Stephen George Simpson (born September 8, 1945) 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.

[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.

[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.