#[1]Shtetl-Optimized RSS Feed [2]Shtetl-Optimized » John Horton Conway (1937-2020) Comments Feed [3]When events make craziness sane [4]alternate [5]alternate [6]Shtetl-Optimized The Blog of Scott Aaronson If you take just two pieces of information from this blog: START HUMAN CHALLENGE TRIALS FOR VACCINES AND HOLD THE NOVEMBER US ELECTION BY MAIL __________________________________________________________________ « [7]When events make craziness sane [8]John Horton Conway (1937-2020) While it hasn’t yet been officially confirmed, the news has spread across social media (see e.g. [9]here, [10]here, [11]here) that [12]John Horton Conway, one of the great mathematicians and math communicators of the past half-century, has died at age 82. Just a week ago, as part of her quarantine homeschooling, I introduced my seven-year-old daughter Lily to the famous [13]Conway’s Game of Life. Compared to the other stuff we’ve been doing, like fractions and right triangles and the distributive property of multiplication, the Game of Life was a huge hit: Lily spent a full hour glued to the screen, watching the patterns evolve, trying to guess when they’d finally die out. So this first-grader knew who John Conway was, when I told her the sad news of his passing. “Did he die from the coronavirus?” Lily immediately asked. “I doubt it, but I’ll check,” I said. Apparently it was the coronavirus. Yes, the self-replicating snippet of math that’s now terrorizing the whole human race, in part because those in power couldn’t or wouldn’t understand exponential growth. Conway is perhaps the nasty bugger’s most distinguished casualty so far. I regrettably never knew Conway, although I did attend a few of his wildly popular and entertaining lectures. His [14]The Book of Numbers (coauthored with Richard Guy, who himself recently passed away at age 103) made a huge impression on me as a teenager. I worked through every page, gasping at gems like e^π√163 (“no, you can’t be serious…”), embarrassed to be learning so much from a “fun, popular” book but grateful that my ignorance of such basic matters was finally being remedied. A little like Pascal with his triangle or Möbius with his strip, Conway was fated to become best-known to the public not for his “deepest” ideas but for his most accessible—although for Conway, a principal puzzle-supplier to Martin Gardner for decades, the boundary between the serious and the recreational may have been more blurred than for any other contemporary mathematician. Conway invented the [15]surreal number system, discovered three of the 26 [16]sporadic simple groups, was instrumental in the discovery of [17]monstrous moonshine, and did many other things that bloggers more qualified than I will explain in the coming days. Closest to my wheelhouse, Conway together with Simon Kochen waded into the foundations of quantum mechanics in 2006, with their [18]“Free Will Theorem”—a result Conway liked to summarize provocatively as “if human experimenters have free will, then so do the elementary particles they measure.” I confess that I wasn’t a fan at the time—partly because Conway and Kochen’s theorem was really about “freshly-generated randomness,” rather than free will in any sense related to agency, but also partly because I’d already known the conceptual point at issue, but had considered it folklore (see, e.g., my [19]2002 review of Stephen Wolfram’s A New Kind of Science). Over time, though, the “Free Will Theorem” packaging grew on me. Much like with the [20]No-Cloning Theorem and other simple enormities, sometimes it’s worth making a bit of folklore so memorable and compelling that it will never be folklore again. At a lecture of Conway’s that I attended, someone challenged him that his proposed classification of knots worked only in special cases. “Oh, of course, this only classifies 0% of knots—but 0% is a start!” he immediately replied, to roars from the audience. That’s just one line that I remember, but nearly everything out of his mouth was of a similar flavor. I noted that part of it was in the delivery. As a mathematical jokester and puzzler who could delight and educate anyone from a Fields Medalist to a first-grader, Conway had no equal. For no one else who I can think of, even going back centuries and millennia, were entertainment and mathematical depth so closely marbled together. Here’s to a well-lived Life. Feel free to share your own Conway memories in the comments. [21]Email, RSS Follow This entry was posted on Sunday, April 12th, 2020 at 2:22 am and is filed under [22]Nerd Interest. You can follow any responses to this entry through the [23]RSS 2.0 feed. You can [24]leave a response, or [25]trackback from your own site. 13 Responses to “John Horton Conway (1937-2020)” 1. Gil Kalai Says: Comment #1 [26]April 12th, 2020 at 5:20 am It is sad to hear that John H Conway passed away. He was an amazing mathematician, among the few who invented a new simple group, among the few