This Mathematical Month: 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.

See information about the 2008 Calendar of Mathematical Imagery.

February 1905: AMS President Thomas S. Fiske's Presidential Address delivered before the American Mathematical Society at its eleventh Annual Meeting December 29, 1904, appeared in the February 1905 issue of the Bulletin of the AMS. His topic: Mathematical Progress in America. His introduction states, "In tracing the development of pure mathematics in America, it seems convenient to recognize three periods. The first period extends from colonial days up to the establishment of the Johns Hopkins University in 1876; the second period extends from the establishment of the Johns Hopkins University up to 1891, when the New York Mathematical Society took on a national character and began the publication of its BULLETIN; the third period extends from 1891 up to the present time." Read the entire address. Readers may now view online the first century of the Bulletin of the American Mathematical Society, from 1891 to 1991, searchable and fully integrated with the modern Bulletin. The approximately 84,000 pages of the Bulletin are freely accessible to all.

February 1909: On the 11th of that month, Claude Chevalley was born in Johannesberg, Transvaal, South Africa. He died on June 28, 1984, in Paris. Chevalley had a major impact on the development of algebra in the 20th century. What are now known as Chevalley groups have become fundamental objects in algebra and are important in the classification of finite simple groups, one of the outstanding challenges in the mathematics. Chevalley studied at the École Normale Supérieure in Paris before going to Germany to study under Emil Artin and Helmut Hasse. Chevalley received his doctorate from the Université de Paris in 1933 and the following year joined the now famous group of mathematicians known as Bourbaki. In 1938 he moved to the United States, teaching at Princeton and Columbia Universities and becoming a U.S. citizen. He returned to France in 1957 and became a professor at the Université de Paris VII. Chevalley wrote several influential books, including the three-volume work Theory of Lie Groups, which became a standard reference. The 1941 AMS Cole Prize went to Chevalley for his paper "La théorie du corps de classes", published in the Annals of Mathematics the year before. Chevalley died in 1984, and obituaries about him appeared in the Bulletin of the AMS (by J. Dieudonné and J. Tits, volume 17, number 1, 1987), and in the Notices of the AMS (by Pierre Cartier, volume 31, 1984, page 775). This brief sketch of his life is based on the biography of Chevalley on the MacTutor History of Mathematics web site.

February 1931: On the 20th of that month, John W. Milnor was born in Orange, New Jersey. He went on to become one of the most influential mathematicians of the twentieth century. He was an undergraduate and a graduate student at Princeton University, where he received his doctorate in 1951, under the direction of the noted topologist Ralph Fox. Milnor broke new ground with his proof that the 7-dimensional sphere has several distinct differential structures, sparking the development of differential topology. For this achievement he received the Fields Medal in 1962. Milnor went on to make significant contributions in many areas, such as algebraic topology, K-theory, and differential geometry. He is one of the mathematicians responsible for the emergence of low-dimensional dynamics as a lively area of research within dynamical systems theory. Around 2000 he became interested in problems of complexity in the life sciences. Milnor's honors include the 1967 National Medal of Science, as well as the the AMS Steele Prize for a Seminal Contribution to Research (1982) and the Steele Prize for Exposition (2004). Read more about John Milnor on the MacTutor History of Mathematics web site.

February 1903: The mathematician B. L. van der Waerden was born in Amsterdam, the Netherlands. He studied under Emmy Noether in Göttingen and Emil Artin in Hamburg, absorbing their innovative ideas about algebra. van der Waerden assimilated those ideas into the text Moderne Algebra, which appeared in German in 1930 and transformed the teaching of the subject in Germany and elsewhere. After receiving a doctorate from the University of Amsterdam, van der Waerden spent the World War II years in Germany. He then went back to the Netherlands, working as an applied mathematician for Shell oil corporation. He held a position at the University of Amsterdam before moving in 1951 to the University of Zurich, where he remained for the rest of his career. His wide-ranging mathematical interests had a profound impact on the mathematical life in Zurich, and he had more than forty doctoral students. Read more about van der Waerden in "Interview with Bartel Leendert van der Waerden," interviewed by Yvonne Dold-Samplonius, and "van der Waerden's Modern Algebra," by Saunders Mac Lane, Notices of the AMS, March 1997.

February 1993: The AMS makes its second round of small grants to support mathematicians in the former Soviet Union (fSU). With the fall of Communism in Eastern Europe, many mathematicians in the former Soviet Union emigrated to the West in search of political stability and better economic opportunities. This exodus posed a serious threat to the vibrant Russian mathematical tradition. The AMS formulated a plan to help mathematicians in the fSU by providing small grants and donating mathematical literature. Funding was provided by generous donations from AMS members as well as grants from the Sloan Foundation, the Soros Foundation, the International Science Foundation, and the National Science Foundation. Ultimately grants from the AMS fSU Aid Fund assisted about 350 mathematicians.

January:
January 1988: The first issue of Journal of the AMS appeared. The AMS began the journal in its centennial year, with the idea of making it an elite journal. Indeed JAMS quickly established itself as one of the top journals in mathematics. In 2002, JAMS was the leading mathematics journal as measured by citation "impact factor". The rapidity with which JAMS became a highly successful journal can be traced to the founding editorial board, which consisted of Michael Artin, H. Blaine Lawson, Jr., Richard Melrose, Wilfried Schmid, and Robert E. Tarjan.

