Robert Daniel Carmichael (March 1, 1879 – May 2, 1967) was an American mathematician.

Carmichael's Ph.D. research in mathematics was done under the guidance of the noted American mathematician G. David Birkhoff, and it is considered to be the first significant American contribution to the knowledge of differential equations in mathematics.

He found the smallest Carmichael number, 561, and over 50 years later, it was proven that there are infinitely many of them.

Carmichael also described the Steiner system S(5,8,24) in his 1931 paper Tactical Configurations of Rank 2 and his 1937 book Introduction to the Theory of Groups of Finite Order, but the structure is often named after Ernst Witt, who rediscovered it in 1938.

While at Indiana University, Carmichael was involved with the special theory of relativity.