
Decades-Old Graph Problem Yields to Amateur Mathematician - digital55
https://www.quantamagazine.org/decades-old-graph-problem-yields-to-amateur-mathematician-20180417/
======
georgewsinger
This guy has a background in computer science, but taught himself biology to
spearhead the regenerative medicine movement. If I'm not mistaken, he
published a book in biology with no formal credentials (16 years after
receiving his BA in computer science), after which Cambridge honored him with
a PhD in the subject.

He's also Thiel backed.

~~~
dabockster
> He's also Thiel backed.

Is having Thiel's association a positive thing still? Serious question.

~~~
toren
I would assume so. I couldn't care less about his political affiliations

~~~
billhendricksjr
His political affiliations are in conflict with his desire for long life,
given who has the nuclear football.

I don’t care, I’m an atheist with no kids who’d be bored out of my mind before
I hit 300 years old, much less 1,000.

~~~
derefr
If you're afraid of the nuclear football, isn't "standing right beside the
person holding it" the _best_ place to be, if you hope to have any shred of
control over whether it gets dropped?

~~~
billhendricksjr
If you think you can convince him not to pull the trigger. I’d rather be
standing at ground zero. Dying of radiation poisoning is an experience I don’t
need to see to believe.

My father in law was at the bikini islands for the test runs (died of cancer),
my great uncle was on the ground in Japan shorty after they dropped Hiroshima
(died of cancer), and great uncle’s kids has Japanese rifles he recovered from
sites that _glowed in the dark_ as late as the mid 70s.

------
IB885588
Aubrey de Grey is chief science officer and co-founder at the SENS Research
Foundation, which is the only charity that I personally support because I
think it has small resources compared to the potential good it could do to
increase healthy life and reduce human suffering.

[http://www.SENS.org](http://www.SENS.org)

~~~
iak8god
Here's some info pulled right from
[https://www.againstmalaria.com/](https://www.againstmalaria.com/):

* Half a million people die each year and 400 million fall ill [with malaria]

* 70% of them are children under 5

* #1 killer of pregnant women

* Malaria is preventable

Malaria nets cost $2. Antimalarial drugs are dirt cheap in the developing
world. If you want to impact human suffering and increase human health, this
is a good place to start. Not with trying to extend the long and already
pleasant lives of rich people in the West.

~~~
natalyarostova
That assumes your goal is to maximize utility with all humans as
interchangeable. On the other hand, I'm more interested in my own life and
longevity than people with malaria, as a result I'm more interested in this
type of work.

It's also, in a sense, an unfair argument. You could say the same thing about
any other startup. "Oh your goal is to create some new app/service/software?
Why not instead focus your efforts on preventing malaria?" The fact that this
startup is focused on longevity should not make it more deserving of your
above criticism.

~~~
asfgionio
This is how most people work. They value their own lives and their own
happiness over that of others. They will gladly buy their luxuries and let
dozens of people die as long as they don't have to see them suffer. We all
know this.

Just don't fool yourself. The reason we value our own happiness over the lives
of others is because we are weak. That's something we have to live with, but
it doesn't make it good.

>You could say the same thing about any other startup.

And I do!

~~~
natalyarostova
I don't know the answer to that. Am I weak? Is it wrong that I'm on a vacation
right now, when I could have donated that money instead? Some EA say just
donate 10% or so of your money and don't feel bad, which is a wonderful social
convention, but it is just a convention.

If you say the same about other startups, then at least you're being
consistent, and it's the inconsistency that irks me.

I don't know if I'm weak or if I should be comfortable with my selfishness. I
donate, but not as much as I could. I'm not sure I'll ever know the answer. I
find that wrestling with the question, at least, prevents me from going down
the path of buying luxury goods and signalling, so I guess it's somewhat
useful.

------
moomin
Graph Theory, unlike number theory, is a strangely shallow subject. By this I
mean that a lot of the results don’t require a large number of previous
results (there’s definitely some).

Compare this to number theory, where every interesting extant problem appears
to require ten years study.

(I realise people may infer a value judgement from shallow/deep, but none is
intended.)

