Richard James Milgram (born 5 December 1939 in

South Bend, Indiana South Bend is a city in St. Joseph County, Indiana, United States, and its county seat. It lies along the St. Joseph River (Lake Michigan), St. Joseph River near its southernmost bend, from which it derives its name. It is the List of cities in ...

) is an American mathematician, specializing in

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

. He is the son of mathematician

Arthur Milgram Arthur Norton Milgram (3 June 1912 – 30 January 1961) was an American mathematician. He made contributions in functional analysis, combinatorics, differential geometry, topology, partial differential equations, and Galois theory. Perhaps one of h ...

Biography

Milgram graduated from the

University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...

with a bachelor's degree and a master's degree in 1961. He received his doctorate in 1964 from the

University of Minnesota The University of Minnesota Twin Cities (historically known as University of Minnesota) is a public university, public Land-grant university, land-grant research university in the Minneapolis–Saint Paul, Twin Cities of Minneapolis and Saint ...

with thesis ''The homology ring of symmetric products of Moore spaces'' under the supervision of Alfred Aeppli (1928–2008). Milgram taught from 1970 as a professor at

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

, where he is now emeritus. He was a visiting professor at the

University of Lille The University of Lille (, abbreviated as ULille, UDL or univ-lille) is a French public research university based in Lille, Hauts-de-France. It has its origins in the University of Douai (1559), and resulted from the merger of three universities ...

(2001), the

Chinese Academy of Sciences The Chinese Academy of Sciences (CAS; ) is the national academy for natural sciences and the highest consultancy for science and technology of the People's Republic of China. It is the world's largest research organization, with 106 research i ...

(2000) in Beijing, at the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...

(1987 as Gauss Professor), and at the University of Minnesota (1986 as Ordway Professor), as well as the

ETH Zurich ETH Zurich (; ) is a public university in Zurich, Switzerland. Founded in 1854 with the stated mission to educate engineers and scientists, the university focuses primarily on science, technology, engineering, and mathematics. ETH Zurich ran ...

, Edinburgh, Montreal, Barcelona, the MSRI, and the

University of New Mexico The University of New Mexico (UNM; ) is a public research university in Albuquerque, New Mexico, United States. Founded in 1889 by the New Mexico Territorial Legislature, it is the state's second oldest university, a flagship university in th ...

. In 1974, Milgram was an Invited Speaker with talk ''The structure of the oriented topological and piecewise linear bordism rings'' at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

Vancouver Vancouver is a major city in Western Canada, located in the Lower Mainland region of British Columbia. As the List of cities in British Columbia, most populous city in the province, the 2021 Canadian census recorded 662,248 people in the cit ...

. He was an editor for the ''

Pacific Journal of Mathematics The Pacific Journal of Mathematics is a mathematics research journal supported by several universities and research institutes, and currently published on their behalf by Mathematical Sciences Publishers, a non-profit academic publishing organisa ...

'' from 1973 to 1983, for the ''

Duke Mathematical Journal ''Duke Mathematical Journal'' is a peer-reviewed mathematics journal published by Duke University Press. It was established in 1935. The founding editors-in-chief were David Widder, Arthur Coble, and Joseph Miller Thomas. The first issue inclu ...

'' from 1976 to 1984, and for the A.M.S. ''Contemporary Mathematics'' series (from its inception in 1980 to 1984). In August 1999 Stanford University held a mathematical conference in his honor. His doctoral students include Gunnar Carlsson.

Research

With Charles P. Boyer, Jacques Hurtubise, and Benjamin M. Mann, he proved in 1992 the Atiyah–Jones conjecture on the topology of the moduli space of instantons on spheres. He has also done research on robotics and protein folding.

Mathematics education

In addition to algebraic and geometric topology, he has written on mathematics education and served on numerous committees, including the National Board for Education Sciences (since 2005). He is one of the major authors of the mathematical standards for schools in California and has advised the school authorities in Michigan, New York, and Georgia.

Selected publications

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References

External links