Stephen Wolfram

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Stephen Wolfram
Stephen Wolfram PR (cropped).jpg
Wolfram in 2008
Born (1959-08-29) 29 August 1959 (age 61)
London, England
NationalityBritish, American
EducationDragon School[1]
Eton College
Alma mater
Known for
AwardsMacArthur Fellowship (1981)
Scientific career
ThesisSome Topics in Theoretical High-Energy Physics (1980)
Doctoral advisorRichard D. Field[5]

Stephen Wolfram (/ˈwʊlfrəm/; born 29 August 1959) is a British-American[6] computer scientist, physicist, and businessman. He is known for his work in computer science, mathematics, and in theoretical physics.[7][8] In 2012, he was named an inaugural fellow of the American Mathematical Society.[9]

As a businessman, he is the founder and CEO of the software company Wolfram Research where he worked as chief designer of Mathematica and the Wolfram Alpha answer engine. His recent work has been on knowledge-based programming, expanding and refining the Wolfram Language, which is the programming language of the mathematical symbolic computation program Mathematica.

Early life[edit]


Stephen Wolfram was born in London in 1959 to Hugo and Sybil Wolfram, both German Jewish refugees to the United Kingdom.[10]

Wolfram's father, Hugo Wolfram (1925–2015), a textile manufacturer born in Bochum, Germany, served as managing director of the Lurex Company, makers of the fabric Lurex. He was also the author of three novels.[11][12][13][14] He emigrated to England in 1933.[15] When World War II broke out, he left school at 15 and subsequently found it hard to get a job since he was regarded as an "enemy alien". As an adult, he took correspondence courses in philosophy and psychology.[11]

Wolfram's mother, Sybil Wolfram (1931–1993; born Sybille Misch), originally from Berlin, Germany, was a Fellow and Tutor in Philosophy at Lady Margaret Hall at University of Oxford from 1964 to 1993. She published two books, Philosophical Logic: An Introduction (1989)[16] and In-laws and Outlaws: Kinship and Marriage in England (1987).[17][18] She was the translator of Claude Lévi-Strauss's La Pensée sauvage (The Savage Mind), but later disavowed the translation.[19][20] She was the daughter of criminologist and psychoanalyst Kate Friedlander (1902–1949), an expert on the subject of juvenile delinquency,[21] and the physician Walter Misch (1889–1943) who, together, wrote Die vegetative Genese der neurotischen Angst und ihre medikamentöse Beseitigung.[22] After the Reichstag fire in 1933, she emigrated from Berlin, Germany, to England with her parents and Jewish psychoanalyst Paula Heimann (1899–1982).[23][24][25]

Stephen Wolfram is married to a mathematician. They have four children together.[26][27]


Stephen Wolfram's Dragon School report card from age 7.[28]

Wolfram was educated at Eton College, but left prematurely in 1976.[29] At Eton, he was taught mathematics by Norman Routledge (1928–2013), a friend of Alan Turing.[30][31] He entered St. John's College, Oxford, at age 17 but found lectures "awful",[18] and left in 1978[32] without graduating[33][34] to attend the California Institute of Technology the following year, where he received a PhD[35] in particle physics on 19 November 1979 at age 20.[36] Wolfram's thesis committee was composed of Richard Feynman, Peter Goldreich, Frank J. Sciulli and Steven Frautschi, and chaired by Richard D. Field.[36][37]

Early career[edit]

As a young child, Wolfram had difficulties learning arithmetic.[38] At the age of 12, he wrote a directory of physics.[39] By age 14, he had written three books on particle physics.[40][41][42]

Particle physics[edit]

Wolfram, at the age of 15, began research in applied quantum field theory and particle physics and published scientific papers. Topics included matter creation and annihilation, the fundamental interactions, elementary particles and their currents, hadronic and leptonic physics, and the parton model, published in professional peer-reviewed scientific journals including Nuclear Physics B, Australian Journal of Physics, Nuovo Cimento, and Physical Review D.[43] Working independently, Wolfram published a widely cited paper on heavy quark production at age 18[2] and nine other papers,[18] and continued research and to publish on particle physics into his early twenties. Wolfram's work with Geoffrey C. Fox on the theory of the strong interaction is still used in experimental particle physics.[44]

