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« [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.
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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…

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