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 achieves goals and solves problems by non-standard means. The term has become associated in popular culture with a security hackersomeone with knowledge of bug (computing), bugs or exp ...

community, and he holds a place of pride in the

Lisp Lisp (historically LISP, an abbreviation of "list processing") is a family of programming languages with a long history and a distinctive, fully parenthesized Polish notation#Explanation, prefix notation. Originally specified in the late 1950s, ...

community. The

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

and

Gosper's algorithm In mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. ...

are named after him.

Becoming a hacker

In high school, Gosper was interested in

model rocket A model rocket is a small rocket designed to reach low altitudes (e.g., for a model) and #Model rocket recovery methods, be recovered by a variety of means. According to the United States National Association of Rocketry, National Associati ...

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 research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and sc ...

in 1961, and he received his

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

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 Lab ...

. 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 schemat ...

and the MIT

Maclisp Maclisp (or MACLISP, sometimes styled MacLisp or MacLISP) is a programming language, a dialect of the language Lisp. It originated at the Massachusetts Institute of Technology's (MIT) Project MAC (from which it derived its prefix) in the late 19 ...

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 and ...

Project MAC Computer Science and Artificial Intelligence Laboratory (CSAIL) is a research institute at the Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in ...

's computer algebra system. Gosper later worked with

Symbolics Symbolics, Inc., is a privately held American computer software maker that acquired the assets of the former manufacturing company of the identical name and continues to sell and maintain the Open Genera Lisp (programming language), Lisp sy ...

and Macsyma, Inc. on commercial versions of Macsyma. In 1974, he moved to

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

, where he lectured, and worked with

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

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

Xerox PARC Future Concepts division (formerly Palo Alto Research Center, PARC and Xerox PARC) is a research and development company in Palo Alto, California. It was founded in 1969 by Jacob E. "Jack" Goldman, chief scientist of Xerox Corporation, as a div ...

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

, the Lawrence Livermore Laboratory, and Macsyma Inc.

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. He was active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many b ...

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 In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions ...

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 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 Chronology (from Latin , from Ancient Greek , , ; and , ''wikt:-logia, -logia'') is the science of arranging events in their order of occurrence in time. Consider, for example, the use of a timeline or sequence of events. It is also "the deter ...

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 of a function, range reaches every point in a higher dimensional region, typically the unit square (or more generally an ''n''-dimensional unit hypercube). Because Giuseppe Pea ...

s—the Koch-Peano curve, Cesàro and Lévy C curve, all special cases of the general

de Rham curve In mathematics, a de Rham curve is a continuous fractal curve obtained as the image of the Cantor space, or, equivalently, from the base-two expansion of the real numbers in the unit interval. Many well-known fractal curves, including the Cantor ...

—and following the path of

Benoit Mandelbrot Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of phy ...

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

References

External links

* *
Autobiography

Bill Gosper's Graphics
* {{DEFAULTSORT:Gosper, Bill 1943 births Living people 20th-century American mathematicians 21st-century American mathematicians American 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)