A 1981 letter from Feynman to Gerald Freund giving reference for Wolfram for the MacArthur grant appears in Feynman's collected letters, Perfectly Reasonable Deviations from the Beaten Track. Following his PhD, Wolfram joined the faculty at Caltech and became the youngest recipient[45] of the MacArthur Fellowships in 1981, at age 21.[33]

Later career[edit]

Complex systems and cellular automata[edit]

Stephen Wolfram in his office at the Institute for Advanced Study in Princeton.

In 1983, Wolfram left for the School of Natural Sciences of the Institute for Advanced Study in Princeton, where he conducted research into cellular automata,[46][47][48][49][50] mainly with computer simulations. He produced a series of papers systematically investigating the class of elementary cellular automata, conceiving the Wolfram code, a naming system for one-dimensional cellular automata, and a classification scheme for the complexity of their behaviour.[51] He conjectured that the Rule 110 cellular automaton might be Turing complete, which was later proved correct.[52]

A 1985 letter from Feynman to Wolfram also appears in Feynman's letters. In it, in response to Wolfram writing to him that he was thinking about creating some kind of institute where he might study complex systems, Feynman tells Wolfram, "You do not understand ordinary people", and advises him "find a way to do your research with as little contact with non-technical people as possible."[53]

In the mid-1980s, Wolfram worked on simulations of physical processes (such as turbulent fluid flow) with cellular automata on the Connection Machine alongside Feynman[54] and helped initiate the field of complex systems. In 1984, he was a participant in the Founding Workshops of the Santa Fe Institute, along with Nobel laureates Murray Gell-Mann, Manfred Eigen, and Philip Warren Anderson, and future laureate Frank Wilczek.[55] In 1986, he founded the Center for Complex Systems Research (CCSR) at the University of Illinois at Urbana–Champaign[56] and, in 1987, the journal Complex Systems.[56] As the first journal in the field, Complex Systems has published many papers over the course of three decades. Complex Systems has developed a broad base of readers and contributors from academia, industry, government and the general public in over 50 countries around the world.

Symbolic Manipulation Program[edit]

Wolfram led the development of the computer algebra system SMP (Symbolic Manipulation Program) in the Caltech physics department during 1979–1981. A dispute with the administration over the intellectual property rights regarding SMP—patents, copyright, and faculty involvement in commercial ventures—eventually caused him to resign from Caltech.[57] SMP was further developed and marketed commercially by Inference Corp. of Los Angeles during 1983–1988.

Institute for Advanced Study[edit]

In 1983, Wolfram joined the Institute for Advanced Study, Princeton. But by that time, he was no longer interested in particle physics. Instead, he began pursuing what he viewed as more creative areas — specifically, cellular automata. Wolfram methodically analyzed sets of rules, developing a classification system that rated the complexity of various cellular automata — all with the intention of clarifying the way we view complexity in the real world. In Wolfram's mind, studying the results of cellular-automata runs on the computer could unlock deep truths about the universe itself.[58]

Wolfram's cellular-automata work came to be cited in more than 10,000 papers.[58]


In 1986, Wolfram left the Institute for Advanced Study for the University of Illinois at Urbana–Champaign where he founded their Center for Complex Systems Research and started to develop the computer algebra system Mathematica, which was first released on 23 June 1988, when he left academia. In 1987, he founded Wolfram Research which continues to develop and market the program.[2]

Near the end of Sybil Wolfram's life, as part of her research for In-laws and Outlaws, she used her son's program Mathematica to analyze her data.[23]

Wolfram's younger brother, Conrad Wolfram, serves as CEO of Wolfram Research Europe, Ltd.[59][60]

A New Kind of Science[edit]

From 1992 to 2002, he worked on his controversial book A New Kind of Science,[2][61] which presents an empirical study of simple computational systems. Additionally, it argues that for fundamental reasons these types of systems, rather than traditional mathematics, are needed to model and understand complexity in nature. Wolfram's conclusion is that the universe is discrete in its nature, and runs on fundamental laws which can be described as simple programs. He predicts that a realization of this within the scientific communities will have a major and revolutionary influence on physics, chemistry and biology and the majority of the scientific areas in general, which is the reason for the book's title.