who invented a major knot invariant, among the few who invented a new system of numbers, and more than anybody he also invented many many many games. Conway was also a master of codes and sphere packings. And this is a very nice post, Scott. Here are few quick memories. (Last time when Scott asked for memories, about Boris Tsirelson, I was too slow and ended up [27]writing them in a post. So I will try to be quick this time) 1) The first (and most meaningful) time I met Conway in person was in 1979 in the common room at the (old) Cambridge (UK) mathematics building, when I came there, as part of an an after-army travel, to a combinatorics meeting in Cambridge. Conway showed me the draft of his monumental book with Berlekamp and Guy “winning ways” and offered me to play a board game called (as far as I can remember) “football”. We played for a while and simultaneously Conway also talked with others (some across the room), including with his wife. Conway set a special rule for me: Everytime I am convinced that I loose, we can switch sides. Needless to say that we switched sides several times; I was sure that my position is desperate beyond repair, we switched sides, and shortly afterward I was again sure that my position in the game is beyond repair. 2) In the following decades I attended some highly entertainment talks by him (I remember that his 1994 plenary talk in Zurich was especially wild but I don’t remember the details). Once at Yale (in the early 2000s) we went after a lecture by Conway to dinner with Hillel Furstenberg. There, Conway showed us the [28]ultimate riddle (I already knew it) and Hillel tried in vein to replicate it. 3)* Once Conway thought that he can prove that every triangulated surface of genus g which is linearly embedded in space, must have at least a linear number of vertices in terms of the genus. I brought to his attention a 1983 paper by McMullen, Schultz and Wills with a construction of only g/log g vertices. This is still the world record, for topological embeddings, square root g vertices suffice and for linear embedding no better lower bound is known. 4) Here is a famous problem asked by Conway in the late 60s (Conway offered 1,000$ for solving it.): A thrackle is a planar drawing of a graph of n vertices by edges which are smooth curves between vertices, such that nonincident edges cross exactly once, and no incident edges share an interior point. The conjecture is that a thrackle has at most n edges. (If the smooth curves are line intervals this is a famous result by Hopf and E. Pannwitz from 1934 .) In the mid 80s my academic brother Yaakov Kupitz workd with our supervisor Micha A. Perles on related questions (and their work initiated a rich area of geometric graph theory), and Kupitz thought that it would be a good idea for him to spend a year with John Conway. All the arrangements were made, including visa, and lodging, but then Yaakov discovered that he connected with a different (famous) mathematician named John Conway, and he cancelled the visit and went for a year to Aarhus, Denmark instead. 2. [29]New top story on Hacker News: John Horton Conway (1937-2020) – News about world Says: Comment #2 [30]April 12th, 2020 at 5:27 am […] John Horton Conway (1937-2020) 22 by weinzierl | 1 comments on Hacker News. […] 3. [31]Robin Whitty Says: Comment #3 [32]April 12th, 2020 at 5:28 am I heard him lecture once. He said “I worried for a long time about what the term ‘random variable’ means. In the end I concluded it means: ‘variable’.” 4. [33]Clive Says: Comment #4 [34]April 12th, 2020 at 6:04 am John Horton Conway’s “Game of Life” was one of many amazing things Martin Gardner wrote about in his Mathematical Games column in Scientific American a few decades ago. I used to read those columns as a schoolboy in the 70s, and “Life” was something I found totally fascinating back then and have revisited periodically every since. I’m very sad to hear of his passing. 5. asdf Says: Comment #5 [35]April 12th, 2020 at 6:19 am I got to hang out with Conway a little as an undergraduate. He had a way to solve a Rubik’s cube that wasn’t the most efficient, but whose “subroutines” were so few and simple that he could teach it to a regular person (like me) in just a few minutes. So for a while, I knew how to solve a cube. Not any more, though, I’m sure. He asked me was I was doing and I showed him a differential equation someone had shown me, asking for a function whose derivative is the same as the function’s inverse, (hmm I thought there was a way to use TeX in here? I don’t see it). Anyway, you want f such that f'(x) is the same as f^{-1}(x). This is a cute and not too hard puzzle that I’ll leave as an exercise. Anyway, Conway not surprisingly solved it in about a minute, so I asked if there might be other solutions (I had been trying to figure some out, getting nowhere). Within another minute or two he came up with a proof that any solution must have an infinite series