Multiplication by Infinity: Bill Gosper

Tuesday, July 20, 2010

Bill Gosper

First picture: Bill Gosper. Second picture and lone animation: Gosper's Gliding Gun, from cellular automata and John Conway's "The Game of Life".

Ralph William Gosper, Jr., (born 1943) known as Bill Gosper, is an American mathematician and programmer from Pennsauken Township, New Jersey.^[1] Along with Richard Greenblatt, he may be considered to have founded the hacker community, and holds a place of pride in the Lisp community. Perhaps his most profound contribution is that he was the first person to realize the possibilities of symbolic computation on a computer as a mathematics research tool, whereas computer methods were previously limited to purely numerical methods. In particular, this research resulted in his work on continued fraction representations of real numbers, and for more famously, developing Gosper's algorithm for finding closed form hypergeometric identities. Because his mathematics is largely self-taught and a number of his completely original formulas have inspired professional mathematicians to write papers developing them into full fledged theories, he has been considered a modern day Ramanujan.

Gosper enrolled in MIT in 1961, and received his bachelor's degree in mathematics from MIT in 1965. After taking a course on programming in his second year with John McCarthy, Gosper became affiliated with the MIT AI Lab. His contributions to computational mathematics include HAKMEM [1] and the MIT Maclisp system. He also made major contributions to the Macsyma computer algebra system at MIT, later working with Symbolics and Macsyma, Inc. on the greatly improved commercial versions.

He became intensely interested in the Game of Life shortly after John Horton Conway had proposed it. Conway conjectured on the existence of infinitely growing patterns, and offered a reward for an example. Gosper was the first to find such a pattern (specifically, the Glider gun), and won the prize. Gosper was also the originator of the hashlife algorithm that can speed up the computation of Life patterns by many orders of magnitude.

In the 1970s Gosper moved to California for a three year stint at Stanford, where he lectured and helped Donald Knuth write volume II of The Art of Computer Programming.

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

Gosper has created numerous packing problem puzzles, such as "Twubblesome Twelve".