January 1991: The AMS Ruth Lyttle Satter Prize was awarded for the first time, to Dusa McDuff of SUNY Stony Brook. This prize was established through a gift from Joan Birman, a mathematician at Barnard College, in memory of her sister, Ruth Lyttle Satter. Satter earned a bachelor's degree in mathematics and then joined the research staff at AT&T Bell Laboratories during World War II. After raising a family, she received a Ph.D. in botany at the age of 43 from the University of Connecticut at Storrs, where she later became a faculty member. Her research on the biological clocks in plants earned her recognition in the U.S. and abroad. The $5,000 Satter Prize honors her commitment to research and to encouraging women in science. Many were touched by McDuff's remarks upon receiving the prize (her remarks appeared in the prize announcement in the March 1991 issue of the AMS Notices). A list of Satter Prizewinners is on the AMS web site.

January 1978: Donald Knuth presented the Gibbs Lecture entitled "Mathematical Typography." This lecture announced the creation of TeX, the revolutionary composition system for mathematical text now widely used by mathematicians all over the world. Knuth put the software in the public domain so that it would be easy for others to create software packages based on TeX. The result was rapid and wide adoption of TeX as the standard basis for electronic typesetting in mathematics. Not only did TeX offer mathematicians a powerful and flexible means for typesetting their own papers, it also ushered in a new era of sharing of mathematical literature electronically. Electronic journals and preprint servers, as well as much of traditional paper publishing of mathematics, are almost universally based on TeX. The written version of his lecture appeared in the Bulletin of the AMS (1979, no. 2, pages 337--372). In a review in Mathematical Reviews, Richard S. Palais wrote that this paper "is destined to become a classic reference in the subject of its title."

January 1983: Julia Robinson begins her two-year term as president of the AMS, the first woman to hold this office. Robinson, who was a professor of mathematics at the University of California, Berkeley, was best known for her work on Hilbert's Tenth Problem: Is there an effective way to determine whether a Diophantine equation is solvable? Together with Martin Davis and Hilary Putnam, she proved a result crucial to the solution of the problem, which was completed by the Russian mathematician Juri Matijasevich in 1970. In 1980 she presented the AMS Colloquium Lectures, discussing computability, Hilbert's Tenth Problem, and other topics. She was elected to the National Academy of Sciences in 1976, the first woman member in the mathematics section. In 1983, she received a "genius" fellowship from the MacArthur Foundation. In 1985, Robinson died of leukemia at the age of 65. [For more information on Julia Robinson, see the biographies section of the MacTutor Web site.]

January 1988: The AMS held a referendum on five motions related to funding of research in the mathematical sciences. During the 1980s, controversy simmered over the funding of mathematical sciences research by agencies of the Department of Defense. The horrors of the Vietnam War and the threat of nuclear catastrophes during the Cold War were clearly on the minds of Society members who opposed military funding for mathematics. In addition, many were wary of the recently proposed Strategic Defense Initiative (SDI), commonly known as "Star Wars." Broadly speaking, the five motions of the referendum opposed military funding of mathematics and the SDI (their text can be found in the Notices, November 1987, page 1014). A large proportion of the membership had an interest in these issues: 7000 referendum ballots were received, a much larger number than in a typical AMS election. The motions passed by a wide margin.

January 1996: MathSciNet, the internet version of Mathematical Reviews (MR), came online. MathSciNet provides access to the MR database of reviews and bibliographic information for the mathematical sciences literature and has become an indispensable tool for mathematicians all over the world. Because of its accessibility, searchability, and ease of use, MathSciNet has come to be used in ways that the old paper MR never was. These new uses have in turn inspired improvements in the MR database: For example, MR now routinely adds for each paper entered into the database the full list of references appearing in the paper, together with links from the references to the MR reviews. A forward-looking consortium pricing scheme has brought MathSciNet access to many institutions that in the past were hard pressed to afford the paper subscription. Visit the MathSciNet web page for more details.

December:
December 1994: John Nash received the Nobel Prize in Economics Sciences from the King of Sweden. Nash, John C. Harsanyi, and Reinhard Selten were honored for "their pioneering analysis of equilibria in the theory of non-cooperative games". The story of Nash's struggle with mental illness is movingly told in the best-selling biography A Beautiful Mind by Sylvia Nasar, which was made into a widely acclaimed movie. The book recounts the cliff-hanger deliberations of the Nobel Prize committee as it considered whether to give Nash the prize. Some were concerned that his mental illness meant that he was no longer the person who actually did the work to be honored; others feared an embarassing scene during the prize ceremony with the King of Sweden. By a narrow margin, the Nobel committee voted to give Nash the prize. "All the Swedes' fears ... about how Nash would cope with the pomp in Stockholm proved groundless," Nasar wrote. "Everything went swimmingly." Read a brief autobiography of Nash on the Nobel Prize web site.