~~~
daniel-levin
>> Compare this to number theory, where every interesting extant problem
appears to require ten years study.

I don't often come here to comment but as someone in progress on an original
research masters in number theory I can say this is utter bullshit. I assume
your 'interesting' qualification (somehow) excludes obvious candidates like
Landau's problems [0]. Some examples. I was taught about the ABC conjecture as
an undergrad. You can easily teach the Brun sieve [1] method of working out
that the sum of the reciprocal of the twin primes converges. Novel solutions
to Diophantine problems are sometimes accessible to undergrads. Richard K. Guy
wrote a whole book on unsolved problems in NT, some of which have been solved
using undergraduate number theory and someone's upper bound you can just use
(as easy as apt-get installing this_dope_bound). You can start reading papers
without a PhD, never mind ten years of study. I think it's possible to get an
utterly unrepresentative sample of either field by only sticking to
"elementary" results. There are some extraordinarily subtle results in graph
theory! Conversely, you can find NT problems amenable to elementary techniques
[2].

[0]
[https://en.wikipedia.org/wiki/Landau%27s_problems](https://en.wikipedia.org/wiki/Landau%27s_problems)

[1]
[https://en.wikipedia.org/wiki/Brun%27s_theorem](https://en.wikipedia.org/wiki/Brun%27s_theorem)

[2]
[https://en.wikipedia.org/wiki/Quadratic_reciprocity](https://en.wikipedia.org/wiki/Quadratic_reciprocity)

~~~
moomin
I’ll defer to your superior experience here. Only done fairly introductory
number theory and graph theory stuff. That was just the impression I got from
what I’d studied.

------
simulate
The discovery was made by Aubrey de Grey, the same person who believes that
humans will eventually live past 1,000. Weird!

> [de Grey] found his way to the chromatic number of the plane problem through
> a board game. Decades ago, de Grey was a competitive Othello player, and he
> fell in with some mathematicians who were also enthusiasts of the game. They
> introduced him to graph theory, and he comes back to it now and then.
> “Occasionally, when I need a rest from my real job, I’ll think about math,”
> he said. Over Christmas last year, he had a chance to do that.

~~~
zitterbewegung
Recreational math / CS is so much fun . I usually try thinking of knot theory.
Haven’t really discovered anything yet but it’s still fun. So far the best
question I have asked is
[https://cstheory.stackexchange.com/questions/32292/knot-
reco...](https://cstheory.stackexchange.com/questions/32292/knot-recognition-
as-a-proof-of-work-system) .

------
sajid
Interesting tidbit, there was a bug in the computer assisted part of the proof
(now fixed):

"Many thanks to Brendan McKay and Gordon Royle for letting me know overnight
that they had successfully 4-coloured my 1567er; as a result I found a bug in
the part of my code that implements the relaxation described in section 5.4
and now it agrees. "

Source: [https://gilkalai.wordpress.com/2018/04/10/aubrey-de-grey-
the...](https://gilkalai.wordpress.com/2018/04/10/aubrey-de-grey-the-
chromatic-number-of-the-plane-is-at-least-5/#comment-40108)

------
ndr
Aubrey de Grey is much more than just an Amateur Mathematician, I highly
recommend Rob Reid's podcast episode with him: [https://after-
on.com/episodes/020](https://after-on.com/episodes/020)

~~~
spuz
This was great, thanks.

------
vladislav
In my experience, being an amateur mathematician is more fun that doing it
professionally, and potentially just as productive. You don't get nearly as
much time for math, so you make the most of it and work only on the most
interesting problems as opposed to just writing another paper. There's no time
for beating your head against the wall, so you just do it when you're
inspired, which is how problems get solved anyway.

