James B. Carrell (1940, Seattle) is an American and Canadian mathematician, who is currently an emeritus professor of mathematics at the University of British Columbia, Vancouver, British Columbia, Canada. His areas of research are algebraic geometry, Lie theory, transformation groups and differential geometry. He obtained his Ph.D. at the University of Washington (Seattle) under the supervision of Allendoefer. In 1971 together with Jean Dieudonné he received Leroy P. Steele Prize for his work Invariant theory, old and new. He is a fellow of the American Mathematical Society.