People here might know him best for the "Game of Life"[0], but he did so much more. The book about Conway by Siobhan Roberts is an interesting read about the man and his work. There's a review here.[1]
Some will know Conway via is work on the Classification of Finite Simple Groups (with many others), some via his "Look and Say" sequence, while still others will know his book "Winning Ways"[2], written with Richard Guy[3] and Elwyn Berlekamp[4]. My copy signed by all three is something I treasure.
I was privileged to know all three of them, and I mourn their passing.
Such a long list even without mentioning: FRACTRAN, Conway's soldiers, the angel problem, the Conway base 13 function, the 15 theorem (and 290 theorem)… incredible how he got so many mind-bending and unique ideas.
On Conway the showman: I heard the following from my friend who went to Princeton for his PhD. First day of class, Conway walks in, after some introduction, picks up a piece of chalk with his left-hand, starts at the left-hand corner of the blackboard writing quickly and neatly. Everyone thinks "Ah, he must be left-handed". When he's filled half the blackboard he smoothly switches the chalk to his right hand and continues writing just as quickly and neatly.
He told me many such anecdotes about Conway dazzling everyone; all the students were in awe of him. One of them is mentioned on the Wikipedia page for Doomsday rule: “Conway can usually give the correct answer [the day of the week for any year/month/date] in under two seconds. To improve his speed, he practices his calendrical calculations on his computer, which is programmed to quiz him with random dates every time he logs on.”
There were better contemporary mathematicians than John Conway, and there were (a handful of) better contemporary popularizers of mathematics, but no one else came close to doing both nearly as well.
I met him on a few different occasions when I was very young (middle and high school), and he was always extremely generous with his time, especially with an interlocutor not legally old enough to drink, and clearly brilliant in person. One example of his generosity was his collaboration on a book about triangle centers[0] with the late Steve Sigur, who was not a research mathematician but a high school teacher.
Of course the Game of Life is an enduring classic, but I’ll also always have fond memories of Winning Ways for Your Mathematical Plays and Sphere Packings, Lattices and Groups (affectionately known as SPLAG). The mathematical world has truly lost a living legend.
I think one of the interesting things about Conway is that there were better contemporary mathematicians by a contemporary measure of “better”. He just sort of did his thing and worked on problems that he found interesting, not necessarily ones that were considered “important” in the mathematical community at the time. The courage to stick to that is pretty amazing.
Oh, I absolutely love the surreal numbers! The surreals are a superset of the reals, but that's not why I think they are interesting.
In mainstream pure mathematics, you first create the naturals (whole numbers). Then from there you create the rationals, as fractions of naturals. Then from there you can create the reals as infinite sequences of rationals.
This works, but it is arguably inelegant. We like to say naturals are a subset of rationals, and rationals are a subset of reals. But by this construction they're not ontologically the same. (We can of course find a subset of the reals that look like the rationals, etc., but they aren't identical, only equivalent.)
In contrast, the surreal numbers are all constructed in one go. Very elegant.
That article in The Guardian is especially good. The author clearly loves mathematics and knows how to tell a good story.
> Conway’s is a jocund and playful egomania, sweetened by self-deprecating charm. He has on many occasions admitted: “I do have a big ego! As I often say, modesty is my only vice. If I weren’t so modest, I’d be perfect.”
And sadly all three authors of "Winning Ways" have now passed away within almost exactly a year: Berlekamp died on Apr 9 last year, and Richard Guy died in March (he was 103!).
It was my first program in Turbo Pascal. Until then I'd been a BASICA programmer and opposed to "structured programming," which I thought would stifle my creativity. I'd spend long days with code printouts all over the floor, tracing through GOTOs to find my bugs.
Then dad brought home Turbo and I tried it out with the GoL. It worked correctly the first time it ran. That had never happened to me before. I never touched BASICA again.
Sad to see Conway go. He was born the same year as my dad, who died several months ago.
I still remember how "Game of Life" blew my mind. I couldn't probably understand the rest of his work. So GoL probably hit in the right spot for moderately smart people.
Some will know Conway via is work on the Classification of Finite Simple Groups (with many others), some via his "Look and Say" sequence, while still others will know his book "Winning Ways"[2], written with Richard Guy[3] and Elwyn Berlekamp[4]. My copy signed by all three is something I treasure.
I was privileged to know all three of them, and I mourn their passing.
[0] https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life
[1] https://www.theguardian.com/science/2015/jul/23/john-horton-...
[2] https://en.wikipedia.org/wiki/Winning_Ways_for_your_Mathemat...
[3] https://en.wikipedia.org/wiki/Richard_K._Guy
[4] https://en.wikipedia.org/wiki/Elwyn_Berlekamp
Added in Edit:
From his wikipedia page:
Known for: Surreal numbers, Conway groups, Monstrous moonshine, Doomsday algorithm, Look-and-say sequence, Icosians, Mathieu groupoid, Free will theorem, Conway chained arrow notation, Conway criterion, Conway notation (knot theory), Conway polyhedron notation, ATLAS of Finite Groups, Conway's Game of Life