants. Harish-Chandra’s father, Chandrakishore, was a civil engineer who monitored and maintained the dikes and irrigation canals that sustain agri- 3 B IOGRA P HICAL MEMOIRS culture on the North Indian plains. -
Henri Darmon
Henri Darmon Address: Dept of Math, McGill University, Burnside Hall, Montreal, PQ. E-mail: [email protected] Web Page: http://www.math.mcgill.ca/darmon Telephone: Work (514) 398-2263 Home: (514) 481-0174 Born: Oct. 22, 1965, in Paris, France. Citizenship: Canadian, French, and Swiss. Education: 1987. B.Sc. Mathematics and Computer Science, McGill University. 1991. Ph.D. Mathematics, Harvard University. Thesis: Refined class number formulas for derivatives of L-series. University Positions: 1991-1994. Princeton University, Instructor. 1994-1996. Princeton University, Assistant Professor. 1994-1997. McGill University, Assistant Professor. 1997-2000. McGill University, Associate Professor. 2000- . McGill University, Professor. 2005-2019. James McGill Professor, McGill University. Other positions: 1991-1994. Cercheur hors Qu´ebec, CICMA. 1994- . Chercheur Universitaire, CICMA. 1998- . Director, CICMA (Centre Interuniversitaire en Calcul Math´ematique Alg´ebrique). 1999- . Member, CRM (Centre de Recherches Math´ematiques). 2005-2014. External member, European network in Arithmetic Geometry. Visiting Positions: 1991. IHES, Paris. 1995. Universit´a di Pavia. 1996. Visiting member, MSRI, Berkeley. 1996. Visiting professor and guest lecturer, University of Barcelona. 1997. Visiting Professor, Universit´e Paris VI (Jussieu). 1997. Visitor, Institut Henri Poincar´e. 1998. Visiting Professor and NachDiplom lecturer, ETH, Zuric¨ h. 1999. Visiting professor, Universit`a di Pavia. 2001. Visiting professor, Universit`a di Padova. 2001. Korea Institute for Advanced Study. 2002. Visiting professor, RIMS and Saga University (Japan). 1 2003. Visiting Professor, Universit´e Paris VI, Paris. 2003. Visiting professor, Princeton University. 2004. Visiting Professor, Universit´e Paris VI, Paris. 2006. Visiting Professor, CRM, Barcelona, Spain. 2008. Visiting Professor, Universit´e Paris-Sud (Orsay). -
Prizes and Awards
DENVER • JAN 15–18, 2020 January 2020 Prizes and Awards 4:25 PM, Thursday, January 16, 2020 PROGRAM OPENING REMARKS Michael Dorff, Mathematical Association of America AWARD FOR DISTINGUISHED PUBLIC SERVICE American Mathematical Society BÔCHER MEMORIAL PRIZE American Mathematical Society CHEVALLEY PRIZE IN LIE THEORY American Mathematical Society FRANK NELSON COLE PRIZE IN NUMBER THEORY American Mathematical Society LEONARD EISENBUD PRIZE FOR MATHEMATICS AND PHYSICS American Mathematical Society LEVI L. CONANT PRIZE American Mathematical Society JOSEPH L. DOOB PRIZE American Mathematical Society LEROY P. S TEELE PRIZE FOR MATHEMATICAL EXPOSITION American Mathematical Society LEROY P. S TEELE PRIZE FOR SEMINAL CONTRIBUTION TO RESEARCH American Mathematical Society LEROY P. S TEELE PRIZE FOR LIFETIME ACHIEVEMENT American Mathematical Society LOUISE HAY AWARD FOR CONTRIBUTION TO MATHEMATICS EDUCATION Association for Women in Mathematics M. GWENETH HUMPHREYS AWARD FOR MENTORSHIP OF UNDERGRADUATE WOMEN IN MATHEMATICS Association for Women in Mathematics MICROSOFT RESEARCH PRIZE IN ALGEBRA AND NUMBER THEORY Association for Women in Mathematics SADOSKY RESEARCH PRIZE IN ANALYSIS Association for Women in Mathematics FRANK AND BRENNIE MORGAN PRIZE FOR OUTSTANDING RESEARCH IN MATHEMATICS BY AN UNDERGRADUATE STUDENT American Mathematical Society Mathematical Association of America Society for Industrial and Applied Mathematics COMMUNICATIONS AWARD Joint Policy Board for Mathematics CHAUVENET PRIZE Mathematical Association of America DAVID P. R OBBINS PRIZE Mathematical Association of America EULER BOOK PRIZE Mathematical Association of America DEBORAH AND FRANKLIN TEPPER HAIMO AWARDS FOR DISTINGUISHED COLLEGE OR UNIVERSITY TEACHING OF MATHEMATICS Mathematical Association of America YUEH-GIN GUNG AND DR.CHARLES Y. HU AWARD FOR DISTINGUISHED SERVICE TO MATHEMATICS Mathematical Association of America CLOSING REMARKS Jill C. -
