This Mathematical Month - October: 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 2010 Calendar of Mathematical Imagery

October 1815: Karl Theodor Wilhelm Weierstrauss was born on October 31 in Ostenfelde, Westphaslia (now Germany). Although his father arranged for him to study finance and planned on his working in the Prussian administration, Weierstrauss was always torn between the wishes of his father and pursuing the subject he loved--mathematics. He studied the subject on his own, while qualifying to become a teacher and holding various jobs. Upon publication of his paper "Zur Theorie der Abelischen Functionen" in Crelle's Journal in 1854, mathematicians took notice. The University of Königsberg awarded him an honorary doctor's degree in 1854, after which he became a lecturer, published a full version of his theory of inversion of hyperelliptic integrals, and received offers of positions at several universities. He eventually accepted the position of professor then chair at the University of Berlin. When Sofia Kovalevskaya came to Berlin he taught her privately as she was not allowed admission to the university. (She went on to receive an honorary doctorate from Göttingen and the two corresponded for 20 years.) He edited the complete works of Jakob Steiner and Carl Gustav Jacob Jacobi, and is widely regarded as the father of modern analysis. For more details on his life and work, see his biography on the MacTutor website.

October 1911: On the 26th of that month, Shiing-Shen Chern was born in Jiaxing, China. When he was a youngster, China was just starting to establish western-style universities. Chern entered Nankai University at the age of 15 and attended graduate school at Tsinghua University. In 1934, he obtained a three-year scholarship to study in the west, and he decided to go to Hamburg. He completed his PhD in two years and spent the third year of his scholarship in Paris, working with the great geometer Elie Cartan. After his return to China, Chern was quite isolated, but he studied reprints that Cartan had sent him, and he continued to publish. His work drew international attention, and in 1943 he was invited to the Institute for Advanced Study in Princeton. It was there that he completed his proof of the generalized Gauss-Bonnet theorem, which marries local geometry to global topological invariants. In an interview with the AMS Notices, Chern spoke of the differential geometry of fiber bundles, which led to his proof of Gauss-Bonnet, as being what he considered to be his most important work. Among his other outstanding achievements is the discovery of what are now known as Chern characteristic classes in fiber spaces, which have proved to be of great importance not only in mathematics but also in mathematical physics. In 1949 Chern became a professor at the University of Chicago and later moved to the University of California, Berkeley, where he was founding director of the Mathematical Sciences Research Institute. After his retirement he returned to China and was a major figure in building mathematical research there, founding the Nankai Institute for Mathematics in Tianjin in 1985. Chern died at his home in Tianjin on December 3, 2004, at the age of 93.

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].