December 1997: The establishment of the Beal Prize for the solution of a conjecture in number theory was announced in the December 1997 issue of the Notices of the AMS. The conjecture was made by Andrew Beal, a prominent banker who is also a mathematics enthusiast. Beal's original prize for the solution of the conjecture, US$50,000, has been raised to US$100,000. The AMS is custodian of the funds and uses the income to support the annual Paul Erdos Memorial Lecture, presented at AMS meetings, and other activities. Beal's conjecture asserts that if A^x +B^y = C^z, where A, B, C, x, y, and z are positive integers and x, y, and z are all greater than 2, then A, B, and C must have a common prime factor. Is it true, or is it false? No one knows for sure, as neither a proof nor a counterexample has been found to date (December 2005). Read more about the Beal prize and conjecture in the Notices article and at the Beal Conjecture web site.

December 1934: The first meeting of the Bourbaki group was held. Nicolas Bourbaki is the pseudonym for a group of mathematicians (most of them French) who collaborated on writing mathematical books to provide modern tools for the working mathematician. The founders of Bourbaki were Henri Cartan, Claude Chevalley, Jean Delsarte, Jean Dieudonne, and Andre Weil. Although the members of Bourbaki were outstanding mathematicians, their identities were kept secret and the individual members did not claim credit for the works the group produced. Contributing time and effort to a publication that does not bear one's own name is highly unusual in mathematics, and in science in general; indeed the Bourbaki group may be the only such example. Bourbaki had a profound impact on mathematics, especially in the 1950s and 1960s; later on the Bourbaki books were often criticized as being too abstract and formal. The group's impact was also felt through the Bourbaki Seminar, which has taken place in Paris since 1948. [See "Twenty-Five Years with Nicolas Bourbaki, 1949-1973," by Armand Borel, Notices, March 1998.]

December 1988: Everett Pitcher retired as Secretary of the AMS. He was elected as Secretary in 1967 and served in that capacity for 22 years. "Professor Pitcher ends a 22-year tenure marked by a sincere belief in the value of the Society and a profound affection for the field of mathematics," says a December 1988 article in the AMS Notices, published on the occasion of his retirement as Secretary. "By all accounts, he consistently conducted the business of the Society with diplomacy, efficiency, and fairness." Pitcher was born in 1912 and received his PhD in 1935 from Harvard University, under the direction of Marston Morse. He joined the faculty at Lehigh University in 1938, retiring as Distinguished Professor Emeritus of Mathematics in 1978. Each spring Lehigh University sponsors the Pitcher Lectures, presented by an outstanding mathematician; a special lecture was held in July 2002 to mark his 90th birthday. [Read information on the lectures.]

November:
November 1983: On the 16th of that month, AMS President Julia Robinson sent a letter with the following message to Rhode Island Representative Claudine Schneider: "The Council of the American Mathematical Society has authorized me to petition the 102nd Congress to expunge the contempt citation of our colleague H. Chandler Davis which was imposed in 1954 by the 83rd Congress. I am asking you to carry the bill since you are the representative of Providence, the permanent home of the Society." Davis was indicted on a charge of contempt of Congress after refusing to answer questions about his political beliefs posed by the Congressional Committee on Un-American Activities. He was dismissed from his position at the University of Michigan and served six months in a Connecticut prison. Finding himself blacklisted from academic jobs in the United States, Davis left for Canada in 1962 and joined the faculty of the University of Toronto, where he is now a professor emeritus. Despite several efforts, including the letter from Julia Robinson quoted above, the contempt charge against Davis has never been reversed. The University of Michigan has never apologized for dismissing him, but it did establish in 1990 a lecture series in honor of Davis and two other Michigan faculty who had been similarly mistreated. Davis has served in various capacities in AMS governance and was an especially active and vocal member of the Committee on Human Rights of Mathematicians. A feature article in the Michigan Daily Online provides a good account of the story.

November 6, 1906: Emma Lehmer was born in Samara, Russia. In 2006, she celebrates her 100th birthday. She and her husband Derrick Lehmer were one of the most famous husband-and-wife mathematician teams; he passed away in 1991 at the age of 86. The two made distinguished contributions to number theory, in both their individual and joint work. Emma Lehmer, née Trotskaia, was raised in Harbin, China, where her father worked as a representative of a sugar company. She was tutored at home until the age of 14, when she attended school and took mathematics courses from an exceptionally gifted teacher. Emma traveled to the United States to do her undergraduate studies at the University of California, Berkeley. There she met her future husband Derrick, who was the son of one of Emma's professors at Berkeley. The couple moved together to Brown University, where Derrick earned a PhD and Emma a master's degree. Eventually they returned to Berkeley, where Derrick joined the faculty of the mathematics department. Nepotism rules forbade Emma from being offered a position in the same department, though she did do some teaching during the World War II years when the rules were relaxed. In 1945-46, her husband worked on military applications with the legendary ENIAC computer, and sometimes at night, when the computer was free, the couple used it to work on number theory problems. With no teaching duties, Emma devoted herself to mathematics research and wrote about 60 papers in number theory, 20 of them jointly with her husband. As John Brillhart wrote: "In the sixty years during which they collaborated, the Lehmers were a research team who personally influenced a large number of people with their knowledge, their courtesy and sociability, and their fine mathematical work." This account of Emma Lehmer's life is based on the portrait found in the MacTutor History of Mathematics biography of Emma Lehmer.