~~~
hermitdev
I think for a large number of people, myself included, the "Eureka!" moment
often occurs when you're least focused on the problem at hand. I remember in
college, studying EE, I was struggling to make sense of how a flip-flop worked
(the basis of a register). My ah-ha moment was literally in the shower.

~~~
8bitsrule
For more on this subject, see the 1945 essay by French mathematician Jacques
Hadamard, _An Essay on the Psychology of Invention in the Mathematical Field_.
[https://archive.org/details/eassayonthepsych006281mbp](https://archive.org/details/eassayonthepsych006281mbp)

~~~
ctchocula
Thank you for sharing. One thing that impressed me about Hamming's essay on
how to produce world-class research [1] is that it suggests a necessary, but
not sufficient prerequisite is to spend your waking life thinking hard about
some problem. This is necessary in order to provoke the unconscious mind into
doing the heavy-lifting required for a "Eureka!" moment, so I was pleasantly
surprised when Hadamard's book has a chapter titled "The Unconscious and
Discovery". It amazed me that even in the modern world we do not understand
the processes that led to these breakthroughs, so we can only leave them in
the realm of the otherworldly and the mystical.

[1]
[http://www.cs.virginia.edu/~robins/YouAndYourResearch.html](http://www.cs.virginia.edu/~robins/YouAndYourResearch.html)

~~~
8bitsrule
Another example: Kekule 'said that he had discovered the ring shape of the
benzene molecule after having a reverie or day-dream of a snake seizing its
own tail.'

[https://en.wikipedia.org/wiki/August_Kekul%C3%A9#Kekul%C3%A9...](https://en.wikipedia.org/wiki/August_Kekul%C3%A9#Kekul%C3%A9%27s_dream)

Musicians commonly report waking up with song ideas fully formed. We shouldn't
be too surprised, really; the complex sentences out of our mouths (more often
than not) arrive without any conscious thinking. Jung said that our egos are
like planets orbiting a Sun they're unaware of.

~~~
mygo
where do people have these discussions and can I join? I wake up almost every
morning with music in my head from the dream that is (more often than not)
original, and IMO sounded like any hit on the radio.

And then within a few minutes I quickly forget the music. And there’s no way
to remember it because it’s not anything that I can just find and listen to.

------
gowld
The paper has beautiful illustrations.
[https://arxiv.org/pdf/1804.02385.pdf](https://arxiv.org/pdf/1804.02385.pdf)

Animations showing how the larger graphs are built from smaller graphs would
be amazing and illustrative for mortal non-mathematical-geniuses.

------
gowld
[Edit: because the drawing has unit edges. My mistake]

Why is the Moser Spindle drawn to make it look non-planar, when it obviously
is planar? The drawing obscures the point of the Moser Spindle, which is how
to construct a 4-color graph from 2 simple 3-color graphs.

It's also confusingly colored to make it not clear why it requires 4 colors

[https://d2r55xnwy6nx47.cloudfront.net/uploads/2018/04/Chroma...](https://d2r55xnwy6nx47.cloudfront.net/uploads/2018/04/ChromaticNumber_560Inline.jpg)

Better:
[https://en.wikipedia.org/wiki/Moser_spindle#Application_to_t...](https://en.wikipedia.org/wiki/Moser_spindle#Application_to_the_Hadwiger%E2%80%93Nelson_problem)

~~~
topynate
You can embed the graph of the Moser spindle into the Euclidean plane without
its edges crossing, but not in such a way that each edge is straight and of
unit length.

------
wwwtyro
If you haven't watched an Aubrey de Grey talk, you owe it to yourself to give
the man a listen. Beyond the admittedly interesting topic, he's genuinely
entertaining.

------
SirHound
Better headline would be "Decades-old Graph Problem Yields to Amateur
Mathematician and Straight-Up Genius Aubrey de Fucking Grey"

------
21
Is anyone else disturbed by the fact that the header image is incorrect? In
that the distances between vertices are not all equal. See for example the
blue node just beneath the outermost red node on the left side.

