# Stephen Wolfram

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Stephen Wolfram
Wolfram in 2008
Born29 August 1959 (age 60)
London, England, United Kingdom
ResidenceConcord, Massachusetts,
United States
NationalityBritish, American
EducationDragon School[1]
Eton College
Alma mater
Known for
AwardsMacArthur Fellowship (1981)
Scientific career
Fields
Institutions
ThesisSome Topics in Theoretical High-Energy Physics (1980)
Website

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 programming language of Mathematica into what is now called the Wolfram Language.

## Early life

### Family

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's son, Christopher, began a degree course in mathematics and computer science in 2018. He is the co-inventor of a patented method and computing device for optically recognizing mathematical expressions. Christopher has presented and led workshops at several highly regarded conferences and events including South by Southwest Interactive, University of Oxford Summer School, and MIT Independent Activities Period. In 2016, he was awarded as Best Technical Advisor at the Raw Science Film Festival for his work on the movie, Arrival. He also works as a programmer for Wolfram Research.

### Education

Wolfram was educated at Eton College, but left prematurely in 1976.[28] He entered St. John's College, Oxford at age 17 but found lectures "awful",[18] and left in 1978[29] without graduating[30][31] to attend the California Institute of Technology, the following year, where he received a PhD[32] in particle physics on 19 November 1979 at age 20.[33] Wolfram's thesis committee was composed of Richard Feynman, Peter Goldreich, Frank J. Sciulli and Steven Frautschi, and chaired by Richard D. Field.[33][34]

## Early career

As a young child, Wolfram had difficulties learning arithmetic.[35] At the age of 12, he wrote a directory of physics.[36] By age 14, he had written three books on particle physics.[37][38][39]

### Particle physics

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.[40] 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.[41]

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[42] of the MacArthur Fellowships in 1981, at age 21.[30]

## Later career

### Complex systems and cellular automata

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,[43][44][45][46][47] 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.[48] He conjectured that the Rule 110 cellular automaton might be Turing complete, which was later proved correct.[49]

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."[50]

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[51] 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.[52] In 1986, he founded the Center for Complex Systems Research (CCSR) at the University of Illinois at Urbana–Champaign[53] and, in 1987, the journal Complex Systems.[53] 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

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.[54] SMP was further developed and marketed commercially by Inference Corp. of Los Angeles during 1983–1988.

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.[55]

Wolfram's cellular-automata work came to be cited in more than 10,000 papers.[55]

### Mathematica

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.[56][57]

### A New Kind of Science

From 1992 to 2002, he worked on his controversial book A New Kind of Science,[2][58] 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 digital 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.[59]

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.

### Wolfram axiom

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[60] of his search was an axiom with six NAND operations and three variables equivalent to Boolean algebra:

${\displaystyle ((a|b)\,|\,c)\;|\;(a\,|\,((a|c)\,|\,a))=c}$

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).[61]

### Applications of A New Kind of Science

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. 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 is the idea of exploring a new abstract universe: a computational universe of simple programs. In A New Kind of Science, Wolfram shows how simple programs in his computational universe capture the essence of the complexity – and beauty – of many systems in nature. This led to the creation of Wolfram Tones which works by taking simple programs from Wolfram's computational universe, applying music theory, and Wolfram Language algorithms to render them as music. Each program in effect defines a virtual world, with its own special story — and Wolfram Tones captures it as a musical composition.

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[62] to prove his findings.

### Wolfram Alpha computational knowledge engine

In March 2009, Wolfram announced Wolfram|Alpha, an answer engine. Wolfram|Alpha later launched in May 2009,[63] and a paid-for version with extra features launched on February 2012.[64] 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.[65] Wolfram believes that as Wolfram Alpha comes into common use, "It will raise the level of scientific things that the average person can do."[66]

Wolfram Alpha is one of the answer engines behind Microsoft's Bing[67][68] and Apple's Siri answering factual questions.[69]

### Touchpress

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.[70]

### Wolfram Language

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[71] 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.[72] Wolfram's son, Christopher Wolfram, appeared on the program of SXSW giving a live-coding demonstration using Wolfram Language[73] and has blogged about Wolfram Language for Wolfram Research.[74]

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.[75] The release of the second edition of the book[76] coincided with a "CEO for hire" competition during the 2017 Collision tech conference.[77]

## In popular culture

Beginning in 2017, Wolfram began to live stream internal Wolfram Language development meetings.[78] 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.tv, YouTube Live, and Facebook Live. All archived live streams can also be accessed on his personal website.

