#
This Mathematical Month - February: 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.**

< **January** o **March** >
**Featured Item for February**
**February 2013:** Black History Month is celebrated in the United States each year in February. One way to mark this occasion is to look back at distinguished Black mathematicians. One outstanding figure is statistician **David Blackwell**. He was born in Centralia, Illinois, on April 24, 1919. He was fortunate to attend an integrated school, and with the help of good teachers he developed an interest in geometry. It was when he entered the University of Illinois at the age of 16 that his interest in mathematics deepened. Six years later he had finished a doctorate under the direction of **Joseph Doob,** one of the founders of modern probability theory and an AMS President, 1963-64. Doob had a profound impact on Blackwell's thinking and research. He was also instrumental in helping Blackwell to secure a postdoctoral fellowship to do research at the Institute for Advanced Study in Princeton. At the time, African Americans were not welcome in most research universities: Princeton University, which had never had a Black student or faculty member, complained about having to give Blackwell an honorary professorship by virtue of his Institute appointment. When trying to find a permanent job, Blackwell focused on historically Black colleges and universities. Faculty members at the University of California at Berkeley expressed interest in hiring him, but prejudice was too strong at the time for an offer to be made. By 1944, he had a position at Howard University, considered to be the top Black university in the nation. Ten years later it was undeniable that Blackwell was an outstanding figure in probability and statistics, and he received and accepted an offer from Berkeley and remained there for the rest of his career. In 1954 he gave an invited address at the International Congress of Mathematicians. He served as President of the Institute of Mathematical Statistics and as a Vice-president of the AMS. In 1965, he was elected to the National Academy of Sciences. He received the 1986 R.A. Fisher Award, one of the top distinctions in probability and statistics. Blackwell died on 8 July 2010. An obituary in the *New York Times* appeared on 17 July 2010; the *AMS Notices* obituary appeared in the August 2011 issue. A biography of Blackwell is on the MacTutor History of Mathematics web site.

**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.

**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 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 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 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 1900:** A report, "The Sixth Annual Meeting of the American Mathematical Society", appeared in the *Bulletin of the AMS*. The AMS, originally called the New York Mathematical Society, had been founded in 1888, and this seven-page report, written by AMS secretary **Frank Nelson Cole**, provides a snapshot of one aspect of the Society's activities in its early days. The report says that the AMS had 337 at the time and contains a list of the 38 Society members in attendance at the meeting (including at least three women). Thirteen lectures were presented, some of which appeared in the same issue of the *Bulletin*; abstracts of the other talks are presented in the report. The lectures ranged over a variety of topics, from algebra to differential equations to geometry, and included a couple of lectures on applied mathematics, such as the Presidential Address by **R. S. Woodward**, "The Century's Progress in Applied Mathematics". Woodward's paper had appeared earlier in the *Bulletin* and also in *Science*. This report provides a vivid contrast with today's AMS meetings that take place as part of the Joint Mathematics Meetings. The January 2011 JMM, which took place in New Orleans, attracted over 6,000 mathematicians, exhibitors and students and featured hundreds of talks and sessions.

**February 1826:** In a session of the Department of Physico-Mathematical Sciences at Kazan University, **Nicolai Lobachevsky** spoke about his ideas for a new kind of geometry. His work was eventually published in the paper "A concise outline of the foundations of geometry was sent to referees", which appeared in the *Kazan Messenger* in 1829. Euclid's fifth postulate states that, given a line and one point not on that line, there is exactly one line that passes through the point and that is parallel to the given line. Lobachevsky realized that one could replace this postulate with one stating that there can be more than one parallel passing through the point, and the resulting geometry is perfectly consistent. Now typically referred to as hyperbolic geometry, Lobachevsky's discovery remains in wide use in mathematics and physics. Around the same time, and independently of Lobachevksy, **János Bolyai** made the same discovery.

< **January** o **March** >