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John Conway has died (twitter.com/cardcolm)
2305 points by ColinWright on April 11, 2020 | hide | past | favorite | 178 comments

I only once saw John Conway giving a talk. I don't remember the topic (it was >20y ago), but I remember how it went. He gave some definitions, then started to give some examples and work out on the blackboard some calculations. It all felt quite trivial. At some point one calculation doesn't work out. He checked again, but still it didn't work. He started pacing in front of the blackboard, and said that this is quite embarrassing. "Hm, I wanted to give a talk about this, but since we found this mistakes, I'm not sure what to say for the remaining 50 minutes". Ok, he said, let's take a step back and start again. And he started again, and the talk was amazing. The whole "embarrassing" thing had been staged. He played a bit of misdirection on us. He started with something that seemed quite trivial, pretended to make a mistake, then showed us how much deeper the topic was.

This was not the only math talk I've seen that was actually a performance, but it was the best.

Rest in peace.

That’s very imaginative and empathetic to the audience. And of course that’s the lecture you remember 20 yrs layer

Hoping you read this ... can you get in touch with me please? Contact email is in my profile ... thanks.

What was the lecture about? I don't suppose there were any recordings?

>20y ago so the odds are low but not impossible (feynman's lectures are on youtube). just sad to think how many great lectures have been lost to time tho

> feynman's lectures are on youtube

Only a tiny handful. Feynman gave a guest lecture at our physics class at Caltech in the 70's on potato chip worlds. As far as I know, it only persists in my memory.

I sometimes wonder why I didn't buy a cheap cassette recorder and record a bunch of lectures from then. Probably because nobody else did, either.

care to put down some bullet points on your potato chip recollections on a blogpost? others who were there might chip in

> might chip in

Pun perhaps not intended, but good.

I had the opportunity to watch him lecture for a week, almost a decade ago.

I don't remember what it was about (maybe Catalan numbers?), but ten years later, I wish I'd been able to recall more.

Rest in peace.

Conway was a legend in the math department. Possibly because he actually lived there -- at one point he got kicked out of his house, and took the office opposite his as a bedroom. A few months later, an artist showed up to paint portraits of famous mathematicians around the border of the ceiling.

Apart from that, the login to his computer required calculating the correct day of week of 10 dates in the last 2000 years. I believe that the record was around 10 seconds. He showed me the algorithm (which isn't actually that hard), but he had a calculating ability that was truly impressive.

He also bet his salary on a series of backgammon games that were played in the common room -- he won, but just barely.

Apart from that, he'd sometimes grab an undergraduate and give them a very brief tutorial on cutting edge mathematics just so he could try to explain a new theorem or paper -- he could be amazingly generous.

On the other hand, he could be astoundingly mercurial -- there was a rumor that he used the stair method for grading, or that the grade was proportional to the length of the answer -- he loved math so much that he couldn't conceive of why anyone cared about their grade in his classes.

Amazingly beloved by everyone who came in contact with him.

It indeed isn't a particularly difficult algorithm. It's just modulo 7 arithmetic and some divisions combined with a table lookup. Martin Gardner of course covered it. I first encountered it in Shakuntala Devi's book Figuring: The Joy of Numbers, which has a slightly different lookup table. With practice, one can run it as the date is being given, a common lightning calculator trick for making things faster, and the lookup table becomes directly memorized. In practice, the algorithm is rarely applied outwith the past 400 years or even the past 100, for obvious reasons. Tweaking for the century is an afterthought in several accounts that I've read over the years.

There are at least two algorithms. The one you outline here feels more like the one I use (and, coincidentally, Art Benjamin[0][1][2] uses), whereas Conway used one of his own devising called the Doomsday Algorithm[3].

So you're right, it's not that hard, but be aware that you may not be thinking of the algorithm Conway used.

[0] https://en.wikipedia.org/wiki/Arthur_T._Benjamin

[1] https://math.hmc.edu/benjamin/

[2] https://www.ted.com/talks/arthur_benjamin_a_performance_of_m...

[3] https://en.wikipedia.org/wiki/Doomsday_rule

> Possibly because he actually lived there -- at one point he got kicked out of his house, and took the office opposite his as a bedroom.

I get a bit envious of these stories of American academics actually being able to live in their offices. In my experience in Central Europe, you can stay overnight in your office to work, but sleeping is forbidden, even if you are the head of your department. It is not uncommon for security to patrol the offices every night to ensure that no one is using that nice sofa in their office to get some sleep.

When I did my PhD there was another PhD student of Biology who lived for 3-4 months in the lab. That was in Central Europe btw. :) He had to move out of the dorm he lived in and then didn’t want to look for something new since rents were too high for his taste. After the aforementioned months the Prof told him to find somewhere to sleep than the labs cafeteria where we used to have a couch, so he found a new place eventually.

