Stephen Carl Milne is an American mathematician who works in the fields of analysis, analytic number theory, and combinatorics.

Milne received a bachelor's degree from San Diego State University in 1972 and a Ph.D. from the University of California, San Diego (UCSD) in 1976. His thesis, Peano curves and smoothness of functions, was written under Adriano M. Garsia.^[1] From 1976 to 1978 he was a Gibbs Instructor at Yale University. Milne taught at Texas A&M University, UCSD, the University of Kentucky, and Ohio State University, where he became in 1982 an associate professor and in 1985 a full professor.

Milne works on algebraic combinatorics, classical analysis, special functions, analytic number theory, and Lie algebras (generalizations of the Macdonald identities).

From 1981 to 1983 he was a Sloan Fellow. In 2007 he was the joint recipient with Heiko Harborth of the Euler Medal. In 2012 Milne was elected a Fellow of the American Mathematical Society.^[2]

• Milne, Stephen C. (1978). "A q-analog of restricted growth functions, Dobinski's equality, and Charlier polynomials". Trans. Amer. Math. Soc. 245: 89–118. doi:10.1090/s0002-9947-1978-0511401-8. MR 0511401.
• with Glenn Lilly: Milne, Stephen C.; Lilly, Glenn M. (1992). "The A_ℓ and C_ℓ Bailey transform and lemma". Bull. Amer. Math. Soc. (N.S.). 26: 258–263. arXiv:math/9204236. doi:10.1090/s0273-0979-1992-00268-9. MR 1118702. S2CID 119144316.
• Milne, S. C. (1996). "New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan's tau function". Proc Natl Acad Sci U S A. 93 (26): 15004–15008. arXiv:math/0008068. Bibcode:1996PNAS...9315004M. doi:10.1073/pnas.93.26.15004. PMC 26345. PMID 11038532.
• Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions. Kluwer Academic Publishers. 2002. ISBN 9781402004919.

• Homepage at Ohio State University