Prize Is Awarded Every Three Years at the Joint Mathematics Meetings
AMERICAN MATHEMATICAL SOCIETY LEVI L. CONANT PRIZE This prize was established in 2000 in honor of Levi L. Conant to recognize the best expository paper published in either the Notices of the AMS or the Bulletin of the AMS in the preceding fi ve years. Levi L. Conant (1857–1916) was a math- ematician who taught at Dakota School of Mines for three years and at Worcester Polytechnic Institute for twenty-fi ve years. His will included a bequest to the AMS effective upon his wife’s death, which occurred sixty years after his own demise. Citation Persi Diaconis The Levi L. Conant Prize for 2012 is awarded to Persi Diaconis for his article, “The Markov chain Monte Carlo revolution” (Bulletin Amer. Math. Soc. 46 (2009), no. 2, 179–205). This wonderful article is a lively and engaging overview of modern methods in probability and statistics, and their applications. It opens with a fascinating real- life example: a prison psychologist turns up at Stanford University with encoded messages written by prisoners, and Marc Coram uses the Metropolis algorithm to decrypt them. From there, the article gets even more compelling! After a highly accessible description of Markov chains from fi rst principles, Diaconis colorfully illustrates many of the applications and venues of these ideas. Along the way, he points to some very interesting mathematics and some fascinating open questions, especially about the running time in concrete situ- ations of the Metropolis algorithm, which is a specifi c Monte Carlo method for constructing Markov chains. The article also highlights the use of spectral methods to deduce estimates for the length of the chain needed to achieve mixing. -
On the History of Fermat's Last Theorem: a Down-To-Earth
On the History of Fermat’s Last Theorem: A Down-to-Earth Approach Leo Corry - Tel Aviv University DRAFT ov. 2007 – OT FOR QUOTATIO 1. Introduction .............................................................................................................. - 1 - 2. Origins – in the margins .......................................................................................... - 5 - 3. Early stages – in the margins as well ..................................................................... - 8 - 4. FLT between 1800 and 1855 – still in the margins .............................................. - 13 - 5. Marginality within diversification in number theory (1855-1908) ....................... - 22 - 6. The Wolfskehl Prize and its aftermath ................................................................. - 34 - 7. FLT in the twentieth century: developing old ideas, discovering new connections .................................................................................................... - 44 - 8. Concluding Remarks: the Fermat-to-Wiles drama revisited .............................. - 56 - 9. REFERENCES......................................................................................................... - 60 - 1. Introduction Andrew Wiles’ proof of Fermat’s Last Theorem (FLT), completed in 1994, was a landmark of late twentieth century mathematics. It also attracted a great deal of attention among both the media and the general public. Indeed, not every day a mathematical problem is solved more than 350 years after it was first -
Harish Chandra the Iisc and Set up the Molecular Biophysics Unit (MBU)
I NDIAN Ramachandran resigned from Madras in 1970 and then spent two years as a visiting professor at the Biophysics Department of the University of Chicago. During this visit he devised a new method to reconstruct three-dimensional N A images from two-dimensional data, thus laying the foundations of TIONAL computerized tomography. On his return from Chicago Ramachandran joined Harish Chandra the IISc and set up the Molecular Biophysics Unit (MBU). In 1977 he visited S the National Institute for Health in Bethesda, Maryland, USA as a Fogarty CIENCE (1923 – 1983) Scholar. In the same year he was elected a Fellow of