"Living" was a bit of a misnomer. The rumor was that he'd stopped opening his mail, and thus his wife got the house in the divorce by default. The second office had a fairly long couch that he slept on, but I'd imagine he showered at the gym, and it didn't look particularly home-like.

His office was always one of the more welcoming places -- he picked the one closest to the Common Room and the classrooms so he'd have more interaction with students. He also had all nature of toys, geometric models, puzzles, and games strewn around -- it was really a joy to be near him.

Here's my John Conway story:

I went to Canada/USA Mathcamp in 2009, which fell in the period when he would come for about a week, giving talks and just hanging out with all us kids. You might have lunch with him and he'd talk about his "Free Will Theorem", or the Doomsday Algorithm[1]. He would often play games with us in the afternoon. I remember seeing him play Phutball[2], a game of his own design, taking heavy handicaps. One afternoon, he challenged us to 3x3 Dots and Boxes. Each challenger "won" if they could win a single game against him in a match of 10. You got to choose each game whether you went first. We played for an hour or so, a crowd gathered around the piece of paper he was using, everyone offering suggestions and trying to figure it out. I think the 5th or 6th challenger finally managed to win.

[1] http://rudy.ca/doomsday.html

[2] https://en.wikipedia.org/wiki/Phutball

I got to be witness to the Dots & Boxes challenge in the mid-90s. He was less sure, only one of us got to play him.

I later put several hours in and figured out the guaranteed win and why it was so hard to find. But have since forgotten it.

Numberphile has a good video on it: https://www.youtube.com/watch?v=KboGyIilP6k

There were several videos that Numberphile did with Conway, including one where he talked about what problems he'd like to see before he died and his own mortality [0]. In particular he wanted to know why the Monster group [1] exists, what it's about, why it's there [2]. I don't know enough about it to know if progress was made toward that in the past few years since the video was made.

[0] https://www.youtube.com/watch?v=xOCe5HUObD4

[1] https://en.wikipedia.org/wiki/Monster_group

[2] https://youtu.be/xOCe5HUObD4?t=409

The Monster group is fascinating because we know it exists without quite knowing why it exists. There's a pattern that we can sense but it still escapes our understanding. There's just enough structure that you can imagine future generations someday saying, "Of course, of course."

TIL John Conway's son was once known as "the baby monster", and that Jupiter has a whole lot of elementary particles, but I can't quite grasp the rest of what I just read.


>What is... The Monster? By Richard E. Borcherds.

>When I was a graduate student, my supervisor John Conway would bring into the department his one year-old son, who was soon known as the baby monster. A more serious answer to the title question is that the monster is the largest of the (known) sporadic simple groups. Its name comes from its size: The number of elements is 8080, 17424, 79451, 28758, 86459, 90496, 17107, 57005, 75436, 80000, 00000 = 2^46 . 3^20 . 5^9 . 7^6 . 11^2 . 13^3 . 17 . 19 . 23 . 29 . 31 . 41 . 47 . 59 . 71, about equal to the number of elementary particles in the planet Jupiter.

That article is aimed at mathematicians. A high level summary is that there are two completely unrelated things, the Monster group and modular forms. (Groups are sets of symmetries. Modular functions are special functions of complex numbers. The related topic of modular forms come up in the proof of Fermat's last theorem.) These two things are obviously unrelated, so when someone spotted a numerical coincidence in some numbers that show up in each, people scoffed. (Conway is the one that nicknamed it "moonshine".)

It turns out it's completely true, and the proof uses a bunch of mathematical techniques that were developed when studying string theory for physics. The whole thing is an incredibly unlikely story.

> These two things are obviously unrelated

Skimming just quickly gives a different impression.

> It was clear to many people that this was just a mean- ingless coincidence; after all, if you have enough large integers from various areas of mathematics, then a few are going to be close just by chance, and John McKay was told that his observation was about as useful as looking at tea leaves. John Thompson took McKay’s observation further and ...

what follows is nothing to scoff at.

Finally, Borcherd's article concludes (2002, that was linked above):

> So the question “What is the monster?” now has several reasonable answers:

> ...

> It is a group of diagram automorphisms of the monster Lie algebra. Unfortunately none of these definitions is completely satisfactory. At the moment all con- structions of the algebraic structures above seem artificial; they are constructed as sums of two or more apparently unrelated spaces, and it takes a lot of effort to define the algebraic structure on the sum of these spaces and to check that the monster acts on the resulting structure. It is still an open problem to find a really simple and natural construction of the monster vertex algebra.

Which means, showing a natural relation should be outstanding?

It's an introduction to Monstrous Moonshine, an unexpected connection between the monster group M and modular functions, with applications in theoretical physics, see Wikipedia [0] for a summary.