November 1996: The AMS Executive Committee and Board of Trustees approves funding for Society participation in the Mass Media Fellowship program of the American Association for the Advancement of Science. This program places mathematics and science graduate students to work in media outlets for ten weeks over a summer. The AMS chooses from among mathematics graduate student applicants and has supported one or two fellows every year since 1997. The AMS-sponsored fellows have worked in such high-profile venues as Time magazine, the Chicago Tribune, Scientific American, Discovery Channel Online, National Geographic Television, and National Public Radio. The fellows gain valuable experience in communicating about mathematics with the general public, and the media outlets profit from the fellows' expertise in mathematics. Some of the fellows have gone on to careers in journalism and media relations; one outstanding example is Sara Robinson, a 1998 AMS-sponsored fellow who has reported on mathematics for the New York Times. More information is available on the AMS web site.

November 1995: The mathematics department at the University of Rochester was hit with the news that the university administration planned to eliminate the department's graduate program and greatly reduce its faculty. The news sent shock waves through the mathematical and scientific communities, which saw the move as a threat to the intellectual integrity of universities. The outcry was swift and strong: The Rochester administration received over 100 letters from mathematicians and scientists across the U.S., and even a few from abroad, protesting the proposal to cut the mathematics graduate program. The AMS sent a fact-finding group to the university, and at its January 1996 meeting the AMS Council passed a resolution decrying the cuts. All the outside pressure seems to have exerted an influence, as the Rochester administration later reversed the decision to cut the mathematics department. But what really seems to have made a difference was the department's willingness to work hard at improving its teaching and to reach out to other departments. The Notices of the AMS carried extensive coverage about these events in the March, April, May, and June issues in 1996, and in the December 1997 issue. An epilogue, "Rochester Four Years Later: From Crisis to Opportunity," appeared in the September 1999 issue.

November 1998: The AMS Executive Committee and Board of Trustees initiated discussions leading to the Epsilon Fund for Young Scholars. Today the Epsilon Fund helps support for summer programs for mathematically talented high school students. The fund has provided modest grants to several programs, including Ross Mathematics Program at Ohio State University, Texas State University Honors Summer Math Camp, PROMYS at Boston University, Canada/USA Mathcamp of the Math Foundation of America, Hampshire College Summer Studies in Mathematics, All Girls/All Math at the University of Nebraska, and University of Chicago Young Scholars Program. The Epsilon Fund is supported by generous donations by those concerned about nurturing mathematical talent in young people. Visit the AMS development home page for more information about the Epsilon Fund.

October:
October 1927: Friedrich Hirzebruch was born on 17 October 1927, in Hamm, Germany. An outstanding researcher with an international reputation, Hirzebruch has been a key figure in revitalizing mathematics in postwar Germany. He received his PhD in 1949 from the University of Münster under the direction of Heinrich Behnke. Another major influence was Heinz Hopf, whom Hirzebruch encountered while visiting the Eidgenössisches Technische Hochschule in Zurich. During 1952-54, Hirzebruch visited the Institute for Advanced Study in Princeton (1952-54), where he came into contact with other leaders in algebraic geometry and topology, the subjects in which he has made his mark. His major results include the signature theorem and the Riemann--Roch theorem, which were an important influence on and starting point for Atiyah and Singer in their development of the general index theorem for elliptic operators on manifolds. Hirzebruch's groundbreaking monograph on topological methods in algebraic geometry is still widely read, decades after its publication. Together with Grothendieck and Atiyah, Hirzebruch is one of the architects of K-Theory, which has grown into an important subject in its own right, straddling the fields of algebra, geometry, and topology. In 1957, having settled at the University of Bonn, Hirzebruch started an annual meeting called the Arbeitstagung, which has a unique structure and which quickly established itself as an important venue for presenting new research. In 1980, he founded the Max Planck Institute for Mathematics in Bonn, which has since developed into one of the world's main mathematical research centers. Among Hirzebruch's many honors are the Wolf Prize (1988) and the Cantor Medal of the German Mathematical Society (2004). The entry about Hirzebruch provides further details about his life and work.

October 1990: The European Mathematical Society (EMS) was founded. Sir Michael Atiyah was one of the main initiators, and Friedrich Hirzebruch served as the first EMS president. The purpose of the EMS is the development of all aspects of mathematics in the countries of Europe, particularly the promotion of research in mathematics and its applications. The EMS membership base consists of European mathematical societies as well as individual members. The society has helped to foster mathematical activity within Europe, primarily through meetings and publications. The main EMS meeting, the European Congress of Mathematics, was first held in Paris in 1992, and ECMs have been held every four years since then. The ECM is the occasion for awarding the prestigious EMS Prizes, which honor outstanding work by young European mathematicians. The EMS Article Competition is intended to raise public understanding and awareness of mathematics by honoring articles written by mathematicians and intended for a wide audience. The EMS Publishing House is the publications arm of the society, producing books and journals as well as the membership publication the EMS Newsletter. More information may be found on the EMS web site.