the Royal Society, London. He retired from MBU in 1978 but continued as a Professor of Mathematical Philosophy at the IISc until 1989. A CADEMY From the early 1980’s he developed Parkinson’s disease and was cared for by his wife Rajam whom he married in 1945. In 1998, Rajam suddenly died of a Harish Chandra was an outstanding mathematician of his generation. He was heart attack and this was a grievous shock from which Ramachandran never a mathematician who transformed the peripheral topic of ‘representation theory’ recovered. In 1999, the International Union of Crystallography awarded him INSA into a major field which became central to contemporary mathematics. the 5th Ewald Prize for his outstanding contributions to crystallography. In PLA Harish was born on 11 October 1923 in Kanpur. His grandfather was a senior 1999 he had a cardiac arrest and since then remained in the hospital until his railroad clerk in Ajmer. He was deeply committed to give his son Chandrakishore death on 7, April 2001. -
From Simple Algebras to the Block-Kato Conjecture Alexander Merkurjev
Public lecture From simple algebras to the Block-Kato conjecture Alexander Merkurjev Professor at the University of California, Los Angeles Guest of the Atlantic Algebra Centre of MUN Distinguished Lecturer Atlantic Association for Research in the Mathematical Sciences Abstract. Hamilton’s quaternion algebra over the real numbers was the first nontrivial example of a simple algebra discovered in 1843. I will review the history of the study of simple algebras over arbitrary fields that culminated in the proof of the Bloch-Kato Conjecture by the Fields Medalist Vladimir Voevodsky. Time and Place The lecture will take place on June 15, 2016, on St. John’s campus of Memorial University of Newfound- land, in Room SN-2109 of Science Building. Beginning at 7 pm. Awards and Distinctions of the Speaker In 1986, Alexander Merkurjev was a plenary speaker at the International Congress of Mathematicians in Berkeley, California. His talk was entitled "Milnor K-theory and Galois cohomology". In 1994, he gave an invited plenary talk at the 2nd European Congress of Mathematics in Budapest, Hungary. In 1995, he won the Humboldt Prize, a prestigious international prize awarded to the renowned scholars. In 2012, he won the Cole Prize in Algebra, for his fundamental contributions to the theory of essential dimension. Short overview of scientific achievements The work of Merkurjev focuses on algebraic groups, quadratic forms, Galois cohomology, algebraic K- theory, and central simple algebras. In the early 1980s, he proved a fundamental result about the struc- ture of central simple algebras of period 2, which relates the 2-torsion of the Brauer group with Milnor K- theory. -
Introduction of Langlands
Peter Roquette 4. Nov. 2004 Mathematisches Institut, Universit¨at Heidelberg Introduction of Langlands at the Arf lecture, 11 November 2004.1 Ladies and Gentlemen ! It is my pleasure and a great honor to me to introduce Robert Langlands as the speaker of the Arf Lecture of this year 2004, here at the Middle East Technical University. Professor Langlands is a permanent member of the Institute for Advanced Study in Princeton, which is one of the most pres- tigious places for mathematical research studies. He has received a number of highly valued awards, among them the Cole Prize in Number Theory from the American Mathematical Society in 1982, the National Academy of Sciences reward in Mathema- tics in 1988, and the Wolf prize from the Wolf foundation in Israel 1996. He is elected fellow of the Royal Society of Canada and the Royal Society of London, and he has received honorary doctorates from at least 7 universities (to my knowledge). In the laudation for the Wolf prize it was said that he received the prize for his “ path-blazing work and extraordinary insights in the fields of number theory, automorphic forms and group representations”. 