John Horton Conway

John Horton Conway (1937–2020) was a renowned English mathematician known for his work in group theory, number-theory, and combinatorial game theory. He is perhaps best known for inventing the Game of Life, a cellular automaton that sparked widespread interest in complex systems.

Key Contributions

• The Game of Life: A zero-player game demonstrating emergence and complexity from simple rules.
• Conway’s Constant: A mathematical constant related to the Look-and-say sequence.
• Surreal Numbers: Co-developed the class of numbers that includes real numbers, infinitesimals, and transfinite ordinals.
• Monstrous Moonshine: Significant contributions to the theory of finite simple groups and their connection to modular functions.

Mathematical Curiosities

Conway was known for creating functions and objects that challenged standard mathematical intuition.

• Conway’s Base 13 Function: A pathological function that takes on every real value in every interval. It is constructed using base-13 representation to encode decimal digits, allowing it to exhibit the Darboux property while being discontinuous everywhere.
  • For a detailed explanation of its unique definition and construction, see Conway’s Base 13 Function: Explaining its Unique Mathematical Definition.
  • This concept is further explored in the Numberphile video by Asaf Karagila, which discusses how the function challenges the intuitive understanding of function (mathematics) as simple input-output rules.

References

• Conway’s Base 13 Function: Explaining its Unique Mathematical Definition (Numberphile). https://www.youtube.com/watch?v=zsBaApyf_Ns