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 Gu…
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.”
[1]: https://www.futilitycloset.com/2010/06/27/conways-prime-prod... / https://en.wikipedia.org/wiki/FRACTRAN
[2]: https://en.wikipedia.org/wiki/Conway%27s_Soldiers
[3]: https://en.wikipedia.org/wiki/Angel_problem