of a certain form, and the puzzle solution was in fact unique (maybe modulo a constant or something). I was amazed. Being a dumb teenager at the time, I knew that Conway was a great combinitorialist, inventor of the Game of Life, did some famous thing with finite groups etc., but I thought that kind of mathematician was all about algebra and discrete math and would barely know what a derivative was. So it was cool to see him reach into his memory and immediately pull out the right trick from DE theory that I had never heard of. I looked it up today and I think it is called (TIL) the Method of Frobenius, so I’ll see if I can reconstruct the proof. I heard more recently that Conway apparently hated being best known for inventing Life. He did a lot of really terrific math that few people realize that. I guess it’s like von Neumann being best known for computers, or for cellular automata, when he had such huge impact in many other areas. Similarly with Shakespeare actor Alec Guinness being most famous as Obi-wan Kenobi, etc. 6. Bernard Says: Comment #6 [36]April 12th, 2020 at 7:24 am Conway was truly exceptional. In Spring 1967, during my first year reading mathematics at Cambridge, a fellow maths student told me I had to join him in a class on the foundations of mathematics being taught by a mad Liverpudlian professor with a huge ginger beard. Of course it was Conway who was only 3 years out of his PhD work. I was having great difficulty with the mathematics curriculum. Most other students were far better prepared that I had been and I was struggling to keep up, with limited success. But Conway’s enthusiasm was infectious and inspiring. He was also funny. All our other classes covered material from the early 19th century but John was teaching us about work that had been done in 1964 (Paul Cohen’s proof that the continuum hypothesis is independent of set theory). When I moved to Princeton in the 1990s I was astonished to find that John lived one street away. Despite the geographic proximity, it was years before I had a chance to speak to him. I told him I’d taken his class in 1967 and enjoyed it. His reply was Diracian in its brevity: “you survived”. Rest in peace. 7. alpha Says: Comment #7 [37]April 12th, 2020 at 7:49 am He is also to have said P=NP. 8. Aaron G Says: Comment #8 [38]April 12th, 2020 at 7:53 am Scott, I’ve been scouring the Internet for news about Conway’s death and haven’t found anything reported outside of social media. How reliable are the sources? 9. Amin Says: Comment #9 [39]April 12th, 2020 at 8:19 am This is very sad. I was also fascinated by Conway’s Game of Life when my maths teacher showed us some animations in middle school. Looking back it’s probably the first example of Turing completeness I saw. Although I must confess I had no idea what Turing machines were at the time :d 10. Anon Says: Comment #10 [40]April 12th, 2020 at 8:22 am Several years back, I met John Conway at a math summer camp for high school students. He gave several talks and also joined us for lunch sometimes. I remember thinking that this old man was a bit eccentric, but also really did see the fun in math (a phrase he used was “nerdish delights”). While I personally did not exchange many words with him, I was there while fellow high school students much more knowledgeable and passionate about math than I talked with him at length – this man truly could talk about math on any level to anyone. I really enjoyed him telling us about his Doomsday algorithm, a surprisingly simple way to figure out the day of a week for an arbitrary date (for the year or so after that, I would conscientiously always use the Doomsday algorithm to figure out the day of a week rather than actually check a calendar). Rest in peace, John Conway. 11. [41]mjgeddes Says: Comment #11 [42]April 12th, 2020 at 8:36 am I had just been researching ‘Monstrous Moonshine’ – there’s actually a very large amount of background knowledge in algebra you need to build up to that – I had to read many wikipedia articles to lay the foundation. It’s thought to be important to String theory. Conway’s Game of Life, of course, very interesting, it’s a cellular automaton , gets you thinking about computation and complexity in a fun way ! My suspicion now is that it may be valid to consider the universe (as a whole) as a singular dynamical complex system – it’s not a closed system ! And Game of Life definitely nudged my thinking in the right direction, towards complex systems theory. Speaking of Stephen Wolfram, he’s apparently about to make a big announcement, he’s claiming that he’s made a huge physics breakthrough , and as far I can make out , it’s a new model of space and time that gives a new interpretation of quantum mechanics – looks quite intriguing. This could be quite big news, so look forward to hearing your thoughts on it Scott…. 