Since the release of the book in 2002,[4] Wolfram has split his time between developing Mathematica and encouraging people to get involved with the subject matter of A New Kind of Science by giving talks, holding conferences, and starting a summer school devoted to the topic.[62]

Beginning in May 2017 (the 15th anniversary of its hardcover publication), a free electronic version of A New Kind of Science was launched that includes complete access and high-resolution images.[63]

Wolfram axiom[edit]

The Wolfram axiom is the result of a computer exploration in A New Kind of Science looking for the shortest single axiom equivalent to the axioms of Boolean algebra (or propositional calculus). The result[64] of his search was an axiom with six NAND operations and three variables equivalent to Boolean algebra:

where the vertical bar represents the NAND logical operation (also known as the Sheffer stroke). The 25 candidates are precisely the set of Sheffer identities of length less or equal to 15 elements (excluding mirror images) that have no noncommutative models of size less or equal to 4 (variables).[65]

Applications of A New Kind of Science[edit]

In 2003, Wolfram hosted the first Wolfram Summer School at Brown University — a program designed to provide educational and career opportunities by learning and conducting projects at the frontiers of science, technology, and innovation.[66][67] In 2007, the summer school began being hosted by the University of Vermont at Burlington, with the exception of the year 2009 which was held at the Istituto di Scienza e Tecnologie dell'Informazione of the CNR in Pisa, Italy. In 2012, the program was held at Curry College in Milton, Massachusetts. Since 2013, the Wolfram Summer School has been held annually at Bentley University in Waltham, Massachusetts.

In A New Kind of Science, Wolfram found what was then the simplest known universal Turing machine — with 2 states and 5 colors. However, he also did an extensive search of simpler Turing machines and in doing that, found a much simpler candidate for universality, a 2,3 Turing machine. On 14 May 2007, (the fifth anniversary of the publication of A New Kind of Science), Wolfram announced a $25,000 prize for the first person to determine whether or not the 2,3 Turing machine was actually universal or not, and could provide proof. Five months after the contest's announcement, an undergraduate student from Birmingham, UK, successfully found the 2,3 Turing machine to be universal and provided a 40-page paper[68] to prove his findings.[69]

Wolfram Alpha computational knowledge engine[edit]

In March 2009, Wolfram announced Wolfram|Alpha, an answer engine. Wolfram|Alpha later launched in May 2009,[70] and a paid-for version with extra features launched in February 2012.[71] The engine is based on natural language processing and a large library of algorithms, and answers queries using the approach described in A New Kind of Science. The application programming interface allows other applications to extend and enhance Alpha.[72] Wolfram believes that as Wolfram Alpha comes into common use, "It will raise the level of scientific things that the average person can do."[73]

Wolfram Alpha is one of the answer engines behind Microsoft's Bing[74][75] and Apple's Siri answering factual questions.[76]


In 2010, Wolfram co-founded Touchpress along with Theodore Gray, Max Whitby, and John Cromie. The company specialised in creating in-depth premium apps and games covering a wide range of educational subjects designed for children, parents, students, and educators. Since the launch, Touchpress has published more than 100 apps.[77]

Wolfram Language[edit]

