
A fleet of computers helps settle a 90-year-old math problem - doppp
https://www.wired.com/story/a-fleet-of-computers-helps-settle-a-90-year-old-math-problem/
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isolli
The four color theorem was proven with the help of a computer in 1976 [0]. The
event gave rise to the concept of non-surveyable proof [1]. As far as I can
tell, it has never been proven without the help of a computer.

[0]
[https://en.wikipedia.org/wiki/Four_color_theorem#Proof_by_co...](https://en.wikipedia.org/wiki/Four_color_theorem#Proof_by_computer)
[1] [https://en.wikipedia.org/wiki/Non-
surveyable_proof](https://en.wikipedia.org/wiki/Non-surveyable_proof)

~~~
ogogmad
As the Wikipedia article states, the main countermeasure to non-surveyability
is to express the proof in formal logic, which can then be verified by an
automated proof checker. In fact, this is exactly what the authors of the
proof of Keller's conjecture have done. And likewise, the Four Colour Theorem
has been verified in this way.

I don't think non-surveyability is really the issue here.

~~~
isolli
Non-surveyability was introduced precisely as a criticism of the 1976 proof. I
believe that the four color theorem was proven with the help of an automated
proof checker only in 2005.

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plafl
I had to search the original publication to see what kind of computer cluster
they used. Here it is in case you are curious:

"We ran all three experiments simultaneously on 20 nodes on the Lonestar5
cluster and computing on 24 CPUs per node in parallel."

It seems it took less than an hour. I think that calling it a "fleet of
computers" is a little too much. It makes it look like they brute-forced the
problem while the truth is that as usually the merit was on the algorithm.

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hirsin
I brushed up against SAT solvers in school, but never quite got a grasp on
them. The "proof" at the end is 200 GB - is that size related to SAT solvers
in general, this particular problem, the dimensionality here? A billion-sized
search space giving a 1.6 trillion bit proof sounds awfully exhaustive to me,
but I also can't imagine what such a large proof would even be about.

~~~
maweki
If you're talking about boolean satisfiability, all you have as "memory
locations" are bits and you describe their relationships. I guess the result
you want is "unsat".

Say you want location 1 not equal location 2, then you have

(1 or 2) and (not 1 and not 2) in the expected normal form. This blows up fast
if multiple variables are involved. There are tricks like Tseitin
transformation that can reduce the size of the clauses but introduces
additional variables.

Also, if you want to use 8-bit-numbers, you'd need 8 variables each. Addition
would need more clauses.

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tduberne
Am I the only one wondering why they used 40 computers, if the computation
only lasted for 30 minutes? Does anyone who read the full paper jnow the
reason? The article does not explain anything in that direction, but I would
expect that if they could just do it on one computer and wait for two days,
they would have done it...

~~~
Someone
Paper is at
[https://arxiv.org/abs/1910.03740](https://arxiv.org/abs/1910.03740).

Skimming it the answer appears to be “because they had that cluster”. They say
they only used 20 machines (each with 24 CPUs, so I guess these are fairly
beefy)

Given the 224 GB (binary) size of the proof memory usage might be a problem,
too.

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smabie
For math as an art form (a lot of theoretical math), are computer aided proofs
destroying the core value of the endeavor?

~~~
ogogmad
I guess the problem with many Computer Assisted Proofs is that they don't
explain "why" something is true, only _that_ something is true. But if that's
the best you can do, then it's certainly better than nothing.

Also, advances in CAPs can have applications outside of pure maths.

Finally, CAPs are not common enough - or viable enough in most cases - to make
a dent in the practice of pure maths. At least that's the impression I get.

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ars
Original source: [https://www.quantamagazine.org/computer-search-
settles-90-ye...](https://www.quantamagazine.org/computer-search-
settles-90-year-old-math-problem-20200819/)

~~~
acqq
The author of both articles is the same, as far as I understand, so I don’t
understand how one article can be “more original source” than another.

~~~
azepoi
The other article was discussed here:
[https://news.ycombinator.com/item?id=24220149](https://news.ycombinator.com/item?id=24220149)

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marta_morena_25
Interesting. I hope what the author says isn't actually done. So the computers
generated a proof nobody can understand, but fret not, a second computer
program can assure us of its validity. Well that's heartwarming. I hope they
are not building the foundations of future math on this house of cards.

~~~
throwaway_pdp09
Perhaps you can offer something better?

~~~
Joker_vD
How about: a group of highly sophisticated and very skilled mathematicians
generate a proof no mere mortals (and lesser mathematicians) can understand,
but fret not: another genius mathematician can assure us of its validity.

Hmmmmmmm. Yeah, that sounds much better. What do you think?