October 2005: The AMS hosts the first Einstein Public Lecture in Mathematics, given on October 21, 2005, at the AMS Sectional Meeting in Lincoln, Nebraska. The speaker is Sir Michael Atiyah, 1966 Fields Medalist and a renowned expositor known for his breadth of vision and clarity of style. The lecture, called "The Nature of Space", examines the efforts of mathematicians, philsophers, and physicists working over more than 2000 years to come to grips with the nature of space. This lecture contributes to a worlwide celebration of the 100th anniversary of Albert Einstein's annus mirabilis, the year 1905 when he wrote three fundamental papers that changed the course of modern physics. James G. Arthur of the University of Toronto, AMS President for 2005-2006, initiated the idea of public lectures hosted by the AMS, as a way of raising public awareness of mathematics. Read the biography of Atiyah at the MacTutor web site, and an interview with James Arthur in the Notices of the AMS (Notices articles are free but require registration on the AMS site).

October 1994: Emails began to circulate among mathematicians about a stunning new breakthrough in topology spurred by an observation of theoretical physicists Edward Witten and Nathan Seiberg. More than a decade before, Simon Donaldson spurred great interest in gauge theory when he discovered deep connections between four-dimensional topology and Yang-Mills theory from mathematical physics. The so-called Seiberg-Witten equations simplified many of the massive technical difficulties posed by Donaldson theory and led to important new insights. The equations had actually been around for a while, but it took the insight of Seiberg and Witten to understand the equations' potential impact in gauge theory. Many mathematicians kicked themselves for not having seen the connection before. [See "Gauge Theory is Dead!---Long Live Gauge Theory!" Notices of the AMS, March 1995].

September:
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 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 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.]

August:
August 1966: The International Congress of Mathematicians (ICM) was held in Moscow. Four Fields Medals were awarded, to Michael F. Atiyah, Paul J. Cohen, Alexandre Grothendieck, and Stephen Smale. This Congress was unusual for bringing a focus on world political events. In Moscow during the ICM, Smale held a press conference in which he denounced the United States for the Vietnam War and for the House Un-American Activities Committee. He also criticized the Soviet Union, in particular for its brutal suppression of Hungary ten years earlier and for its persecution of two dissident writers. News of the press conference was carried in the New York Times, the Washington Post, and other outlets. Grothendieck carried out his own protest over the treatment of the dissident writers by refusing to attend the Congress. Léon Motchane, founder and director of the Institut des Hautes Études Scientifiques attended and accepted Grothendieck's Fields Medal on his behalf. Michael Artin recalled that, after the closing banquet held in the Kremlin, he and Hyman Bass roamed through the halls bearing a petition criticizing the Vietnam War. For the full story about Smale's political activities, see the book Stephen Smale: The Mathematician Who Broke the Dimension Barrier, by Steve Batterson (AMS, 2000).

August 1989: The AMS Council passed a motion to begin having contested elections for the office of AMS President. For most of its history, the AMS had uncontested elections for President. The election ballots listed only one Presidential candidate, that chosen by the Nominating Committee; there was the possibility of write-in candidates, but in practice the Nominating Committee's candidate always won. During the 1980s, members began questioning this practice. There were no complaints about past Presidents; there were complaints only about the election procedure, which some jokingly labeled "Soviet-style". At the same time, the Presidency was becoming a more active and less honorific post. During discussions within the Council and by a specially appointed committee, a consensus developed that the person elected as President should have a strong enough desire to fill the post to be willing to run for the office and risk defeat. On August 6, 1989, at its meeting in Boulder, Colorado, the Council approved the following motion: "The Nominating Committee and the Council shall put forward two candidates for President." The motion passed with the amendment: "The Council should review this policy after three elections for the office of President-Elect." As it turned out, the policy has remained in place ever since. August 1998: The Kiiti Morita Gardens are dedicated at the AMS. Kiiti Morita (1915-1995) made significant contributions to both algebra and topology during a long and fruitful career. An obituary in the June/July 1997 Notices stated that his work in algebra "emerges as not only supplying immensely useful results, but as strongly contributing to our present mode of thinking about algebraic and geometric structures within categorical settings." The obituary also noted, "Undoubtedly, [Morita] is now considered worldwide as one of the great founders of modern general topology". When he died, his family made a generous gift to the unrestricted endowment of the AMS. To express its appreciation, the AMS designated a section of the garden in front of its headquarters building in Providence as the Kiiti Morita Gardens. Members of Morita's family attended the dedication ceremony on August 4, 1998.

August 1893: The Chicago Mathematics Congress was held in conjunction with the World's Columbian Exposition. This meeting was a significant event for the mathematicians at the newly established University of Chicago. Led by E. H. Moore, the Chicago mathematics department had begun hiring some outstanding German mathematicians, notably Oskar Bolza and Heinrich Maschke. Felix Klein traveled from G&oumlaut;ttingen to attend the Congress, and his opening remarks were the basis for his paper "The Present State of Mathematics," in which he called for mathematicians to form ties internationally. "[T]he Chicago Congress acted as a harbinger of a new era of international cooperation in mathematics: shortly afterward European national organizations began laying plans for the First International Congress of Mathematicians, to be held in Zurich in 1896," wrote Karen H. Parshall and David E. Rowe in their book The Emergence of the American Mathematical Research Community, 1876-1900: J. J. Sylvester, Felix Klein, and E. H. Moore (American Mathematical Society/London Mathematical Society, 1994).