1Each year there is scheduled a special colloquium lecture at the Middle East Technical University in Ankara, commemorating Cahit Arf who had served as a professor for many years at METU. In the year 2004 the invited speaker was Robert Langlands, and I had been asked to chair his lecture. The following text was read to introduce the speaker. P.Rq. Introduction of Langlands 4.11.04 Seite 2 Ladies and gentlemen, while I was preparing the text for this introduction it soon became clear to me that in this short time I would not be able to describe, not even approximately, Lang- lands’ rich work, its underlying ideas, its enormous impact on the present mathematical research world wide, and its consequence for the future picture of Mathematics. -
William Osgood
NATIONAL ACADEMY OF SCIENCES WILLIAM FOGG OSGOOD 1864–1943 A Biographical Memoir by JOSEPH L. WALSH Any opinions expressed in this memoir are those of the author and do not necessarily reflect the views of the National Academy of Sciences. Biographical Memoirs, VOLUME 81 PUBLISHED 2002 BY THE NATIONAL ACADEMY PRESS WASHINGTON, D.C. Photo courtesy of the American Mathematical Society. WILLIAM FOGG OSGOOD March 10, 1864–July 22, 1943 BY JOSEPH L. WALSH ILLIAM FOGG OSGOOD WAS born in Boston, Massachusetts, W the son of William and Mary Rogers (Gannett) Osgood. He prepared for college at the Boston Latin School, en- tered Harvard in 1882, and was graduated with the A.B. degree in 1886, second in his class of 286 members. He remained at Harvard for one year of graduate work in math- ematics, received the degree of A.M. in 1887, and then went to Germany to continue his mathematical studies. Dur- ing Osgood’s study at Harvard, the great Benjamin Peirce (1809-1880), who had towered like a giant over the entire United States, was no longer there. James Mills Peirce (1834- 1906), son of Benjamin, was in the Mathematics Depart- ment, and served also later (1890-1895) as Dean of the Graduate School and (1895-1898) as Dean of the Faculty of Arts and Sciences. William Elwood Byerly was also a mem- ber of the Department (1876-1913) and is remembered for his excellent teaching and his texts on the Calculus and on Fourier’s Series and Spherical Harmonics. Benjamin Osgood Peirce (1854-1914) was a mathematical physicist, noted for Reprinted with permission. -
On Tate and His Mathematics – a Glossary∗
ARTICLE-IN-A-BOX On Tate and His Mathematics – A Glossary∗ The subject of number theory has developed into a sophisticated branch of mathematics, inter- acting deeply with other key areas. John Tate is a prime architect of this development, through his accomplishments spanning seven decades. The influence of Tate’s ideas on number theory – and, in fact, in mathematics as a whole – is so pervasive that it will be difficult to even define the notions involved in a way understandable to the uninitiated. Tate has been bestowed with many honours. Already, in 1956, he was awarded the Cole Prize of the American Mathematical Society for outstanding contributions to number theory. In 1995, he received the Steele Prize for Lifetime Achievement from the AMS and the Wolf Prize (shared with M. Sato) in 2002 for his “creation of fundamental concepts in algebraic number theory”. He was twice an invited speaker at the ICMs (1962-Stockholm and 1970-Nice). Tate was elected to the U.S. National Academy of Sciences in 1969. He was named a foreign member of the French Acad´emie des Sciences in 1992 and an honorary member of the London Mathematical Society in 1999. The Abel Prize was awarded to him in 2010. Essential mathematical ideas and constructions initiated by Tate and later named after him abound; some mathematical terms bearing his name are: Tate modules, Tate elliptic curves, Tate uniformization, Tate’s q, Lubin-Tate theory, Honda-Tate theory, Sato-Tate conjecture, Barsotti-Tate groups, Hodge-Tate decomposition, Tate cohomol- ogy, Poitou-Tate duality, Serre-Tate parameters, Tate cycles, Tate conjectures, Mumford-Tate group, Mumford-Tate conjectures, Tate twists, Tate motives, Tate spaces, Tate ring, Tate alge- bra, Tate residue, Cassels-Tate pairing, Neron-Tate heights, Shafarevich-Tate groups, Koszul- Tate resolution, etc.