John Conway is a British mathematician who studied and taught at Cambridge University and is now a professor at Princeton. In the programming community Conway is best known as the inventor of the Game of Life, one of the earliest examples of cellular automata, but he has made significant contributions to mathematics throughout his career.
In 1969, Conway introduced surreal numbers, which include real numbers and ordinal numbers. Every real number is surrounded by surreals, which are closer to it than any other real number. In 1974, Donald Knuth described surreal numbers in his book Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness. The book is notable because Knuth presents the idea of surreal numbers by way of a fictional dialogue.
In 2004, Conway and Simon Kochen, another Princeton University mathematics professor, proved the Free will theorem. The theorem states that if humans have free will, then elementary particles like atoms and electrons must have free will as well.
Conway is also known for being the inventor of the Doomsday algorithm for calculating the days of the week, the puzzle games Sprouts and Phutball, and for providing all 240 solutions for the Soma Cube.
Conway's recent lectures on mathematics and geometry, including his ongoing (at the time of this writing) lecture series on Free Will and Determinism are available for free download through Princeton University.
Books by John Conway
On Numbers and Games
Winning Ways for Your Mathematical Plays, Vol. 2