[0] https://en.wikipedia.org/wiki/Monstrous_moonshine

He visited Australia several times in the 90's and I remember seeing him talk about wallpaper groups back then. One time he was explaining orbifolds [1] by folding up a piece of paper, and he somehow made a cone shape, and it somehow ended up on his head, and then he proceeded to march around like a crazy guy. It was hilarious.

In 2008 I was living in New York city and Conway gave a series of lectures at Princeton on quantum physics and the "free will" theorem [2]. I was able to take the train down to Princeton to see a couple of them, and it was awesome. He was a bit shaky at first because he had just had a health scare, but he soon got into the swing of things.

I would highly recommend the biography: "Genius At Play: The Curious Mind of John Horton Conway" by Siobhan Rob. It is a lot of fun!

[1] https://en.wikipedia.org/wiki/Orbifold_notation [2] https://arxiv.org/abs/quant-ph/0604079

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.

[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

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.”

[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

[4]: https://en.wikipedia.org/wiki/Conway_base_13_function

[5]: https://en.wikipedia.org/wiki/15_and_290_theorems

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.

[0] https://books.google.com/books/about/The_Triangle_Book.html?...

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.”

It is often remarked that I am rarely wrong.

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!).

I think many of us have indeed programmed a GoL at some point. I've repeatedly done that when learning new languages a decade ago.

May he rest in peace

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.

Have a look at Hashlife (eg via https://en.wikipedia.org/wiki/Hashlife) to see some exciting ways to compute GoL faster.

Agreed! The first time I learned about this algorithm, I was pretty mind blown :)

Yeah, I built a Game of Life way back when.

I remember him being kinda bummed about how Game of Life was the thing that made him famous.

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.

He came to terms with it ... see my comment here:


Speaking of Life, a few years back I ran across a photo of Conway confronting a different form of Life that made me laugh out loud:


Always enjoyed Knuth's book _Surreal Numbers_ on Conway's work. It's a very unusual math tutorial.

Thanks to winning ways my github repo is a graveyard of attempted dots and boxes opponents. I didn’t know Conway wrote it.

As a teen, I was obsessed with knot theory, and Conway's knot notation always felt like magic to me.

The notation works by counting the number of twists in a segment, and then looking for another twist directly connected to the previous twist, and so on.

This gives you a sequence of integers, one counting the number (and direction) of twists.

If the entire knot is made of twists connected this way, then the continued fraction you get from the sequence of numbers is a knot invariant!


Can two different knots have the same integer sequence?

No, they can't, since they are just representations of the knot diagram.

As for uniqueness, even "rational knots," the ones from the simplest of the fundamental polyhedra, have multiple fractions representing them.

I'm knot familiar with this one in particular, but a 'unique' knot invariant would be a very big deal. (It would then be a knot identifier...)


I have fond memories of going through reams of graph paper, manually simulating Conway's Game of Life.

This was my first exposure to cellular automata, and I loved to follow the evolution of gliders and other emergent phenomena. This was before the days that personal computer programs existed to do the simulation for you. It's so much more satisfying to do it by hand.

Later, I was fascinated by Conway's chained arrow notation[1], which is used to concisely represent unimaginably gigantic numbers.

[1] - https://en.wikipedia.org/wiki/Conway_chained_arrow_notation

Richard Guy, the discoverer of the glider in Conway's Game of Life, also passed away last month.

In 2017, Richard gave a talk for the 50th Anniversary of the University of Calgary (and his 100th birthday). Much of it was recounting stories of his past in response to questions from the audience. When asked about the glider, he told us how Conway came up with the Game of Life and invited a number of colleagues to help investigate its implications. They spent the next few days just simulating the Game of Life by hand on graph paper. Richard happened to come across it from one of his initial conditions.

Today you could discover the glider in minutes by playing with an interactive simulation. It's interesting how much more effort it used to be. I suppose, though, that you'd build better intuition and understanding doing it by hand.

You'd get more intuition per experiment ran. But don't underestimate the power of quantity.

This is a terrible loss, and seeing the comments here makes me firmly agree with sentiment I've heard a number of times recently: it would be wonderful if culturally, it became more typical to tell our teachers/mentors/idols what they mean to us before they die, instead of saving that outpouring for after their death.


It appears he died by COVID-19:


I went through some of his work in detail while in college. While a mathematician, he clearly had the complexity-compression ability of a top-tier theoretical physicist. A great loss indeed.

I went to math camp as a kid in middle school. John Conway was one of the lecturers. He was clearly a brilliant man, slightly eccentric in the way that most great mathematicians are. But he was humble enough to devote several days of his time to hangout with a bunch of nerdy kids and teach us about ordinals, knot theory, and I believe Ramsey numbers. Really nice of him to do that for what I'm sure was pennies if it paid at all.

