In high school, Gosper was interested in model rockets until one of his friends was injured in a rocketry accident and contracted a fatal brain infection.

[3] Since that time, he has worked at or consulted for Xerox PARC, Symbolics, Wolfram Research, the Lawrence Livermore Laboratory, and Macsyma Inc.

He became intensely interested in the Game of Life shortly after John Horton Conway had proposed it.

[4] Gosper was also the originator of the Hashlife algorithm that can speed up the computation of Life patterns by many orders of magnitude.

In particular, this research resulted in his work on continued fraction representations[6] of real numbers and Gosper's algorithm for finding closed form hypergeometric identities.