His research results include confirmation of the existence of solutions of Einstein's equation containing gravitational radiation, the use of computer algebra to classify exact solutions of Einstein's equation, an analysis of a class of gravitational shock waves (including one of the few known exact 2-body solutions in general relativity), and the study of signature change, a possible model for the Big Bang.

More recently, his work has focused on applications of the octonions to the theory of fundamental particles.

He was a graduate student under Rainer K. Sachs at Berkeley, where he received his Ph.D. in 1981, although much of his dissertation research was done in collaboration with Abhay Ashtekar.

In addition to his ongoing work in mathematical physics, he has made significant contributions in science education, where he directs the Vector Calculus Bridge Project,[3] an attempt to teach vector calculus the way it is used by scientists and engineers, and is part of the development team of the Paradigms Project,[4] a complete restructuring of the undergraduate physics major around several core "paradigms".

[7] In 2017 he received a Deborah and Franklin Haimo Award for Distinguished College or University Teaching of Mathematics.