20th-century American mathematicians

Joseph Leo Doob (February 27, 1910 – June 7, 2004) was an American mathematician, specializing in analysis and probability theory.
The theory of martingales was developed by Doob.

Francis William Lawvere (; February 9, 1937 – January 23, 2023) was an American mathematician known for his work in category theory, topos theory and the philosophy of mathematics.

Joaquín Bustoz Jr. (1939–2003) was an American mathematician who worked as a professor of mathematics at Arizona State University. His mathematical research concerned functional analysis, including orthogonal polynomials and special functions, but he was primarily known as a mentor to underrepresented minorities in mathematics.Bustoz was born in Tempe, Arizona; his parents worked on the local farms and also for the Tempe Elementary School District, which eventually named the Joaquin and Ramona Bustoz Elementary School after them. He graduated from Arizona State University in 1962 with a degree in mathematics, and after two years in California working for Univac returned to ASU, where he completed a doctorate in 1967 under the supervision of Walter Tandy Scott. After teaching at the University of Cincinnati from 1969 to 1976, during which he also spent a year at the National University of Colombia as a Fulbright Scholar, he returned to ASU again as an associate professor in 1976, and was promoted to full professor in 1978. He chaired the ASU mathematics department from 1982 to 1985.In 1985, Bustoz founded the Summer Math–Science Honors program for high school students, which continues at ASU as the Joaquin Bustoz Math–Science Honors Program. Bustoz also worked on mathematics education on the Navajo Nation and the Pima reservations. For his efforts, president Bill Clinton honored him in 1996 with the Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring.He was killed by a car accident on August 13, 2003. As well as the Math–Science Honors program, the Joaquin Bustoz Jr. Professorship at ASU, held by Carlos Castillo-Chavez, is named after Bustoz.

Allen Edward Hatcher (born October 23, 1944) is an American topologist.

Hans Heinrich Wilhelm Magnus known as Wilhelm Magnus (5 February 1907 in Berlin, Germany – 15 October 1990 in New Rochelle, New York) was a German-American mathematician. He made important contributions in combinatorial group theory, Lie algebras, mathematical physics, elliptic functions, and the study of tessellations.

Theodore Samuel Motzkin (26 March 1908 – 15 December 1970) was an Israeli-American mathematician.

Vivienne Lucille Malone-Mayes (née Malone; February 10, 1932 – June 9, 1995) was an American mathematician and professor. Malone-Mayes studied properties of functions, as well as methods of teaching mathematics. She was the fifth African-American woman to gain a PhD in mathematics in the United States, and the first African-American member of the faculty of Baylor University.

George E. Collins (January 10, 1928 in Stuart, Iowa – November 21, 2017 in Madison, Wisconsin) was an American mathematician and computer scientist. He is the inventor of garbage collection by reference counting[G60]
and of the method of quantifier elimination by cylindrical algebraic decomposition.[G75]He received his PhD from Cornell University in 1955. He worked at IBM, the University of Wisconsin–Madison (1966–1986) Ohio State University, RISC-Linz, Delaware University, and North Carolina State University.

Leonard Carlitz (December 26, 1907 – September 17, 1999) was an American mathematician. Carlitz supervised 44 doctorates at Duke University and published over 770 papers.

Charles Coffin Sims (April 14, 1937 – October 23, 2017) was an American mathematician best known for his work in group theory. Together with Donald G. Higman he discovered the Higman–Sims group, one of the sporadic groups. The permutation group software developed by Sims also led to the proof of existence of the Lyons group (also known as the Lyons–Sims group) and the O'Nan group (also known as the O'Nan–Sims group).
Sims was born and raised in Elkhart, Indiana, and received his B.S. from the University of Michigan. He did his graduate studies at Harvard University, where he was a student of John G. Thompson and received his Ph.D. degree in 1963. In his thesis, he enumerated p-groups, giving sharp asymptotic upper and lower bounds. Sims is one of the founders of computational group theory and is the eponym of the Schreier–Sims algorithm. He was a faculty member at the Department of Mathematics at Rutgers University from 1965 to 2007. During that period he served, in particular, as Department Chair (1982–84) and Associate Provost for Computer Planning (1984–87). Sims retired from Rutgers in 2007 and moved to St. Petersburg, Florida.In 2012, he became a fellow of the American Mathematical Society.