In March 2014, at the annual South by Southwest (SXSW) event, Wolfram officially announced the Wolfram Language as a new general multi-paradigm programming language[78] and currently better known as a multi-paradigm computational communication language. The documentation for the language was pre-released in October 2013 to coincide with the bundling of Mathematica and the Wolfram Language on every Raspberry Pi computer. While the Wolfram Language has existed for over 25 years as the primary programming language used in Mathematica, it was not officially named until 2014.[79] Wolfram's son, Christopher Wolfram, appeared on the program of SXSW giving a live-coding demonstration using Wolfram Language[80] and has blogged about Wolfram Language for Wolfram Research.[81]

On 8 December 2015, Wolfram published the book "An Elementary Introduction to the Wolfram Language" to introduce people with no knowledge of programming to the Wolfram Language and the kind of computation it allows.[82] The release of the second edition of the book[83] coincided with a "CEO for hire" competition during the 2017 Collision tech conference.[84]

Wolfram Physics Project[edit]

In April 2020, Wolfram announced the Wolfram Physics Project as an effort to reduce and explain all the laws of physics within a paradigm of a hypergraph that is transformed by minimal rewriting rules which obey the Church-Rosser property.[85][86] The effort is a continuation of the ideas he originally described in A New Kind of Science.

The foundational idea is the exploration of the emergent complexity of abstract rewriting systems (termed "substitution system" on Wolfram MathWorld), where the systems explored mainly lie at a minimalist extreme. Most examples come from a rewriting system on ordered graphs; some concepts are illustrated by examples pertaining to string rewriting systems. Many of the computational phenomena obtained in these systems bear analogy to Wolfram's previous investigations into cellular automata. This newly introduced ordered-graph system lends itself to geometrical interpretation in a way that cellular automata did not, and it is mainly these geometrical interpretations that provide an entry point into analogy with physical law.[87]

Wolfram claims that "From an extremely simple model, we're able to reproduce special relativity, general relativity and the core results of quantum mechanics". Physicists are generally unimpressed with Wolfram's claim, and state that Wolfram's results are non-quantitative and arbitrary.[88][89]

In popular culture[edit]

Beginning in 2017, Wolfram began to live stream internal Wolfram Language development meetings.[90] During these meetings, viewers are encouraged to submit questions and comments related to the development of the programming language. Viewers have been known to suggest new functions that they would like to see developed, name new functions, and help solve complex issues faced by Stephen and the Wolfram Research development team. These live streamed meetings can be viewed on Twitch, YouTube Live, and Facebook Live. All archived live streams can also be accessed on his personal website.

Personal interests and activities[edit]

The significance data has on the products Wolfram creates transfers into his own life. He has an extensive log of personal analytics, including emails received and sent, keystrokes made, meetings and events attended, phone calls, even physical movement dating back to the 1980s. In the preface of A New Kind of Science, he noted that he recorded over one-hundred million keystrokes and one-hundred mouse miles. He has stated "[personal analytics] can give us a whole new dimension to experiencing our lives".[91]

Wolfram testifying before the US Senate

Both Stephen Wolfram and Christopher Wolfram were involved in helping create the alien language for the film Arrival, for which they used the Wolfram Language.[92][93][94]

Since 2018, Wolfram has been producing a podcast,[95] where he discusses topics ranging from the history of science to the future of civilization and ethics of AI.

In 2019, Wolfram was part of a panel of four witnesses who testified before the US Senate Subcommittee on Communications, Technology, Innovation, and the Internet in a hearing titled "Optimizing for Engagement: Understanding the Use of Persuasive Technology on Internet Platforms."[96]


  • A Project to Find the Fundamental Theory of Physics (2020), Publisher: Wolfram Media, ISBN 978-1-57955-035-6
  • Adventures of a Computational Explorer (2019)
  • Idea Makers: Personal Perspectives on the Lives & Ideas of Some Notable People (2016)[97]
  • Elementary Introduction to the Wolfram Language (2015)[98]
  • A New Kind of Science (2002)
  • The Mathematica Book (multiple editions)
  • Cellular Automata and Complexity: Collected Papers (1994)
  • Theory and Applications of Cellular Automata (1986)


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External links[edit]