# John Horton Conway

> English mathematician (1937–2020)

**Wikidata**: [Q268961](https://www.wikidata.org/wiki/Q268961)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/John_Horton_Conway)  
**Source**: https://4ort.xyz/entity/john-horton-conway

## Summary
John Horton Conway was an English mathematician (1937–2020) known for his groundbreaking contributions to combinatorial game theory, knot theory, and cellular automata. He is best recognized for inventing the "Game of Life," a two-dimensional cellular automaton that became a foundational concept in computer science and mathematics.

## Biography
- Born: December 26, 1937, in Liverpool, England
- Nationality: British
- Education:
  - Gonville and Caius College, University of Cambridge (BA, MA, PhD)
- Known for: Pioneering work in combinatorial game theory, knot theory, and the invention of the Game of Life
- Employer(s):
  - Princeton University (Professor)
  - University of Cambridge (Professor)
- Field(s):
  - Mathematics
  - Combinatorial game theory
  - Knot theory
  - Cellular automata

## Contributions
- **Game of Life (1970)**: Invented the two-dimensional cellular automaton, which became a foundational concept in computer science and mathematics, influencing fields like artificial life and algorithmic research.
- **Conway notation for knots (1970)**: Developed a system for describing and classifying knots, which became a standard in knot theory.
- **Surreal numbers (1976)**: Co-developed the concept of surreal numbers, a proper class that extends the real numbers to include infinitesimals and infinite quantities.
- **Conway's Soldiers (1975)**: Created a mathematical puzzle that explores the properties of finite groups and their representations.
- **Hackenbush (1967)**: Designed a mathematical pen-and-paper game that demonstrates concepts in combinatorial game theory.
- **Conway's base 13 function (1976)**: Provided a counterexample to the converse of the intermediate value theorem, contributing to real analysis.
- **Look-and-say sequence (1964)**: Discovered the integer sequence, which has applications in number theory and computer science.

## FAQs
**What was John Horton Conway's most famous invention?**
John Horton Conway is best known for inventing the "Game of Life," a two-dimensional cellular automaton that became a foundational concept in computer science and mathematics.

**Where did John Horton Conway study?**
Conway studied at Gonville and Caius College, University of Cambridge, where he earned a BA, MA, and PhD in mathematics.

**What is the Game of Life?**
The Game of Life is a cellular automaton devised by John Horton Conway in 1970, where cells evolve based on simple rules, creating complex patterns and behaviors.

**What is combinatorial game theory?**
Combinatorial game theory is the branch of mathematics that studies two-player sequential games with perfect information, where no chance moves or hidden information occur.

**What are surreal numbers?**
Surreal numbers are a proper class of numbers that extends the real numbers to include infinitesimals and infinite quantities, co-developed by John Horton Conway.

## Why They Matter
John Horton Conway's work revolutionized multiple fields of mathematics, particularly combinatorial game theory and knot theory. His inventions, such as the Game of Life and surreal numbers, have had lasting impacts on computer science, artificial intelligence, and theoretical mathematics. Conway's contributions to knot theory, through his notation system, standardized the classification of knots, which has applications in physics and biology. His mathematical puzzles and games, like Hackenbush and Conway's Soldiers, have inspired generations of mathematicians and computer scientists. Conway's ability to bridge abstract theory with practical applications made him a pivotal figure in modern mathematics.

## Notable For
- Inventor of the Game of Life, a foundational concept in cellular automata and computer science.
- Pioneer of combinatorial game theory, contributing to the rigorous mathematical framework for analyzing deterministic games.
- Developer of the Conway notation for knots, which became a standard in knot theory.
- Co-developer of surreal numbers, extending the real number system to include infinitesimals and infinite quantities.
- Creator of mathematical puzzles and games, such as Hackenbush and Conway's Soldiers, that have inspired further research.
- Professor at Princeton University and the University of Cambridge, shaping the next generation of mathematicians.
- Recipient of prestigious awards, including the Pólya Prize, Berwick Prize, and Nemmers Prize in Mathematics.
- Fellow of the Royal Society, recognizing his contributions to science and academia.

## Body
### Early Life and Education
John Horton Conway was born on December 26, 1937, in Liverpool, England. He attended the University of Cambridge, where he studied mathematics and earned a BA, MA, and PhD. His early work in combinatorial game theory laid the groundwork for his later contributions to the field.

### Career and Academic Positions
Conway held professorships at both the University of Cambridge and Princeton University, where he taught and mentored future mathematicians. His academic career spanned over four decades, during which he made significant contributions to mathematics.

### Contributions to Mathematics
#### Combinatorial Game Theory
Conway's work in combinatorial game theory introduced new methods for analyzing games with perfect information. His research focused on two-player sequential games, where players have complete knowledge of the game state and no random elements are involved. This work provided a rigorous framework for understanding game strategies and optimal play.