August 1955: Algebraic Number Theory Symposium was held in Tokyo and Nikko, Japan. This was one of the first international mathematical conferences held in Japan after World War II and a crucial event in helping Japanese mathematicians reestablish international contacts. Among the Japanese attendees were two young mathematicians, Goro Shimura and Yutaka Taniyama. It was at this conference that Taniyama formulated was to become the Taniyama-Shimura Conjecture, which, forty years later, was a key element in Andrew Wiles's proof of Fermat's Last Theorem.

August 1990: Edward Witten was awarded the Fields Medal at the International Congress of Mathematicians in Kyoto. This was the first time that someone who is primarily a physicist was awarded the Fields Medal. Witten received the medal "for his work connecting theoretical physics to modern mathematics." The Fields Medal is the world's highest honor in mathematics, and at the time there was some controversy over its being awarded to Witten, because he is not a mathematician in the traditional sense. Within a few years, however, as the impact of his work on mathematics continued to grow, the controversy dissipated. Any remaining doubts were extinguished in 1994, with the revolution wrought in topology and geometry by the so-called Seiberg-Witten equations.

July:
July 25, 1980: Euphemia Lofton Haynes, the first African-American woman to receive a doctorate in mathematics, died of a stroke. She was born in 1890 into a fourth-generation Washington family. Her father was a black dentist with a practice in the District of Columbia and also a financier of black businesses in the area. Euphemia Haynes received a bachelor's degree in mathematics (with a minor in psychology) in 1914 from Smith College and a master's degree in education from the University of Chicago in 1930. In 1943, Haynes earned a doctorate in mathematics from Catholic University. She had a distinguished career as an educator in Washington, DC, teaching mathematics for nearly 50 years in the public schools and, after her retirement from teaching in 1959, serving as chair of the board of education. She was also an outspoken critic of "tracking" policies, which resulted in de facto discrimination against African American students, and she played a prominent role in the integration of the Washington public schools. In 1930 she established a mathematics department at Miners Teachers College in Washington. She also taught at the District of Columbia Teachers College and at Howard University. She received a papal medal in 1959 for her services to Catholic organizations. This summary of the life of Haynes is based on the biography on the web site Mathematicians of the African Diaspora.

July 1904: Henri Cartan was born in Nancy, France. In 2004, the mathematical community celebrated the 100th birthday of this eminent mathematician, who witnessed so much of and contributed so greatly to the development of mathematics in the 20th century. He is the son of Élie Cartan, one of the founders of modern differential geometry. Henri Cartan's own work made a lasting impact in a variety of areas, including analytic functions, the theory of sheaves, homological algebra, algebraic topology, and potential theory. His book Homological Algebra, written with Sammy Eilenberg, has become a classic and remains in print to this day. Cartan had a major influence on mathematics through his seminar in Paris, which attracted the leading lights of mathematics and provided a training ground for many young mathematicians. On the initiative of André Weil, Cartan and a group of French mathematicians started the legendary Bourbaki group, whose approach to mathematics, embodied in several influential books, had a big impact on the field. Read more about Henri Cartan and his life in the interview that appeared in the August 1999 issue of the Notices.

July 1973: Pierre Deligne announced his proof of the last and most difficult of the Weil conjectures. Deligne described his proof in a series of six lectures delivered at a conference in Cambridge, England, honoring the 70th birthday of the mathematician W. V. D. Hodge. These conjectures, proposed in 1949 by André Weil, suggested a profound link between topology and algebraic geometry and held out the promise that some of the new tools then being developed in topology could also be deployed in algebraic geometry. The first Weil conjecture was proved by Bernard Dwork in 1959. Alexandre Grothendieck, with whom Deligne worked closely during the 1960s, produced an alternate proof in 1964. Grothendieck and other co-workers, notably Michael Artin, developed the theory of étale cohomology, as a means for attacking the Weil conjectures and managed to prove the second one as well. But the last Weil conjecture, sometimes called the "congruence Riemann Hypothesis" because of its similarity to the Riemann Hypothesis, turned out to be the most difficult. Deligne's proof brought new ideas to bear on the problem and is considered a landmark result in 20th century mathematics. For this work Deligne received the Fields Medal in 1978. A brief description of the Weil conjectures may be found in the entry in the Wikipedia.

July 1957: The first "Arbeitstagung" was held at the University of Bonn. This "working meeting" was begun by Friedrich Hirzebruch, one of the outstanding German mathematicians of the postwar era and founder of the Max-Planck-Institut für Mathematik in Bonn. The format of the Arbeitstagung is unusual. Only the opening talk is planned in advance, and the other talks are scheduled during the "program discussion," held on the first day of the meeting, during which participants throw out names of people they want to hear speak (they cannot suggest themselves). The names are collected and listed on the board, and then the list is refined and finalized. This highly unusual "democratic" way of scheduling speakers on the spot was an innovation of Hirzebruch's. He presided over the Arbeitstagung program discussion for three decades, during which time his tact and mathematical taste were crucial to the meetings' success. Today the Arbeitstagung is held every other year, and the program discussion is handled by the current directors of the Max-Planck-Insitut.