I was fortunate enough to attend a maths talk by John Horton Conway about 8 years ago towards the start of my PhD. I was working on things related to the algebraic closure of \F_2, and Conway had a neat observation that all ordinals smaller that \omega^\omega^\omega formed a field that was isomorphic to the closure. So it felt timely.

But what I took from the talk is how casually he'd make references to deep personal life experiences throughout his mathematics. He referenced his divorces, suicide attempts, et cetera. All very casually, like it was no big deal. I was an angsty teenager and continued to be angsty in my early 20s. It helped me realize my issues were no big deal.

RIP John Conway.

How sad :-( Game of life was one of the first things I've coded in the early 80s I was really proud of as a kid (highly optimized Z80 maschine code to make it as fast as possible per frame).

I was hugely inspired by the concept, especially by gliders. I thought Conway to be a Genius. He might have gone but the Game of Life and the inspiration it brings will always be with us.

I don't think there's a better example of complex behavior emerging from simple rules. He was truly a genius.

Yes, that was so mind blowing to me as a kid and still is decades later.

So, this may not actually have happened.

The confusing thing is that, today, John Sharp, also an elderly recreation mathematician, also died.

Currently the only source is the tweet above. We are not sure whether Colm has made a mistake. He did know John Horton Conway, but some people are mistaking his scientific american article, and the later guardian article, for an obit...

Terrible news if JHC is dead, and also terrible that John Sharp is dead. If not... will be weird for him waking up tomorrow to let people know that reports of his death are greatly exaggerated...

Wikipedia has a few sources, may just be them all echoing from the same source, but it seems that a close friend is the source of one of the articles.



A valid concern, and sad news, but Colm's latest tweet isn't consistent with mistaken identity.


I'm hearing it's a mistake (I'm signing up just to share this, as a former assistant of his). But what I'm hearing could be wrong as well... in short, I would await an official press release from Princeton.

I've spent the last year or two obsessed with Conway operators ( https://en.wikipedia.org/wiki/Conway_polyhedron_notation ): https://github.com/IxxyXR/Polyhydra/

and I was planning to get in touch just to say hello and ask him a few geometry questions. If you ever have a thought like that about someone in their 80s then just do go ahead and do it.

The Game of Life came with the example cassette of software for my first computer so he's been with me from the beginning of my journey into algorithms and software.

RIP professor Conway.

Thanks for kicking our butts in Linear Algebra and for all your strange but endearing quirks, like "if you see a John Conway without a bike around his neck, that is not the real John Conway" or throwing your shoe at the window to wake us up in class.

Do we have official confirmation?

Someone on this Twitter thread says it was the coronavirus. Heartbroken.

Wikipedia page still not updated http://archive.is/NieYz

maybe confusion? let's hope

Looks like there was an is/was edit war and the page is now locked pending some sort of confirmation

Yup, I locked it pending the outcome of the talk page discussion; it would be nice to have a non-twitter source to point to.

> edit war

probably, duckduckgo preview even showed "John Conway war a British" a few seconds ago. Aptly typoed

Wikipedia is not the place for "truth", it's only an extremely useful machine that summarizes information from secondary sources. It can only repeat information from trusted, secondary sources (there are exceptions to primary sources, but only when the source is universally considered trusted, which is not the case here). Even if the information is true, if it's not published by a trusted secondary source elsewhere, it cannot claim that. Similarly, the claims by Wikipedia cannot be cited as reliable information, but the sources of the claims can.

So Wikipedia, by its policies, cannot be updated until there's sufficient press coverage (Although verification != press coverage, and there are legitimate criticisms that say verification on Wikipedia via popular press coverage is often given an undue weight, on the other hand reliable professional literature is undercited, which can compromise Wikipedia's integrity, but it's another story). It's frustrating that many people fail to grasp how Wikipedia works.

Is there any confirmation of this? It appears absolutely nowhere else on the web.

I trust Colin's explanation of the source. It would be awful to have fed a mistake, but wonderful if the news turned out not to be true. People are posting such good comments about Conway that I wouldn't want to bury the thread.

Best case scenario, we change the title to "John Conway has not died" and continue to celebrate him.

Mulcahy writes of formal confirmation[0]:

> Not yet. Three of the people who told me heard it from his ex wife Diana. Two knew it was imminent since he fell ill on Wednesday.


> More emails from insiders are arriving regularly. One from a student of his. Etc.


> From 5 of his close associates ...

[0] https://twitter.com/CardColm/status/1249082939423559680

[1] https://twitter.com/CardColm/status/1249082390854729730

[2] https://twitter.com/CardColm/status/1249082119567138819

================================= =================================

Added in edit:

I've now had it confirmed in personal correspondence, but before it can be announced officially it needs to go through the Dean's Office, and it's a Holiday Weekend, so that won't be quick.

