21st-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.

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

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.

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.

Carl Mark Pearcy, Jr. (born August 25, 1935) is an American mathematician whose research has been concentrated on operator theory and operator algebras. He has coauthored several books, including "Introduction to Operator Theory I", Introduction to Analysis", and "Measure and integration", all published by Springer and coauthored by Arlen Brown (and Hari Bercovici in the case of Measure and integration). Pearcy had 31 Ph. D. students at Michigan and TAMU
, several of whom are outstanding mathematicians. Pearcy's bibliography contains more than 150 papers, and his research has concerned the invariant subspace problem and the theory of dual algebras.

Robert Lawson Vaught (April 4, 1926 – April 2, 2002) was a mathematical logician and one of the founders of model theory.

George Rushing Kempf (Globe, Arizona, August 12, 1944 – Lawrence, Kansas, July 16, 2002) was a mathematician who worked on algebraic geometry, who proved the Riemann–Kempf singularity theorem, the Kempf–Ness theorem, the Kempf vanishing theorem, and who introduced Kempf varieties.

Louis de Branges de Bourcia (born August 21, 1932) is a French-American mathematician. He was the Edward C. Elliott Distinguished Professor of Mathematics at Purdue University in West Lafayette, Indiana, retiring in 2023. He is best known for proving the long-standing Bieberbach conjecture in 1984, now called de Branges's theorem. He claims to have proved several important conjectures in mathematics, including the generalized Riemann hypothesis.
Born to American parents who lived in Paris, de Branges moved to the US in 1941 with his mother and sisters. His native language is French. He did his undergraduate studies at the Massachusetts Institute of Technology (1949–53), and received a PhD in mathematics from Cornell University (1953–57). His advisors were Wolfgang Fuchs and then-future Purdue colleague Harry Pollard. He spent two years (1959–60) at the Institute for Advanced Study and another two (1961–62) at the Courant Institute of Mathematical Sciences. He was appointed to Purdue in 1962.
An analyst, de Branges has made incursions into real, functional, complex, harmonic (Fourier) and Diophantine analyses. As far as particular techniques and approaches are concerned, he is an expert in spectral and operator theories.

Alice Turner Schafer (June 18, 1915 – September 27, 2009) was an American mathematician. She was one of the founding members of the Association for Women in Mathematics in 1971.