John Barkley Rosser Sr. (December 6, 1907 – September 5, 1989) was an American logician, a student of Alonzo Church, and known for his part in the Church–Rosser theorem, in lambda calculus. He also developed what is now called the Rosser sieve, in number theory. He was later director of the Army Mathematics Research Center at the University of Wisconsin–Madison. Rosser wrote mathematical textbooks as well.