~~~
sowbug
If you mean the blue node that's connected to the yellow node beneath it, I
think it's actually connected to the yellow node beneath that one (the one
that is distance 1 from the blue node :) ), and the edge happens to travel
very close to the closer yellow node so that it looks like it intersects it.

If those three nodes (blue, yellow, yellow) were in fact connected by short
edges, then another problem would be that the two yellow nodes were connected,
which they couldn't be by the constraints of the original problem.

------
chubot
Wow, impressive. I had heard some disparaging comments about de Gray, kind of
like you hear disparaging comments about Kurzweil (which I mostly don't agree
with). For some people, there appears to be a fundamental aversion to their
ideas which goes beyond mere disagreement.

I don't know much about de Gray, but this piques my interest in what else he
has done.

~~~
slx26
Well, many of their ideas challenge the traditional mental model we have about
humans and humanity. I think people feeling particularly offended or
uncomfortable with that shouldn't surprise us.

~~~
bbctol
There's also the tiny issue that he hasn't produced anything of value.

~~~
chubot
This is precisely what I mean by "beyond mere disagreement". It's not enough
to disagree; his character must be attacked as well.

~~~
bbctol
de Grey seems like a great guy; he's a fantastic speaker, I generally agree
with his vision of humanity, and this proof is impressive. I haven't attacked
his character, nor do I plan to.

With respect to his work on resisting human aging, he hasn't produced anything
of value.

------
GarvielLoken
“Occasionally, when I need a rest from my real job, I’ll think about math,”
Signature material.

------
tejohnso
I'm so glad Aubrey de Grey got a nice win here. I feel like he doesn't get
enough credit for his other endeavours.

------
phkahler
Is it just me or does the image of 1581 vertex graph contain a face that looks
a bit like krusty the clown?

~~~
coldacid
Oh good! I'm not the only one who saw that.

------
andrepd
The huge, flashing "Vote for us" button on the bottom right corner of the
screen (at least on mobile) is incredibly distracting.

------
melling
“The guy” is Aubrey de Grey, who used to get more discussion on HN:

[https://hn.algolia.com/?query=%20Aubrey%20de%20Grey&sort=byP...](https://hn.algolia.com/?query=%20Aubrey%20de%20Grey&sort=byPopularity&prefix&page=0&dateRange=all&type=story)

Curing death doesn’t get much buzz these days. Maybe we’ll give it another
look?

~~~
profosaur
Anti-aging research is stronger than ever, with some very impressive results
recently coming out of David Sinclair's lab at Harvard for example.

------
nailer
> Imagine, he said, a graph — a collection of points connected by lines.
> Ensure that all of the lines are exactly the same length, and that
> everything lies on the plane.

I do not understand what 'everything lies on the plane' means. I take it as
meaning 'everything is laid out in two dimensions' but that doesn't make
sense. Can HN help?

~~~
arundelo
That is what it means. Note that the lines ("edges" in graph theory terms) can
cross each other.

 _Nelson asked: What is the smallest number of colors that you’d need to color
any such graph, even one formed by linking an infinite number of vertices?_

The Wikipedia page describes the infinite-vertices version of this graph as

 _an infinite graph with all points of the plane as vertices and with an edge
between two vertices if and only if the distance between the two points is 1._

This of course is impossible to draw but Wikipedia shows seven-vertex and ten-
vertex subgraphs of it:

[https://en.wikipedia.org/wiki/Hadwiger%E2%80%93Nelson_proble...](https://en.wikipedia.org/wiki/Hadwiger%E2%80%93Nelson_problem)

------
hi41
Math is terse and biology is verbose. Normally a person good in biology
dislikes math and a person good in math dislikes biology. He has done
extremely well in both! How can one be so good in both?!

~~~
mygo
the fact that Biology is verbose just means that we haven’t quite figured it
out yet. And he’s over here trying to figure it out.

------
kensai
A part omitted from the article is that de Gray is a genius. That partly
explains his other achievements in other fields.

