Robert Daniel Carmichael
Robert Daniel Carmichael (March 1, 1879 – May 2, 1967) was an American mathematician born in Goodwater, Alabama. He studied at Lineville College briefly and earned his bachelor’s degree in 1898 while pursuing a PhD at Princeton University. He completed his PhD in mathematics in 1911 under G. D. Birkhoff with the thesis Linear Difference Equations and their Analytic Solutions, an early significant American contribution to differential equations.
Carmichael taught at Indiana University from 1911 to 1915, then at the University of Illinois from 1915 until his retirement in 1947. He is best known for work in number theory, including Carmichael numbers (composite numbers that mimic primes under Fermat’s little theorem). He found the smallest Carmichael number, 561, and it later became known that there are infinitely many of them. He also contributed to ideas now called Carmichael’s totient function conjecture, Carmichael’s theorem, and the Carmichael function.
He described the Steiner system S(5,8,24) in his 1931 paper Tactical Configurations of Rank 2 and in his 1937 book Introduction to the Theory of Groups of Finite Order; the system is often named after Ernst Witt, who rediscovered it in 1938.
While at Indiana University, he worked on the special theory of relativity. His younger brother was Oliver Carmichael, a university administrator.
This page was last edited on 3 February 2026, at 15:00 (CET).