July 1992: The first European Congress of Mathematicians (ECM) was held in Paris. Now an event held every four years, the ECM is sponsored by the European Mathematical Society. The first ECM, centered at the Sorbonne, featured a huge variety of plenary lectures, parallel sessions, and "roundtable" discussions. There were several lavish social events, including a celebration of the 88th birthday of Henri Cartan, held at the German embassy. The ECM also provided the occasion of the first awarding of the ECM prizes, presented by then-mayor of Paris Jacques Chirac to ten young outstanding European mathematicians. Two of the prizewinners, Richard Borcherds and Maxim Kontsevich, went on to receive Fields Medals. The 2004 ECM is being held in Stockholm, Sweden, June 27-July 2, 2004. [See "European Meetings Bring Mathematicians Together," Notices of the AMS, September 1992.]

June:
June 24, 1880: Oswald Veblen was born in Decorah, Iowa. A gifted mathematician who produced influential works, Veblen also had a large impact on the development and organization of mathematical and scientific research in the United States. He received his Ph.D. in mathematics in 1903 from the University of Chicago, under the direction of E. H. Moore. Veblen's doctoral thesis, A System of Axioms for Geometry, clarified aspects of David Hilbert's then-recent work on the foundations of geometry. After two postdoctoral years at Chicago, Veblen took a position at Princeton University, where his mathematical reputation steadily grew and he was made a professor in 1910. Among his most important contributions are the first rigorous proof of the Jordan Curve Theorem and his efforts to make the work of Henri Poincaré accessible to the pioneers of algebraic topology. After the start of the first World War, Veblen was commissioned as an army reserve captain. As the head of experimental ballistics at the Aberdeen Proving Ground in Maryland, he made important contributions to that area. After the war, Veblen worked hard at fund-raising for the support of mathematical research, in particular bringing in funds to rescue the AMS from a budget shortfall at a crucial time in the Society's history. Veblen served as AMS President during 1923-1924. Perhaps his most notable work in nurturing scientific research was his service as first director of the Institute for Advanced Study, which was founded in 1933 with a faculty consisting of, in addition to Veblen as director, James Alexander, Albert Einstein, and John von Neumann; shortly thereafter Hermann Weyl joined the faculty as well. Veblen's early stewardship of the Institute was crucial in making it the world-renowned scholarly center it is today. Much of this summary of Veblen's life comes from "The Vision, Insight, and Influence of Oswald Veblen" by Steve Batterson, which appears in the May 2007 issue of the AMS Notices. Veblen was, as Batterson puts it, a "statesman of mathematics"---an individual who had an important impact through his own work as a mathematician, through his mentorship of young people, and through his advocacy for the field.

June 1912: Alan M. Turing was born in London. He died in 1954, not long before his 42nd birthday. Turing is widely considered to be one of the greatest intellects of the twentieth century. He established the basis for modern computers and originated what is now called the "Turing machine," a mathematical model of an all-purpose computer. Much of his thinking about computing anticipated problems that became important later on; one example is the well known "Turing test" that bears his name. He played a decisive role in helping the British to break German codes during World War II and for this work he received an O.B.E. After the war, Turing continued to work in computing and codes, and his interests expanded to include pattern formation and morphogenesis. He had all his life been openly homosexual, and in 1952 he was arrested and found guilty of homosexuality. Because of his work on code-breaking, he had high-level clearance, but this was withdrawn after his conviction. In June 1954, he was found dead of cyanide poisoning. The poison was in an apple he had been eating. The definitive work about Alan Turing is the compelling and highly readable Alan Turing: The Enigma by Andrew Hodges (1983). Hodges has created an extensive web site about Turing's life and work.

June 1992: The Fields Institute in Canada opens its doors. Originally established on the campus of the University of Waterloo, the Fields Institute is now located at the University of Toronto. It has become one of the world's major mathematics institutes, with an active and diverse program across all areas of mathematics. In 2004, Barbara Lee Keyfitz was named director of the Fields Institute, the first woman to serve as director of a major mathematics institute (the only possible exception is Cathleen Morawetz, who in the 1980s was director of the Courant Institute of Mathematical Sciences at New York University; however, Courant differs from a national mathematics institute in that it functions more like a school of mathematics in offering courses and awarding degrees). "The idea of refreshing the stream of research in Canada by interacting with other countries is an important theme at this institute," Keyfitz remarked. Read about the founding of the Fields Institute in "Canada's Fields Institute Opens Its Doors," Notices, July/August 1992, and about Keyfitz's appointment in "Keyfitz Named Director of Fields Institute," Notices, September 2004.

