This Mathematical Month - March: 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 2008 Calendar of Mathematical Imagery

March 1980: On the 14th of this month, the National Science Foundation issued a news release about the construction by Robert Griess of "the Monster" group. The Monster is one of the finite simple groups, which are among the most basic objects in mathematics. The classification of finite simple groups was an important goal in mathematics during the 20th century and today has largely been completed. Griess's construction was an important milestone in this effort. "A scientist has taken a major step toward the solution of a long-standing problem in mathematics---an accomplishment that involved a structure with so many elements that he had to develop new ways of doing the computations because even high speed computers could have taken many years of full-time continuous operation to do the job," the NSF news release said. The Monster is one of 26 "sporadic" groups that don't fit neatly into any existing categories in the classification. It is called the Monster because it has so many elements---the number runs to 54 digits. The news release noted that it was in 1965 that the mathematical community was "startled by the discovery of a new sporadic group, the first since 1860". Today all 26 sporadic groups are known, but the Monster still stands out among them. "The Monster remains the single most tantalizing simple group" wrote Ronald Solomon in his article "On Finite Simple Groups an Their Classifcation" in the February 1995 issue of the Notices of the AMS. Current details on the classification may be found in "The Status of the Classification of the Finite Simple Groups", by Michael Aschbacher, in the August 2004 Notices.

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 Lamé 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.