It's reasonable for people to be sceptical, I don't have a problem with that.

thanks for the update

Fair enough :)

The Princeton Department of Mathematics page doesn't seem to have anything about his passing. Edit: Of course it's the weekend; I should have realized that there will probably not be anything on that page before Monday.


It's Easter weekend, there probably wouldn't be anything before Tuesday.

I've commented elsewhere[0] on the connectedness and reliability of Colm, but people can always wait for confirmation via other sources before they choose to believe it.

[0] https://news.ycombinator.com/item?id=22843577

Yes, I wouldn't necessarily expect the web site to be updated immediately, but I would think there would be a tweet from https://twitter.com/princeton sometime today at least.

The first who tweeted about this seems to be a french mathematician named Martin Andler : https://twitter.com/MartinAndler/status/1249021279660683265. Also this tweet by the french Science Magazine "La Recherche" : https://twitter.com/maglarecherche/status/124903595451977318...

Mulcahy is a pretty reliable source, and that's definitely his twitter. In lieu of official confirmation, for the time being it seems like this is about as reliable as anybody could hope for.

Don't see it here, so dropping in one of my fav Conway things... Sprouts[0]. A pen and paper game that is both fun and full of combinatorially interesting properties.

What a legend.

[0]: https://en.wikipedia.org/wiki/Sprouts_(game)

When I was 15 years old, I coded a Game of Life (with TurboPascal) and spent days playing with it, not only by activating cells, but also changing the automaton rules.

Eight years later, during my PhD, I had to pack discs on Riemannian manifolds (AKA how to place dictators on a surface so that they are as far as possible from each other). In the top tier of my bibliography, John Conway was there again. At first, I couldn't believe it it was the same person.

Numberphile has some great interviews with him, very interesting man...

Life, Death, and the Monster: https://www.youtube.com/watch?v=xOCe5HUObD4

Look-and-say Numbers: https://www.youtube.com/watch?v=ea7lJkEhytA

I often rewatch the first video, not just for math, game-of-life, and John Conway, but also ASMR, when he's (spoiler alert) ...

eating the "dead" almonds.

To Cellebrate John Conway's Life, I'll repost this description of Rudy Rucker's cellular automata rule "ECOLIBRA", which combines "Brian's Brain" together with "AntiLife" (the 1's-complement of life), so that the void of AntiLife stimulates Brain, and the void of Brain stimulates AntiLife.


>Here's another ecology oriented cellular automata rule called ECOLIBRA, a cross between LIFE, BRAIN (and optionally ANNEAL on the bit plane that determines water/land), from John Walker's and Rudy Rucker's classic CelLab (which Autodesk originally published as a PC application, but John Walker has ported to JavaScript):



>This rule is a cross between Life and Brain. The basic idea is that the cells are divided between dark “sea” cells and light “land” cells. We run Brain in the sea, and on land we run not Life but AntiLife. All the land cells are normally firing cells, and the presence of an active AntiLife cell is signaled by having a land cell which is not firing. Full details on EcoLiBra are in the Cellular Automata Theory chapter.

>The name EcoLiBra suggests 1) an ecology of Life and Brain, 2) a balanced situation (equilibrium), and 3) the human intestinal bacteria Escherichia coli, known as E. coli for short. The third connection is perhaps a bit unsavory, but remember that E. coli cells are in fact the favorite “guinea pigs” for present day gene splicing experiments. As one of the goals of CelLab is to promote the development of artificial life, the designer gene connection is entirely appropriate. I've given EcoLiBra a nice, symmetric start pattern, but it also does fine if you use the Bit Plane Editor to randomize all bit planes.


>The EcoLiBra rule, consisting of Brain and AntiLife, each turned on by the red/black boundary.

>But when the sea runs Brain and the land runs Life, the situation is no longer symmetrical. The pervasive presence of Brain's refractory state makes it less likely for a sea cell to have seven firing neighbors and be turned into a land cell. Unless we change the transition rules, the land will always melt away. So to give land a fighting chance, I now say that a sea cell becomes land if it has seven or six firing neighbors. Also I use better colors: Black, blue, and green for Brain; red and yellow for AntiLife.

Here is a variant I call "ECO" that runs "ANNEAL" on the water/land plane, and (for giggles) a heat diffusion in the upper left-over planes.


[More discussion and code in the original post...]


I spent my early programming days in high school build John’s GOL in Macromedia Flash. This is how I got into programming.

Thank you John for inspiring mankind for many generations to come.

Like many others, this is one of the things I programmed out as a teenager, having tired of doing it by hand. It taught me quite a lot and was fascinating besides. Later, when I went into physics, the "speed of light" made sense already as a kind of propagation of disruption and/or information transfer.

I fire a glider gun into the sky.

The algorithms for simulating Life are more interesting than you might think, even before the advent of GPUs.


He was a great mathematician.

