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Merge/upload from an UX-unfriendly page with Vimeo player on simonsfoundation.org. All rights on this video belong to Simons Foundation. 00:00:00 Highlights 00:02:44 Discovery of Conway Groups 00:12:13 Regular Algebra and Finite Machines 00:15:01 My Job is to Simplify Things 00:16:42 The Life Game 00:27:06 The Life Game and Von Neumann’s First Computer 00:32:01 PRIMEGAME 00:35:49 Childhood Interest in Mathematics 00:43:15 Besicovitch as a Teacher 00:51:42 Discoveries with Games Surreal Numbers 01:04:14 Dots and boxes and Elwyn Berlekamp 01:11:06 On the Book Numbers and Games 01:14:20 Friendship with Elwyn Berlekamp 01:19:15 Five Rainbows 01:35:07 Relationship with Harold Davenport and Waring’s Theorem 01:45:25 Teaching at Cambridge and Moving to Princeton 01:50:04 Atlas of Finite Groups 01:53:26 Bringing Groups to Princeton 01:56:49 Sphere Packings Lattices and Groups 02:02:16 The Monster 02:10:45 Fractran Program 02:19:03 Martin Gardner Stories 02:36:42 Staying with Martin Gardner 02:42:44 The Three by Three Game 02:44:50 Hackenbush Game 02:53:35 Lexicodes 03:09:04 Adapting to Princeton 03:12:36 On the Simplicity of Games 03:16:14 Why Games are Interesting 03:23:15 Gödel as God 03:25:24 Stan Tennenbaum and Gödel 03:31:52 C. W. Gibby Durham and Percy John Heawood 03:34:50 Four Color Theorem and Computer Proofs