#### Knot Theory
Conway developed a notation system for describing and classifying knots, which became a standard in knot theory. His work in this field contributed to the understanding of three-dimensional space and the properties of embedded objects. The Conway knot, named after him, is a prime knot with 11 crossings that has been studied extensively in knot theory.

#### Cellular Automata
The Game of Life, invented by Conway in 1970, is a two-dimensional cellular automaton where cells evolve based on simple rules. This invention became a foundational concept in computer science and mathematics, influencing fields like artificial life and algorithmic research. The Game of Life has been studied for its complex patterns and behaviors, demonstrating the emergence of complex systems from simple rules.

#### Surreal Numbers
Conway co-developed the concept of surreal numbers, a proper class that extends the real numbers to include infinitesimals and infinite quantities. This work has applications in real analysis and has contributed to the understanding of number systems.

### Mathematical Puzzles and Games
Conway created several mathematical puzzles and games, including Hackenbush and Conway's Soldiers. These puzzles explore concepts in combinatorial game theory and have inspired further research in the field. His work on the Look-and-say sequence, discovered in 1964, has applications in number theory and computer science.

### Awards and Recognition
Conway received numerous awards and honors for his contributions to mathematics, including the Pólya Prize, Berwick Prize, and Nemmers Prize in Mathematics. He was also a Fellow of the Royal Society, recognizing his significant contributions to science and academia.

### Legacy and Influence
John Horton Conway's work has had a profound impact on mathematics and computer science. His inventions, such as the Game of Life and surreal numbers, have become foundational concepts in their respective fields. Conway's contributions to knot theory and combinatorial game theory have standardized methods for analyzing complex systems and games. His ability to bridge abstract theory with practical applications has made him a pivotal figure in modern mathematics.

## References

1. John Horton Conway (1937-2020)
2. [Mathematician John Horton Conway, a ‘magical genius’ known for inventing the ‘Game of Life,’ dies at age 82. Princeton University. 2020](https://www.princeton.edu/news/2020/04/14/mathematician-john-horton-conway-magical-genius-known-inventing-game-life-dies-age)
3. [John Horton Conway, a ‘Magical Genius’ in Math, Dies at 82. John Horton Conway, a ‘Magical Genius’ in Math, Dies at 82. 2020](https://www.nytimes.com/2020/04/15/technology/john-horton-conway-dead-coronavirus.html)
4. Czech National Authority Database
5. Genealogics
6. LIBRIS. 2012
7. BnF authorities
8. E-Theses Online Service
9. [John Horton Conway. Curriculum Vitae](https://www.math.princeton.edu/sites/default/files/2017-03/ConwayCV.pdf)
10. [Source](https://www.ams.org/prizes-awards/pabrowse.cgi?parent_id=26)
11. Mathematics Genealogy Project
12. International Standard Name Identifier
13. Virtual International Authority File
14. CiNii Research
15. MusicBrainz
16. [Source](https://www.amacad.org/person/john-horton-conway)
17. Mathematiker John Conway ist gestorben
18. [COVID-19 Kills Renowned Princeton Mathematician, 'Game Of Life' Inventor John Conway In 3 Days. The Daily Voice. 2020](https://dailyvoice.com/new-jersey/mercer/obituaries/covid-19-kills-renowned-princeton-mathematician-game-of-life-inventor-john-conway-in-3-days/786461/)
19. U.S. deaths near 100,000, an incalculable loss
20. [Mathematician and game designer John H. Conway dies from coronavirus complications](https://www.nydailynews.com/coronavirus/ny-coronavirus-john-h-conway-mathematician-game-designer-dies-20200414-msg4nr26azehvfzrg44t5lj6di-story.html)
21. MacTutor History of Mathematics archive
22. [Mathematician John Horton Conway has died after contracting Covid-19. 2020](https://www.theguardian.com/world/live/2020/apr/12/coronavirus-live-pope-easter-lockdown-us-death-toll-uk-boris-johnson-donald-trump-?page=with:block-5e92b7668f08db3109f20f8a#block-5e92b7668f08db3109f20f8a)
23. [Создатель игры «Жизнь» математик Джон Конвей умер от COVID-19. 2020](https://nplus1.ru/news/2020/04/12/conway-died)
24. [Wiskundige Conway was een speels genie en kenner van symmetrie. 2020](https://www.nrc.nl/nieuws/2020/04/12/wiskundige-conway-was-een-speels-genie-en-kenner-van-symmetrie-a3996590)
25. [John H. Conway, 1937–2020. 2020](https://www.math.princeton.edu/news/john-h-conway-1937-2020)
26. Freebase Data Dumps. 2013
27. Open Library
28. [Il matematico John Horton Conway è morto di Covid-19 all’età di 82 anni. 2020](http://maddmaths.simai.eu/news-2/conway-morto/)
29. CONOR.SI
30. Goodreads