I am late to issue this RIP as John Horton Conway died on April 11, 2020, having been born in England, Dec. 26, 1937. He died of coovid-19. I was aware of his death when it happened, but have since become aware of things he did that I did not know about that have pushed me to post this.
Conway was one of the world’s best known mathematicians, most famous for creating the Game of Life a half century ago in 1970, which was publicized by Martin Gardner in Scientific American. It is what I knew of him mostly about, as the canonical cellular automata model that generated simulation models capable of generating chaotic and unpredictable emergent outcomes within a Turing complete framework, the sort of thing that goofy complexity theorists like me salivate over. However, it inspired similar models that have been used in nearly every science, and I am quite sure that such models are being used in the current research push to find a vaccine for the disease that did Conway in. It was an enormous achievement and enormously useful. He deserves recognition for this alone.
I never met him or even saw him speak, but by all accounts he was highly extroverted and lively to the point of becoming at least for awhile “the rock star of mathematics.” Not unrelated with that he invented an enormous array of games, none of which I have ever played, but apparently he would invent them on the spot as he interacted with people he met. Of course in some sense the Game of Life is a kind of game, and Conway himself on more than one occasion claimed that doing mathematics is fundamentally a game.
I had known that he did a lot of work in other areas of math, but had not really checked it out in details, but have recently become more aware of just how widely across math his work varied and how important and innovative so much of it was. I shall not list all these areas and theorems and discoveries as it is a long list that will probably be meaningless to most of you if it is just put out here, but anybody who wants to see a pretty complete version of it, well, his Wikipedia entry provides a pretty thorough one.
Anyway, I shall talk a bit more about a couple of the more out there high level stuff that relates to things that my father and I have long been interested in. My late father was a friend of the late Abraham Robinson and someone Robinson consulted with at length when he developed non-standard analysis, presented in a book of that title in 1966. Non-standard analysis allows for the existence of superreal numbers that have infinite values, real numbers larger than any finite real number. The reciprocals of these numbers are infinitesimals, numbers not equal to zero but smaller than any positive real number. These are ideas originated by Leibniz when he independently invented calculus, and allowed for viewing derivatives as ratios of such infinitesimals, an essentially more intuitive way of doing calculus.
This extension of real numbers into transfinite and infinitesimal values led to further expansions of what might be numbers, with a further extension being hyperreal numbers that can be constructed out of the superreals.