June 1992: The Isaac Newton Institute celebrated its inauguration. Sir Michael Atiyah, founding director of the Newton Institute, said at the time: "I think the view is at the present time that a lot of the future development of mathematics will probably be to use more advanced mathematics in related fields and to bring problems from other fields into mathematics. So our aim is really to bridge the gap by bringing people together." Since then, it has become one of the world's main institutes for research in pure and applied mathematics. Visit the Newton Institute's web site.

June 1993: At a conference at the Isaac Newton Institute, Andrew Wiles gave his first ever lecture on his proof of Fermat's Last Theorem. The institute buzzed with rumors that his lecture would contain a big surprise, but few realized just how big it would be. Using a regular chalkboard, Wiles sketched his proof for the audience of experts, who burst into explosive applause when he came to the end and concluded that he had proved Fermat's Last Theorem. It was a few months later that a gap appeared in the proof, and it wasn't until sometime after that that the proof was finally complete. But many remember Wiles's historic lecture as a high point for mathematics.

May:
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 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 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.

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 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."

April:
April 1973: The first international meeting on topology ever held in Japan took place in Tokyo. This was a significant event in the development of topology in Japan, now a thriving area of research there. The conference brought leading topologists from all over the world. General lectures were presented by Michael Atiyah ("Eigenvalues and Riemannian geometry") and by Christopher Zeeman ("Applications of catastrophe theory"). There were also lectures in the topology of manifolds, singularities, foliations, dynamical systems, algebraic topology, and other subjects. The Mathematical Society of Japan published the proceedings of the conference in 1975.

April 1986: Mathematics Awareness Week was celebrated for the first time. That year, the United States Congress passed legislation inaugurating this annual event, which is designed to promote public awareness of mathematics and its uses. The event comprised dozens of regional and local celebrations, many of them within college and university mathematics departments, as well as a public service announcement that aired on over 200 television stations around the country. Mathematics Awareness Week was eventually expanded to Mathematics Awareness Month (MAM), which is now celebrated each year in April. Each MAM focuses on a particular theme; for 2005 the theme was "Mathematics and the Cosmos", and for 2006 it is "Mathematics and Internet Security". The Joint Policy Board for Mathematics (JPBM), which sponsors MAM, chooses the themes and produces theme essays and a poster, which groups can build on for their own local and regional celebrations. The JBPM is a collaborative project of the AMS, the American Statistical Association, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics.

April 1899: On the 24th of that month, Oscar Zariski was born in Kobrin, Belarus, Russia. He had a tumultuous early life during World War I and eventually went to study mathematics in Rome with the great Italian algebraic geometers of the day. He received his doctorate from the University of Rome in 1925, under the direction of Guido Castelnuovo. Because he was Jewish, his life became increasingly difficult in the years leading up to World War II, and in 1927 he emigrated to the United States. After holding positions at various universities, and also spending a year in Brazil, Zariski went in 1947 to Harvard University, where he remained for the rest of his career. Although he admired the ingenuity of his Italian teachers, Zariski realized the lack of rigor in their methods. With André Weil and B. L. van der Waerden, Zariski began to lay the foundations for a new, more rigorous approach to algebraic geometry. A charismatic and inspiring figure, he attracted at Harvard a large number of excellent doctoral students, including two who would go on to receive Fields Medals, Heisuke Hironaka and David Mumford. Zariski received the AMS Cole Prize in Algebra in 1944 and served as president of the AMS from 1969 to 1971. In 1965, he received the National Medal of Science. Read more about Zariski's life and work in the obituary by David Mumford that appeared in the November 1986 issue of the Notices, and the biography The Unreal Life of Oscar Zariski, by Carol Parikh (Academic Press, 1991). See also the entry about Zariski on the MacTutor History of Mathematics archive.

April 1997: World-famous mathematician and Fields Medalist Enrico Bombieri plays an April Fools Day joke. He sends out an email message claiming that a young physicist giving a talk at the Institute for Advanced Study announced a proof of the Riemann Hypothesis, one of the outstanding problems in mathematics and one that Bombieri has worked on himself for years. The email message circled the globe and more than a few people were fooled--at least for a while. The message contained some hints that it was not entirely serious; it said for example that the physicist was working with particles called "morons".

April 1988: Robert P. Langlands of the Institute for Advanced Study in Princeton receives the first NAS Award in Mathematics from the National Academy of Sciences. The award recognized Langlands' "extraordinary vision that has brought the theory of group representations into a revolutionary new relationship with the theory of automorphic forms and number theory." Established by the AMS in commemoration of its centennial in 1988, the US$5,000 award was made possible through gifts to the Society from Morris Yachter and Sidney Henry Gould. It is given every four years for excellence of research in the mathematical sciences published within the past ten years. Other recipients are Dan Virgil Voiculescu (2004), Ingrid Daubechies (2000), Andrew J. Wiles (1996), and Robert MacPherson (1992). Read more about the prize and recipients.

March:
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 Lam&ecaute; 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.

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 1916: Paul R. Halmos was born in Budapest, Hungary, on March 3, 1916. One of the field's outstanding mathematical expositors, Halmos is 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 is 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 is now 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. [For more information on Paul Halmos see the biographies section of the MacTutor Web site.]

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.

February: