John Horton Conway, one of the most influential mathematicians of the last century, passed away this week due to COVID-19. He was 82 years old. Conway was instrumental in furthering the fields of finite groups, knot theory, number theory, combinatorial game theory, and coding theory. However, his most famous invention was a cellular automaton game called the Game of Life.
The Game of Life takes place on an infinite square grid and has four simple rules. Each space is called a cell and a cell is either populated (alive) or unpopulated (dead). A populated cell with one or no neighbors does, as if by solitude, A populated cell with four or more neighbors dies, as if by overpopulation. A populated cell with two or three neighbors survives. Finally, an unpopulated cell with three neighbors becomes populated. Each iteration (turn) of the game calculates a new pattern of cells based on these rules and the previous pattern of cells. While certain patterns fizzle out into nothing after a few turns, others are able to create some incredible sequences. You can try the Game of Life out for yourself here.
Other creations of his include a new system of numbers called the surreal numbers, the Doomsday algorithm, free will theorem, the Conway criterion in tessellations theory, the Conway polynomial in knot theory, Conway notation in tangle theory, and the group of conjectures known as “monstrous moonshine” which bridged finite groups and complex function theory.