## Personal interests and activities

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".[79]

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.[80][81][82]

Since 2018, Wolfram has been producing a podcast,[83] where he discusses topics ranging from the history of science to the future of civilization and ethics of AI.

## Bibliography

• Idea Makers: Personal Perspectives on the Lives & Ideas of Some Notable People (2016)[84]
• Elementary Introduction to the Wolfram Language (2015)[85]
• 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)

## References

1. ^ My Life in Technology—As Told at the Computer History Museum
2. ^ a b c d Giles, J. (2002). "Stephen Wolfram: What kind of science is this?". Nature. 417 (6886): 216–218. Bibcode:2002Natur.417..216G. doi:10.1038/417216a. PMID 12015565.
3. ^ Wolfram, S. (2013). "Computer algebra". Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation - ISSAC '13. p. 7. doi:10.1145/2465506.2465930. ISBN 9781450320597.
4. ^ a b Stephen Wolfram's publications indexed by the Scopus bibliographic database. (subscription required)
5. ^ "Some topics in theoretical high-energy physics". Caltech Library. Retrieved 8 May 2018.
6. ^ "Biographical Facts for Stephen Wolfram". www.stephenwolfram.com. Retrieved 2 March 2017.
7. ^ "Stephen Wolfram". Wolfram Alpha. Retrieved 15 May 2012. Cite journal requires |journal= (help)
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10. ^ The Universal Mind: The Evolution of Machine Intelligence and Human Psychology, Xiphias Press, 1 Sep 2016, Michael Peragine
11. ^ a b Telling a good yarn by Jenny Lunnon, Oxford Times, Thursday 21 September 2006.
12. ^ PHYSICIST AWARDED 'GENIUS' PRIZE FINDS REALITY IN INVISIBLE WORLD, by GLADWIN HILL, Special to the New York Times, Published: 24 May 1981
13. ^ Howard Gottlieb Archival Research Center: Wolfram, Hugo (1925- ): "The Hugo Wolfram collection consists of manuscripts by Wolfram for novels, short stories, and essays."
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15. ^ Hugo Wolfram. 1925- , Jüdische Schriftstellerinnen und Schriftsteller in Westfalen.
16. ^ Philosophical Logic: An Introduction by Sybil Wolfram, 2014 [1989].
17. ^
18. ^ a b c Levy, Steven. "The Man Who Cracked The Code to Everything ..." Wired. Vol. 10 no. 6. Retrieved 3 March 2015.
19. ^ Wolfram, Sybil (1967). "A Disclaimer". American Anthropologist. 69: 86. doi:10.1525/aa.1967.69.1.02a00160.
20. ^ Times Literary Supplement, 29 October 2008. "The century of Claude Lévi-Strauss: How the great anthropologist, now approaching his 100th birthday, has earned a place in the prestigious Pléiade library", by Patrick Wilcken.
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25. ^ Kate Friedländer née Frankl (1902-1949), Psychoanalytikerinnen. Biografisches Lexikon.
26. ^ "Stephen Wolfram". Sunday Profile. 31 May 2009. Australian Broadcasting Corporation.
27. ^ http://www.stephenwolfram.com/bio-facts/
28. ^ A Speech for (High-School) Graduates by Stephen Wolfram a commencement speech for Stanford Online High School, StephenWolfram.com, 9 June 2014: "You know, as it happens, I myself never officially graduated from high school, and this is actually the first high school graduation I've ever been to."
29. ^ Complexity: A Guided Tour by Melanie Mitchell, 2009, p. 151: "In the early 1980s, Stephen Wolfram, a physicist working at the Institute for Advanced Study in Princeton, became fascinated by cellular automata and the patterns they make. Wolfram is one of those legendary child prodigies people like to tell stories about. Born in London in 1959, Wolfram published his first physics paper at 15. Two years later, in the summer after his first year at Oxford, . . . Wolfram wrote a paper in the field of "quantum chromodynamics" that attracted the attention of Nobel-Prize-winning physicist Murray Gell-Mann, who invited Wolfram to join his group at Caltech…"
