[1] In 1999, Demmel was elected a member of the National Academy of Engineering for contributions to numerical linear algebra and scientific computing.

Born in Pittsburgh,[2] Demmel did his undergraduate studies at the California Institute of Technology, graduating in 1975 with a B.S.

[3][4] He earned his Ph.D. in computer science in 1983 from UC Berkeley, under the supervision of William Kahan; his dissertation was entitled A Numerical Analyst's Jordan Canonical Form.

[1] Prometheus, a parallel multigrid finite element solver written by Demmel, Mark Adams, and Robert Taylor, won the Carl Benz Award at Supercomputing 1999 and the Gordon Bell Prize for Adams and his coworkers at Supercomputing 2004.

Demmel is married to Katherine Yelick, who is also an ACM Fellow and professor of electrical engineering and computer science at UC Berkeley,[11] and Associate Lab Director for Computing Sciences at Lawrence Berkeley National Laboratory.