This Mathematical Month - July: 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 on the 2009 Calendar of Mathematical Imagery

July 1849: Robert S. Woodward was born on July 21, 1849 and served as president of the AMS 1899-1900. In his book, Probability and Theory of Errors he wrote: "The theory of probabilities and the theory of errors now constitute a formidable body of knowledge of great interest and of great practical importance. Though developed largely through the applications to the more precise sciences of astronomy, geodesy and physics, their range of applicability extends to all the sciences; and they are plainly destined to play an increasingly important role in the development and in the applications of the sciences of the future. Hence their study is not only a commendable element in a liberal education, but some knowledge of them is essential to a correct understanding of daily events." Read a brief summary of his background on the AMS Presidents: A Timeline.

July 1958: Fifty years ago the July issue of Bulletin of the AMS included the following articles: "Evolution by mutation," by H. J. Muller, "On 2-spheres in 3-manifolds," by J. H. C. Whitehead; "On isomorphisms of group algebras," by Walter Rudin; "A class of lattice ordered algebras," by Casper Goffman; and "A proof and extension of Dehn's lemma," by Arnold Shapiro and J. H. C. Whitehead. See the Table of Contents of the July 1958 issue, and view the first century of the Bulletin of the American Mathematical Society, from 1891 to 1991 online, searchable and fully integrated with the modern Bulletin. The approximately 84,000 pages of the Bulletin are freely accessible to all.

July 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 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 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 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.]