I’m experiencing the Baader-Meinhof phenomenon, because a few hours ago I was reading about Conway polynomials:

“While there is a unique finite field of order p^n up to isomorphism, the representation of the field elements depends on the choice of the irreducible polynomial. The Conway polynomial is a way of standardizing this choice.”


Of course, Conway was a serious mathematician who was slightly vexed that the thing he might be most remembered for is what he considered a cast-off game that he dabbled with in the late 1960s.

Conway talked about determinism (and free will) from a mathematical and scientific perspective in interviews and lectures. I found what he had to say very interesting - I don't know if he came up with all the ideas he talked about, but I had certainly never heard of many of them before I heard him talk about them.

Based on your comment, I found these lecture series "The Free Will Lectures - John Conway [2009]" = https://www.youtube.com/playlist?list=PLhsb6tmzSpixUGjmJq6g9... and saving to watch later.

>>Conway talked about determinism (and free will)... >>>Based on your comment, I found these...

The math is over my head but this really piqued my curiosity.

I watched the first video yesterday and am looking forward to going through them all. He really is quite interesting.

I'm sure I'll take in one of his other lectures afterwards, but I generally have a hard time following those so maybe these will help ease me into that some. His opening bit about quantum physics might have of cracked open that door a little for me.

I was good at physics math in high school and was at a pretty hardcore STEM highschool, but we never got into quantum physics somehow. I went to economics studies.

So for me, my worldview pretty much stopped at the whole mechanistic worldview. Tbh any times I read something philosophical/spiritual mentioning quantum physics, I was dismissing it as quantum woo.

I also believed in the whole lack of free will thing and was believing it I guess till very recently. I have to say it made my life a lot worse in retrospect.

I guess this is one of the toxic memes that take away agency from people.

This is amazing. You can start with the last lecture if you are short on time (and probably like me more interested in implications and not strong in math to follow the rest).

A great loss. One of my greatest inspriations to train as a mathematician. I'm so sad I never got meet him.

I did get to see one of his lectures in Australia in the 90s. I remember him joking that he has a recurring nightmare that he would meet a man in the street who could draw an icosahedron faster than him. I always hoped that one day I'd get the opportunity to take up that challenge.

I know he resented to be known for the game of life, because of all the other wonderful works, but it will forever standout in our memories of him because of profound influence it had on us.

> I know he resented to be known for the game of life ...

I talked with him about that. There was a period where he got very angry if someone wanted to talk to him about it, because to him it wasn't the most interesting thing, and most people didn't get the point anyway.

Later in life he mellowed a bit, and he certainly talked about it with me without rancour.

Life is great, because it's so easy to explain and understand. And it has a story, a metaphor that connects it with humanity, that makes it more interesting and relatable to more people than the pure beautiful mathematics are.

So if John Conway's Life gets you interested in cellular automata, then continue on to the After-Life!

As cellular automata go, Life is just another counting rule (depending just on the count of its neighbors, not their position), which themselves are a very limited subset of all possibilities.

You can make up your own rules, and combine rules together in different ways, and it helps to understand how other rules work, and whether they were "designed" or "discovered".

There are many more wildly different, interesting, and beautiful rules, many even with their own stories and metaphors that help understand them, like how the spirals of BZ reactions are like two-way chemical reactions, slime molds, and reefs of tube worms:



>You also get beautiful spirals from Belousov–Zhabotinsky reactions. They can be simulated by cellular automata, and are manifested in nature by chemical reactions, slime molds, and reefs of tube worms!

>I don't think they're Turing complete or self replicating per se, but you can start them on a random configuration, and they will form several spiraling "attractors" around oscillating cores ("nucleation"), that send out concentric spiraling waves, which meet waves from other attractors (or boundaries in the environment like a maze) and reinforce or cancel each other out, and also they can solve mazes and climb gradients and find food! (Plus, slime molds are not only beautiful, but make great pets, and they're easy to care for!)

[more at: https://news.ycombinator.com/item?id=22737916 ]

He was my mathematical hero. I never had the opportunity or privilege to be a student of his but I imagine it must have been extraordinary. I really enjoyed his books, ONAG, his work on groups and his contributions to the sphere packing problem. Most of all his playful way of writing and teaching. A true performer.

I will miss him.

Jesus, I just realized I was currently reading a paper by Conway. (The paper is Benson-Conway, "Diagrams for Modular Lattices". I didn't really think about whether it was that Conway. It's pretty far from his normal research areas. What a macabre coincidence.

I had dinner with John Conway in 2013. I was just leaving Princeton as a psychic and a mutual friend set it up as my goodbye party.

He was quite extraordinary to speak to. We talked about a whole host of things, and he signed his book for me. I'm very sorry to hear of his passing.

Very sad news indeed. The Guardian newspaper has reported the death due to coronavirus in their live news feed. Their source is a tweet by a Sam Wang.

