Bill Gosper
Encyclopedia
Ralph William Gosper, Jr. (born 1943), known as Bill Gosper, is an American mathematician and programmer from Pennsauken Township, New Jersey
. Along with Richard Greenblatt
, he may be considered to have founded the hacker community, and holds a place of pride in the Lisp
community.
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. He ultimately wound up in Palo Alto at Stanford's AI Lab with Don Knuth working on Knuth's epic work as well as working for XEROX PARC, Macsyma and others.
His contributions to computational mathematics include HAKMEM
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.
write volume II of The Art of Computer Programming
.
, Symbolics
, Wolfram Research, the Lawrence Livermore Laboratory, and Macsyma Inc.
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.
puzzles, such as "Twubblesome Twelve".
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 far more famously, developing Gosper's algorithm
for finding closed form hypergeometric
identities. Because his mathematics is largely self-taught and a number of his original formulas have inspired professional mathematicians to write papers developing them into full fledged theories, he has been considered a modern day Ramanujan.
Pennsauken Township, New Jersey
Pennsauken Township is a township in Camden County, New Jersey, USA, and a suburb of Philadelphia. As of the 2010 census, the township population was 35,885....
. Along with Richard Greenblatt
Richard Greenblatt (programmer)
Richard D. Greenblatt is an American computer programmer. Along with Bill Gosper, he may be considered to have founded the hacker community, and holds a place of distinction in the Lisp and the MIT AI Lab communities.-Childhood:...
, he may be considered to have founded the hacker community, and holds a place of pride in the Lisp
Lisp programming language
Lisp is a family of computer programming languages with a long history and a distinctive, fully parenthesized syntax. Originally specified in 1958, Lisp is the second-oldest high-level programming language in widespread use today; only Fortran is older...
community.
Becoming a hacker
Gosper enrolled in MITMassachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
in 1961, and received his bachelor's degree
Bachelor's degree
A bachelor's degree is usually an academic degree awarded for an undergraduate course or major that generally lasts for three or four years, but can range anywhere from two to six years depending on the region of the world...
in mathematics from MIT in 1965.
After taking a course on programming in his second year with John McCarthy
John McCarthy (computer scientist)
John McCarthy was an American computer scientist and cognitive scientist. He coined the term "artificial intelligence" , invented the Lisp programming language and was highly influential in the early development of AI.McCarthy also influenced other areas of computing such as time sharing systems...
, Gosper became affiliated with the MIT AI Lab. He ultimately wound up in Palo Alto at Stanford's AI Lab with Don Knuth working on Knuth's epic work as well as working for XEROX PARC, Macsyma and others.
His contributions to computational mathematics include HAKMEM
HAKMEM
HAKMEM, alternatively known as AI Memo 239, is a February 1972 "memo" of the MIT AI Lab that describes a wide variety of hacks, primarily useful and clever algorithms for mathematical computation. There are also some schematic diagrams for hardware...
and the MIT Maclisp
Maclisp
MACLISP is a dialect of the Lisp programming language. It originated at MIT's Project MAC in the late 1960s and was based on Lisp 1.5. Richard Greenblatt was the main developer of the original codebase for the PDP-6; Jonl White was responsible for its later maintenance and development...
system. He also made major contributions to the Macsyma
Macsyma
Macsyma is a computer algebra system that was originally developed from 1968 to 1982 at MIT as part of Project MAC and later marketed commercially...
computer algebra system at MIT, later working with Symbolics
Symbolics
Symbolics refers to two companies: now-defunct computer manufacturer Symbolics, Inc., and a privately held company that acquired the assets of the former company and continues to sell and maintain the Open Genera Lisp system and the Macsyma computer algebra system.The symbolics.com domain was...
and Macsyma, Inc. on the greatly improved commercial versions.
Working with Knuth
In the 1970s Gosper moved to California for a three year stint at Stanford, where he lectured and helped Donald KnuthDonald Knuth
Donald Ervin Knuth is a computer scientist and Professor Emeritus at Stanford University.He is the author of the seminal multi-volume work The Art of Computer Programming. Knuth has been called the "father" of the analysis of algorithms...
write volume II of The Art of Computer Programming
The Art of Computer Programming
The Art of Computer Programming is a comprehensive monograph written by Donald Knuth that covers many kinds of programming algorithms and their analysis....
.
Consultancy
Since that time, he has worked at or consulted for Xerox PARCXerox PARC
PARC , formerly Xerox PARC, is a research and co-development company in Palo Alto, California, with a distinguished reputation for its contributions to information technology and hardware systems....
, Symbolics
Symbolics
Symbolics refers to two companies: now-defunct computer manufacturer Symbolics, Inc., and a privately held company that acquired the assets of the former company and continues to sell and maintain the Open Genera Lisp system and the Macsyma computer algebra system.The symbolics.com domain was...
, Wolfram Research, the Lawrence Livermore Laboratory, and Macsyma Inc.
Game of life
He became intensely interested in the Game of LifeConway's Game of Life
The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970....
shortly after John Horton Conway
John Horton Conway
John Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
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
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 time step of each cell of the automaton...
algorithm that can speed up the computation of Life patterns by many orders of magnitude.
Packing problems
Gosper has created numerous packing problemPacking problem
Packing problems are a class of optimization problems in mathematics which involve attempting to pack objects together , as densely as possible. Many of these problems can be related to real life packaging, storage and transportation issues...
puzzles, such as "Twubblesome Twelve".
Symbolic computation
Perhaps his most profound contribution is that he was the first person to realize the possibilities of symbolic computationSymbolic computation
Symbolic computation or algebraic computation, relates to the use of machines, such as computers, to manipulate mathematical equations and expressions in symbolic form, as opposed to manipulating the approximations of specific numerical quantities represented by those symbols...
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
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 part and another reciprocal, and so on...
representations of real numbers, and far more famously, developing Gosper's algorithm
Gosper's algorithm
In mathematics, Gosper's algorithm is a procedure for finding sums of hypergeometric terms that are themselves hypergeometric terms. That is: suppose we have a + ... + a = S − S, where S is a hypergeometric term ; then necessarily...
for finding closed form hypergeometric
Hypergeometric series
In mathematics, a generalized hypergeometric series is a series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent, defines a generalized hypergeometric function, which may then be defined over a wider domain of the argument by...
identities. Because his mathematics is largely self-taught and a number of his original formulas have inspired professional mathematicians to write papers developing them into full fledged theories, he has been considered a modern day Ramanujan.
External links
- Bill Gosper's webpage which contains a Biography
- Bill Gosper's Graphics
- Twubblesome Twelve Puzzle - version for the free Mathematica Player