12. [43]Scott Says: Comment #12 [44]April 12th, 2020 at 9:08 am Aaron G #8: Scott, I’ve been scouring the Internet for news about Conway’s death and haven’t found anything reported outside of social media. How reliable are the sources? In the end I made a judgment call that the many mathematicians and others reporting this, including on my Facebook, seemed trustworthy. I also reasoned that, in the sadly unlikely event that they were wrong, Conway—like Mark Twain—is the sort of guy who’d greatly enjoy reading his own obituaries. 13. Vijay M. Patankar Says: Comment #13 [45]April 12th, 2020 at 9:43 am What a sad news… I have been reading a lot about him and by him – his discoveries, his theorems, his perspectives. Remarkable, in so many ways. I was planning to teach basics from his book “The Sensual (quadratic) form” to my elementary Number Theory class. Rest in Peace… Leave a Reply Comment Policy: All comments are placed in moderation and reviewed prior to appearing. Comments can be left in moderation for any reason, but in particular, for ad-hominem attacks, hatred of groups of people, or snide and patronizing tone. Also: comments that link to a paper or article and, in effect, challenge me to respond to it are at severe risk of being left in moderation, as such comments place demands on my time that I can no longer meet. You'll have a much better chance of a response from me if you formulate your own argument here, rather than outsourcing the job to someone else. I sometimes accidentally miss perfectly reasonable comments in the moderation queue, or they get caught in the spam filter. If you feel this may have been the case with your comment, shoot me an email. ______________________ Name (required) ______________________ Mail (will not be published) (required) ______________________ Website _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ Submit Comment __________________________________________________________________ Shtetl-Optimized is proudly powered by [46]WordPress [47]Entries (RSS) and [48]Comments (RSS). References Visible links 1. https://www.scottaaronson.com/blog/?feed=rss2 2. https://www.scottaaronson.com/blog/?feed=rss2&p=4732 3. https://www.scottaaronson.com/blog/?p=4719 4. https://www.scottaaronson.com/blog/index.php?rest_route=/oembed/1.0/embed&url=https://www.scottaaronson.com/blog/?p=4732 5. https://www.scottaaronson.com/blog/index.php?rest_route=/oembed/1.0/embed&url=https://www.scottaaronson.com/blog/?p=4732&format=xml 6. https://www.scottaaronson.com/blog/ 7. https://www.scottaaronson.com/blog/?p=4719 8. https://www.scottaaronson.com/blog/?p=4732 9. https://news.ycombinator.com/item?id=22843306 10. https://www.reddit.com/r/news/comments/fziay0/mathematician_john_conway_has_died/ 11. https://meta.mathoverflow.net/questions/3144/news-of-potential-interest-to-the-mo-community/4513#4513 12. https://en.wikipedia.org/wiki/John_Horton_Conway 13. https://en.wikipedia.org/wiki/Conway's_Game_of_Life 14. https://www.amazon.com/Book-Numbers-John-H-Conway/dp/038797993X 15. https://en.wikipedia.org/wiki/Surreal_number 16. https://en.wikipedia.org/wiki/Sporadic_group 17. https://en.wikipedia.org/wiki/Monstrous_moonshine 18. https://en.wikipedia.org/wiki/Free_will_theorem 19. https://arxiv.org/abs/quant-ph/0206089 20. https://en.wikipedia.org/wiki/No-cloning_theorem 21. http://www.specificfeeds.com/follow 22. https://www.scottaaronson.com/blog/?cat=11 23. https://www.scottaaronson.com/blog/?feed=rss2&p=4732 24. https://www.scottaaronson.com/blog/?p=4732#respond 25. https://www.scottaaronson.com/blog/wp-trackback.php?p=4732 26. https://www.scottaaronson.com/blog/?p=4732#comment-1836693 27. https://gilkalai.wordpress.com/2020/04/03/trees-not-cubes-memories-of-boris-tsirelson/ 28. https://gilkalai.wordpress.com/2010/02/02/the-ultimate-riddle/ 29. https://newsblogie.wordpress.com/2020/04/12/new-top-story-on-hacker-news-john-horton-conway-1937-2020/ 30. https://www.scottaaronson.com/blog/?p=4732#comment-1836695 31. http://www.theoremoftheday.org/ 32. https://www.scottaaronson.com/blog/?p=4732#comment-1836696 33. http://eigenratios.blogspot.com/2007/09/self-interpreter-for-conways-game-of.html 34. https://www.scottaaronson.com/blog/?p=4732#comment-1836702 35. https://www.scottaaronson.com/blog/?p=4732#comment-1836703 36. https://www.scottaaronson.com/blog/?p=4732#comment-1836708 37. https://www.scottaaronson.com/blog/?p=4732#comment-1836712 38. https://www.scottaaronson.com/blog/?p=4732#comment-1836713 39. https://www.scottaaronson.com/blog/?p=4732#comment-1836716 40. https://www.scottaaronson.com/blog/?p=4732#comment-1836719 41. http://www.zarzuelazen.com/CoreKnowledgeDomains2.html 42. https://www.scottaaronson.com/blog/?p=4732#comment-1836720 43. http://www.scottaaronson.com/ 44. https://www.scottaaronson.com/blog/?p=4732#comment-1836726 45. https://www.scottaaronson.com/blog/?p=4732#comment-1836730 46. http://wordpress.org/ 47. https://www.scottaaronson.com/blog/?feed=rss2 48. https://www.scottaaronson.com/blog/?feed=comments-rss2 Hidden links: 50. https://twitter.com/share