I can still remember entering the Game of Life program from a book into my ZX81 when I was a young teenager.


There's thin black banner at the top of HN at the moment. Is that in honor of John Conway?


> Rumor has it that extensive interactions with a host of mathematical luminaries are covered, [...] and the French didactic auteur Nicolas Bourbaki.

Wait, I though Bourbaki was a collaborative (a group of people), not an actual person: https://en.wikipedia.org/wiki/Nicolas_Bourbaki

That article was published on April Fool's day.

Before the dot com crash we made a t-shirt with a tribute to Conway: http://swain.webframe.org/tshirts/conway_life_zoom_tshirt.jp... and I continue to use still life configurations in some of my profiles.

I did t meet Conway, nor see him lecture, nor am I a mathematician. When I was young I read about the Conway Game of Life and it sparked a long fascination with alife. I spent a lot of time on a old laptop, playing about with dot, ants, rules, genetic algorithms, mostly in qbasic. Good times.

This compelled me to write a quick Game of Life implementation. This is nearly 40 Lines of Code in Classic BASIC https://repl.it/@amasad/conways-game-of-life

RIP John Conway.

The April Fool's piece from a few years ago mentions that there is a biography, which was published as "Genius At Play: The Curious Mind of John Horton Conway" by Siobhan Roberts. I'm sure that would be a good read.

The Game of Life is responsible for getting me into computing back in the early 80s. Spent a summer implementing classifier systems at VA Tech in the 90s and never had so much fun. A great mind that will be greatly missed.

Cellular Automata got me into computing a few years ago - it's amazing how the Game of Life and other CA's are Turing Complete. So many people will miss him.

Sad to hear this. This motivated me to dig up some old code, perhaps someone here will appreciate it. Maybe you can find a new rule set to Conway's Game of Life that produces undiscovered patterns.

[1] https://hoten.cc/blog/life/

[2] https://connorjclark.github.io/dart-life/#life

Here's my in memoriam exercise in BASIC for the PET 2001 (running in emulation): https://www.masswerk.at/pet/?run=life.txt

I first discovered Game of Life during high school, and it got me fascinated about different cellular automata and writing software implementations of them.

RIP John Conway.

On Numbers and Games is one of the most entertaining mathematical books I've ever read. We've lost a genius in the true sense of the word.

This is worthy of a black bar. John Conway was a legend.

I know that he was annoyed by the association with the game of life, but I still have to credit it with my fascination with cellular automata. For the past ten years, I have used GOL as my “Hello World” for learning a new language.

RIP John.

The twitter account oogle search doesnt back this up - this may be true but in this day and age WTF people why is this number one?

See my comment here:


It's reasonable to be sceptical, but it's also reasonable to research the existing source and understand that it's reliable.

I imagine that there are many reasons.

That said, please note how the YC name and Conway are related. At a minimum, this might provide some insight.

You might be thinking of a different Conway ... John Horton Conway has no association with Y-Combinator that I know of.

I'd be happy to learn otherwise.


The thread on Twitter says yes but I'm not sure that's a reliable source.

Yeah, does anyone have a news source for this besides the one twitter thread? Wikipedia wants to know.

Colm is extremely well-connected in recreational mathematical circles. He's on the board of the G4G committee, and is an active mathematician and populariser of mathematics. It was he who first broke the news of Richard Guy's passing.

Anything he says is reliable, but by all means wait for other confirmation.

WRT wikipedia, I have a story about the Richard Guy page, but that's not a story for here. Another time.

HN now gets about 5 million visitors a month. In case it needs to be said for some of those folks, the OP -- ColinWright -- is also rather well connected from what I gather and part of that circle (of recreational mathematics, etc).


So I imagine the mods granted the black bar in part on the strength of who posted it. They don't do so lightly and have been known to put a hold on threads in the past to wait for confirmation. They haven't chosen to do so this time and there is likely a compelling reason for that.

(Example of HN waiting for confirmation: https://news.ycombinator.com/item?id=17939518 ; https://news.ycombinator.com/item?id=17889547)

There are a lot more Twitter threads now, including this which is apparently from an organization he is involved with:


Apparently so. Confirmed by his biographer in this item:


Looks like it https://twitter.com/SamWangPhD/status/1249132655737790464

(I know I'm curious to know that too - but I don't get why we do care... the result is the same?!)

As for me, it deepens more than anything the sense of horror and emergency of this viral threat. One of my scientific idols is dead of it. That helps me, and probably many others, to get even more aware of the need to keep safe.

RIP John! here a small tribute i created while thinking of you! Was inspired by the idea of your game of life but modded for corona specific use ... note: this is just a game.....


My UG students and I played the Game of Life in class during Week 7 this spring semester....that was about 5 weeks ago. We have played it for so many years during the ABM lecture...I never had the good fortune to meet him, but many years of students know who he is and of his accomplishments..:)

Stay safe, all.

