Ralph William Gosper Jr. (born April 26, 1943), known as Bill Gosper, is an American mathematician and programmer. Along with Richard Greenblatt, he may be considered to have founded the

hacker A hacker is a person skilled in information technology who uses their technical knowledge to achieve a goal or overcome an obstacle, within a computerized system by non-standard means. Though the term ''hacker'' has become associated in popu ...

community, and he holds a place of pride in the Lisp community. The

Gosper curve The Gosper curve, named after Bill Gosper, also known as the Peano-Gosper Curve and the flowsnake (a spoonerism of snowflake), is a space-filling curve whose limit set is rep-7. It is a fractal curve similar in its construction to the dragon c ...

and the

Gosper's algorithm In mathematics, Gosper's algorithm, due to Bill Gosper, is a procedure for finding sums of hypergeometric terms that are themselves hypergeometric terms. That is: suppose one has ''a''(1) + ... + ''a''(''n'') = ''S''(''n'')&nb ...

are named after him.

Becoming a hacker

In high school, Gosper was interested in

model rocket A model rocket are small rockets designed to reach low altitudes (e.g., for model) and be recovered by a variety of means. According to the United States National Association of Rocketry (NAR) Safety Code, model rockets are constructed of ...

s until one of his friends was injured in a rocketry accident and contracted a fatal brain infection.. Gosper enrolled in

MIT The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the m ...

in 1961, and he received his

bachelor's degree A bachelor's degree (from Middle Latin ''baccalaureus'') or baccalaureate (from Modern Latin ''baccalaureatus'') is an undergraduate academic degree awarded by colleges and universities upon completion of a course of study lasting three to six ...

in mathematics from MIT in 1965 despite becoming disaffected with the mathematics department because of their anti-computer attitude. In his second year at MIT, Gosper took a programming course from John McCarthy and became affiliated with the

MIT AI Lab Computer Science and Artificial Intelligence Laboratory (CSAIL) is a research institute at the Massachusetts Institute of Technology (MIT) formed by the 2003 merger of the Laboratory for Computer Science (LCS) and the Artificial Intelligence La ...

. His contributions to computational mathematics include

HAKMEM HAKMEM, alternatively known as AI Memo 239, is a February 1972 "memo" (technical report) of the MIT AI Lab containing a wide variety of hacks, including useful and clever algorithms for mathematical computation, some number theory and schematic ...

and the MIT Maclisp system. He made major contributions to

Macsyma Macsyma (; "Project MAC's SYmbolic MAnipulator") is one of the oldest general-purpose computer algebra systems still in wide use. It was originally developed from 1968 to 1982 at MIT's Project MAC. In 1982, Macsyma was licensed to Symbolics a ...

Project MAC Computer Science and Artificial Intelligence Laboratory (CSAIL) is a research institute at the Massachusetts Institute of Technology (MIT) formed by the 2003 merger of the Laboratory for Computer Science (LCS) and the Artificial Intelligence Lab ...

's computer algebra system. Gosper later worked with Symbolics and

Macsyma, Inc. Macsyma (; "Project MAC's SYmbolic MAnipulator") is one of the oldest general-purpose computer algebra systems still in wide use. It was originally developed from 1968 to 1982 at MIT's Project MAC. In 1982, Macsyma was licensed to Symbolics an ...

on commercial versions of Macsyma. In 1974, he moved to Stanford University, where he lectured and worked with

Donald Knuth Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer sc ...

. Since that time, he has worked at or consulted for

Xerox PARC PARC (Palo Alto Research Center; formerly Xerox PARC) is a research and development company in Palo Alto, California. Founded in 1969 by Jacob E. "Jack" Goldman, chief scientist of Xerox Corporation, the company was originally a division of Xero ...

, Symbolics,

Wolfram Research Wolfram Research, Inc. ( ) is an American multinational company that creates computational technology. Wolfram's flagship product is the technical computing program Wolfram Mathematica, first released on June 23, 1988. Other products include ...

, the

Lawrence Livermore Laboratory Lawrence Livermore National Laboratory (LLNL) is a federal research facility in Livermore, California, United States. The lab was originally established as the University of California Radiation Laboratory, Livermore Branch in 1952 in respons ...

, and

Macsyma Inc. Macsyma (; "Project MAC's SYmbolic MAnipulator") is one of the oldest general-purpose computer algebra systems still in wide use. It was originally developed from 1968 to 1982 at MIT's Project MAC. In 1982, Macsyma was licensed to Symbolics an ...

Key contributions

Conway's Game of Life

He became intensely interested in the Game of Life shortly after

John Horton Conway John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches ...

had proposed it. Conway conjectured the existence of infinitely growing patterns, and offered a reward for an example. Gosper was the first to find such a pattern, the glider gun, and won the prize. Gosper was also the originator of the

Hashlife Hashlife is a memoized algorithm for computing the long-term fate of a given starting configuration in Conway's Game of Life and related cellular automata, much more quickly than would be possible using alternative algorithms that simulate each ...

algorithm that can speed up the computation of Life patterns by many orders of magnitude.

Packing problems

Gosper has created numerous

packing problem Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few conta ...

puzzles, such as "Twubblesome Twelve".

Symbolic computation

Gosper 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 In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer ...

representations of real numbers and

for finding closed form hypergeometric identities. In 1985, Gosper briefly held the world record for computing the most digits of pi with 17 million digits. See

chronology of computation of π The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant pi (). For more detailed explanations for some of these calculations, see Approximations of π, Approximations of . The last 100 dec ...

Space-filling curves

In the continuity of early 20th century examples of

space-filling curve In mathematical analysis, a space-filling curve is a curve whose range contains the entire 2-dimensional unit square (or more generally an ''n''-dimensional unit hypercube). Because Giuseppe Peano (1858–1932) was the first to discover one, spa ...

s—the Koch-Peano curve, Cesàro and

Lévy C curve In mathematics, the Lévy C curve is a self-similar fractal curve that was first described and whose differentiability properties were analysed by Ernesto Cesàro in 1906 and Georg Faber in 1910, but now bears the name of French mathematician Pa ...

, all special cases of the general

de Rham curve In mathematics, a de Rham curve is a certain type of fractal curve named in honor of Georges de Rham. The Cantor function, Cesàro curve, Minkowski's question mark function, the Lévy C curve, the blancmange curve, and Koch curve are all spe ...

—and following the path of Benoit Mandelbrot, Gosper discovered the

Peano-Gosper curve The Gosper curve, named after Bill Gosper, also known as the Peano-Gosper Curve and the flowsnake (a spoonerism of snowflake), is a space-filling curve whose limit set is rep-7. It is a fractal curve similar in its construction to the dragon c ...

, before engaging with variations on the Harter-Heighway dragon. In the late 80s, Gosper independently discovered the Gosper-Lafitte triangle.

References

External links

Bill Gosper's webpage
which contains
Bill Gosper's GraphicsTwubblesome Twelve
Puzzle - version for the free Mathematica Player {{DEFAULTSORT:Gosper, Bill 1943 births Living people 20th-century American mathematicians 21st-century American mathematicians Number theorists Massachusetts Institute of Technology School of Science alumni Cellular automatists Recreational mathematicians People from Pennsauken Township, New Jersey Lisp (programming language) people American computer businesspeople Scientists at PARC (company)