Steve Simpson (mathematician)

Stephen George Simpson is an American mathematician whose research concerns the foundations of mathematics, including work in mathematical logic, recursion theory, and Ramsey theory. He is known for his extensive development of the field of reverse mathematics founded by Harvey Friedman, in which the goal is to determine which axioms are needed to prove certain mathematical theorems.[1] He has also argued for the benefits of finitistic mathematical systems, such as primitive recursive arithmetic, which do not include actual infinity.[2]

Stephen G. Simpson
Stephen Simpson (mathematician).jpg
Steve Simpson at Oberwolfach, 2008
Alma materMIT
Known forReverse mathematics
Scientific career
InstitutionsPennsylvania State University Vanderbilt University
ThesisAdmissible Ordinals and Recursion Theory
Doctoral advisorGerald Sacks
Doctoral students

A conference in honor of Simpson's 70th birthday was organized in May 2016.[3]


Simpson graduated in 1966 from Lehigh University with a B.A. (summa cum laude) and M.A. in mathematics.[4] He earned a Ph.D. from the Massachusetts Institute of Technology in 1971, with a dissertation entitled Admissible Ordinals and Recursion Theory and supervised by Gerald Sacks.[5]


After short-term positions at Yale University, the University of California, Berkeley, and the University of Oxford, Simpson became an assistant professor at the Pennsylvania State University in 1975. At Penn State, he was Raymond N. Shibley professor from 1987 to 1992.[4]

In 2016 his wife, computer scientist Padma Raghavan, moved from Penn State to Vanderbilt University to become vice provost for research,[6] and Simpson followed her, becoming a research professor at Vanderbilt.[7]

Selected publicationsEdit

  • Simpson, Stephen G. (1977), "First order theory of the degrees of recursive unsolvability", Annals of Mathematics, 105 (1): 121–139, doi:10.2307/1971028, JSTOR 1971028, MR 0432435.
  • Friedman, Harvey M.; Simpson, Stephen G.; Smith, Rick L. (1983), "Countable algebra and set existence axioms", Annals of Pure and Applied Logic, 25 (2): 141–181, doi:10.1016/0168-0072(83)90012-X, MR 0725732 CS1 maint: discouraged parameter (link).
  • Carlson, Timothy J.; Simpson, Stephen G. (1984), "A dual form of Ramsey's theorem", Advances in Mathematics, 53 (3): 265–290, doi:10.1016/0001-8708(84)90026-4, MR 0753869.
  • Simpson, Stephen G. (1988), "Partial realizations of Hilbert's Program", Journal of Symbolic Logic, 53 (2): 349–363, doi:10.2307/2274508, JSTOR 2274508, MR 0947843.
  • Simpson, Stephen G. (1999), Subsystems of second order arithmetic, Perspectives in Mathematical Logic, Berlin: Springer-Verlag, doi:10.1007/978-3-642-59971-2, ISBN 3-540-64882-8, MR 1723993. 2nd ed., 2009, MR2517689.


  1. ^ Elwes, Richard (2013), Math in 100 key breakthroughs (PDF), Quercus, New York, p. 397, ISBN 978-1-62365-054-4, MR 3222699.
  2. ^ Wolchover, Natalie (December 6, 2013), "Dispute over infinity divides mathematicians" (PDF), Scientific American.
  3. ^ The Foundational Impact of Recursion Theory: In honor of Steve Simpson's 70th birthday, May 22, 2016, retrieved 2016-05-06 CS1 maint: discouraged parameter (link).
  4. ^ a b Simpson, Stephen G. (January 21, 2016), Curriculum vitae (PDF), retrieved 2016-05-06 CS1 maint: discouraged parameter (link)
  5. ^ Steve Simpson at the Mathematics Genealogy Project
  6. ^ Moran, Melanie (December 2015), "Vanderbilt names Padma Raghavan as vice provost for research", Research news @ Vanderbilt, Vanderbilt University, retrieved 2016-05-06 CS1 maint: discouraged parameter (link).
  7. ^ Faculty profile, Vanderbilt University, retrieved 2016-05-06 CS1 maint: discouraged parameter (link).

External linksEdit