Another famous J.C. - but one that brought more joy to my life with his Winning Ways than the other one did. Rest in peace, John. -- https://www.quora.com/profile/Bruno-Curfs

https://en.wikipedia.org/wiki/FRACperhaps a lesser known contribution

Very likely you meant https://en.wikipedia.org/wiki/FRACTRAN. Agree this is a clever beast.

Game of Life was the first computer program I wrote exactly 50 years while in high school. It was in Dartmouth BASIC on a teletype to PDP 8(?) at some local college.

I remember 50 years ago my dad worked for TRW. He got a call after dinner. And for some reason took me with him to work. I know now that his NASTRAN job had died. But as a 7 year old had no idea.

I just remember walking in to the deserted windowless TRW building and my dad flipping on the IBM vector display, running a batch of cards and suddenly the Game of Life on the display. I was mesmerized.

We have played the game of life in my UG class for years during the ABM lecture....the last time was about 5 weeks ago. The students always loved it....:(

I bought John Conway's Game of Life book that came with a 5 1/4 floppy before I even had a computer.

May he rest in peace, and may his place be among the great mathematicians of all time

RIP John Conway.

I think my interest on digital organism sparked by his famous Game of Life.


The mathematical world has truly lost a legend to the game of life.

And another person with the Erdős-Number 1 passed away :(

Today truly is a doomsday for the old giant.

Rest in peace.

Inspired me to write https://github.com/nixpulvis/doomsday FWIW.

Game of life, ended by COVID-19. Wow.

May his memory be a blessing.

So sad to see Conway’s Game of Life come to an end.

Bad definition of life, which has a beginning and an end unlike a Turing machine, by von Neumann.

Rest in peace.



RIP Conway

The twitter account doesn't back this up with a source - the OP here doesn't back this up this up with a source - my quick Google search doen't back this up, this may be true, but in this day and age WTF people? why is this number one without any verification?

Yes, the source is not citable by Wikipedia's standard, but it appears that Mulcahy is considered an established personality in the recreational mathematics community, and his source was private communication from the close associates of John Conway, which by itself is backed up by Colin Wright, an established personality on Hacker News. [0][1] So it's certain to say the information is true.

By the way, I once said that Twitter is now the center of gravity of the web these days, and someone didn't believe me and argued against it with some user statistics, which missed the point. This is another example on how Twitter is the center of gravity, it is, in the sense of its network effect - that it has a group of active and influential people, which makes it the place where the latest news and rumors break out. Not different from the early blogosphere, the Usenet, or even Hacker News posts about Silicon Valley.

[0] https://news.ycombinator.com/item?id=22843577

[1] https://news.ycombinator.com/item?id=22844444

It’s a little meta given we’re on HN, but I’d trust ColinWright FWIW.

It's been reported in the Guardian newspaper in their live Coronavirus feed. Their source is a tweet by someone by the name of Sam Wang.

This is very sad news. I can still remember typing into my ZX81 the game of life program from a book as a young teenager.

I agree, this should be verified, Mulcahy (https://twitter.com/CardColm) is wearing a jester hat, it may very well be playing a joke on us all.

Worthy of HN border acknowledgment, please.

Second this, very much so. I’ve emailed the mods.

EDIT: I typo’d the email address but we got a black bar so.

I had always wondered about that. Is there a full collection of info about this site? There always seem to be random things like a black bar without even a comment in code or a page like https://news.ycombinator.com/topcolors that I'm not even sure how to find other than I saw someone else mention it once.

Treat the site a little like a text adventure, akin to Colossal Cave Adventure or other text-based interactive fiction. HN is a world to explore, with items to uncover and treasures to discover.

There are clues ...

This is extremely off-topic, but it's a collapsed subthread already, so I think it's fine:

Black bar = honoring the dead.

/topcolors = list of colors that people have set their top bar to be.

Reportedly it was due to COVID-19. Obviously, then, he must have had too many close neighbors. Four or more, to be precise.

Interesting that, at the time of commenting, his Wikipedia page hasn't been updated with his death yet. https://en.wikipedia.org/wiki/John_Horton_Conway

Peace, and rest.

Never mind! It's not that interesting, what with the announcements at the top of the page explaining why the page is locked for editing.

Wow, I didn't realize he was still alive

"One of the most unique mathematicians and human beings who ever lived."

This statement makes no sense and seems like a rather shallow, facile eulogy for such a complex person.

This eulogy makes more sense and rings true:

"Conway was arguably an extreme point in the convex hull of all mathematicians. He will very much be missed." - Terence Tao

Source: https://terrytao.wordpress.com/2020/04/12/john-conway/

The game of life has catched on him

Coronavirus death

Good night, sweet prince

Oh no. Rest in peace John.

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