30. ^ a b Arndt, Michael (17 May 2002). "Stephen Wolfram's Simple Science". BusinessWeek. Retrieved 20 August 2015.
31. ^ Stephen Wolfram: 'The textbook has never interested me': The British child genius who abandoned physics to devote himself to coding and the cosmos, by Zoë Corbyn, The Guardian, Saturday 28 June 2014: "He entered Oxford University at 17 without A-levels and left around a year later without graduating. He was bored and he had been invited to cross the pond by the prestigious California Institute of Technology (Caltech) to do a PhD. "I had written a bunch of papers and so was pretty well known by that time,"" ...
32. ^
33. ^ a b Wolfram, Stephen (1980). Some Topics in Theoretical High-Energy Physics (PhD thesis). California Institute of Technology.
34. ^ Application
35. ^ PHYSICIST AWARDED 'GENIUS' PRIZE FINDS REALITY IN INVISIBLE WORLD, by GLADWIN HILL, Special to the New York Times, Published: 24 May 1981: "When I first went to school, they thought I was behind, he says, because I didn't want to read the silly books they gave us. And I never was able to do arithmetic. It was when he got into higher mathematics, such as calculus, he says, that he realized there was an invisible world that he wanted to explore."
36. ^ S. Wolfram (1972). Concise Directory of Physics (PDF).
37. ^ S. Wolfram (1973). The Physics of Subatomic Particles (PDF).
38. ^ S. Wolfram (1974). Introduction to the Weak Interaction (PDF). 1.
39. ^ S. Wolfram (1974). Introduction to the Weak Interaction (PDF). 2.
40. ^ Stephen Wolfram: Articles on Particle Physics
41. ^ Fox, G.; Wolfram, S. (1978). "Observables for the Analysis of Event Shapes in e^{+}e^{-} Annihilation and Other Processes". Physical Review Letters. 41 (23): 1581. Bibcode:1978PhRvL..41.1581F. doi:10.1103/PhysRevLett.41.1581.
42. ^ "About Stephen Wolfram". www.stephenwolfram.com. Retrieved 13 October 2015.
43. ^ Wolfram, S. (1984). "Computation theory of cellular automata". Communications in Mathematical Physics. 96 (1): 15–57. Bibcode:1984CMaPh..96...15W. doi:10.1007/BF01217347.
44. ^ Martin, O.; Odlyzko, A. M.; Wolfram, S. (1984). "Algebraic properties of cellular automata" (PDF). Communications in Mathematical Physics. 93 (2): 219. Bibcode:1984CMaPh..93..219M. doi:10.1007/BF01223745.
45. ^ Wolfram, S. (1986). "Cellular automaton fluids 1: Basic theory" (PDF). Journal of Statistical Physics. 45 (3–4): 471–526. Bibcode:1986JSP....45..471W. doi:10.1007/BF01021083.
46. ^ Wolfram, S. (1984). "Cellular automata as models of complexity". Nature. 311 (5985): 419–424. Bibcode:1984Natur.311..419W. doi:10.1038/311419a0.
47. ^ Wolfram, S. (1983). "Statistical mechanics of cellular automata". Reviews of Modern Physics. 55 (3): 601–644. Bibcode:1983RvMP...55..601W. doi:10.1103/RevModPhys.55.601.
48. ^ Regis, Ed (1987). Who Got Einstein's Office: Eccentricity and Genius at the Institute for Advanced Study, Addison-Wesley, Reading. ISBN 0201120658
49. ^ Cook, Matthew (2004). "Universality in Elementary Cellular Automata". Complex Systems. 15 (1). ISSN 0891-2513. Retrieved 24 June 2015.
50. ^ "You don't understand "ordinary people"". Retrieved 2 March 2018.
51. ^ W. Daniel Hillis (February 1989). "Richard Feynman and The Connection Machine". Physics Today. Archived from the original on 28 July 2009. Retrieved 3 November 2006.
52. ^ Pines, David (1987). Emerging Syntheses in Science: Proceedings of the Founding Workshops of the Santa Fe Institute (PDF). Menlo Park, Calif.: Addison-Wesley. pp. 183–190.
53. ^ a b "The Man Who Cracked The Code to Everything". Wired. Retrieved 7 April 2012.
54. ^ Kolata, G. (1983). "Caltech Torn by Dispute over Software". Science. 220 (4600): 932–934. Bibcode:1983Sci...220..932K. doi:10.1126/science.220.4600.932. PMID 17816011.
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59. ^ TED (2010): Stephen Wolfram: Scientist, Inventor. Online (accessed 19 January 2010).
60. ^ Rucker, Rudy; Wolfram, Stephen (2003). "A New Kind of Science". The American Mathematical Monthly. 110 (9): 851. doi:10.2307/3647819. JSTOR 3647819.
61. ^ McCune, William; Veroff, Robert; Fitelson, Branden; Harris, Kenneth; Feist, Andrew; Wos, Larry (2002). "Short single axioms for Boolean algebra". Journal of Automated Reasoning. 29 (1): 1–16. doi:10.1023/A:1020542009983. MR 1940227.
62. ^ "Archived copy" (PDF). Archived from the original (PDF) on 28 May 2016. Retrieved 13 January 2019.CS1 maint: archived copy as title (link)
63. ^ Wolfram, Stephen (5 March 2009). "Wolfram|Alpha Is Coming!". Wolfram blog. Retrieved 9 March 2009.
64. ^ "Announcing Wolfram|Alpha Pro". Wolfram|Alpha blog. Retrieved 7 April 2012.
65. ^ Johnson, Bobbie (9 March 2009). "British search engine 'could rival Google'". The Guardian. Retrieved 9 March 2009.
66. ^ Wolfram|Alpha: Searching for Truth by Rudy Rucker, H+ Magazine, 6 April 2009.
67. ^ "Answering your questions with Bing and Wolfram Alpha". "Microsoft's Bing blog". Retrieved 7 April 2012.
68. ^ Stephen Wolfram Talks Bing Partnership, Software Strategy, and the Future of Knowledge Computing by Gregory T. Huang, Xconomy, 5 January 2010.
69. ^ "iPhone features". Apple. Archived from the original on 31 August 2012. Retrieved 7 April 2012.
70. ^ "Popular Science columnist earns prestigious American Chemical Society award". American Chemical Society. Retrieved 25 December 2018.
71. ^ Wolfram Language reference page Retrieved on 14 May 2014
72. ^ Slate's article Stephen Wolfram's New Programming Language: He Can Make The World Computable, 6 March 2014. Retrieved on 14 May 2014.
73. ^ What Tech Makes Possible in EDU Research, SXSW Panelpicker.
74. ^ New in the Wolfram Language: Cryptography, 15 May 2015, by Christopher Wolfram, Connectivity Group
75. ^ Stephen Wolfram - I Wrote a Book — To Teach the Wolfram Language
76. ^ "Machine Learning for Middle Schoolers—Stephen Wolfram". blog.stephenwolfram.com. Retrieved 17 May 2017.
77. ^ "Stephen Wolfram". Twitter. Retrieved 17 May 2017.
78. ^ "What do I do all day? Livestreamed technology ceoing". www.wired.com. Retrieved 18 June 2019.
79. ^ Stephen, Wolfram. "The Personal Analytics of My Life". Wired. Retrieved 18 October 2016.
80. ^ How Arrival's Designers Crafted a Mesmerizing Language, Margaret Rhodes, Wired, 16 November 2016.
81. ^ "Dissecting the alien language in 'Arrival'". Engadget. Retrieved 16 November 2016.
82. ^ "Quick, How Might the Alien Spacecraft Work?—Stephen Wolfram". blog.stephenwolfram.com. Retrieved 16 November 2016.
83. ^ "The Stephen Wolfram Podcast | Free Listening on SoundCloud". Soundcloud. Retrieved 18 September 2019.
84. ^ 'Idea Makers' tackles scientific thinkers' big ideas and personal lives / Human side of science emphasized in new book by Tom Siegfried, Science News, 13 August 2016.
85. ^ Stephen Wolfram Aims to Democratize His Software by Steve Lohr, The New York Times, 14 December 2015.