
Computer Search Settles 90-Year-Old Math Problem - beefman
https://www.quantamagazine.org/computer-search-settles-90-year-old-math-problem-20200819/
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ghj
Yet another graph theory theorem falling to automated reasoning!

I wonder why progress has been so slow though. After the promising result
decades ago where the Four Color Theorem was proven by a computer, I expected
to see a lot more computer assisted proofs.

> They ultimately streamlined the search for a clique of size 128 so that
> instead of checking 2^39,000 configurations, their SAT solver only had to
> search about 1 billion (2^30)

Why is human insight needed for finding symmetries to make problems
computationally tractable? Why can't this part be automated too? This must've
been worked on for decades already, so is there a fundamental reason why
computers can't do it?

EDIT: Also found some more technical links by one of the co-authors:
[http://www.cs.cmu.edu/~mheule/talks/ijcar2020.pdf](http://www.cs.cmu.edu/~mheule/talks/ijcar2020.pdf)
[http://www.cs.cmu.edu/~mheule/Keller/](http://www.cs.cmu.edu/~mheule/Keller/)

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antman
I can't wrap myself around how theorem provers work. Is there something like a
beginner tutorial with examples from simple uses? And which theorem prover
would be intuitive for an introduction to this space?

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currymj
Yes, this exists. it is called the "Natural Number Game" and interactively
teaches you to use the Lean theorem prover to prove simple theorems about
addition, multiplication, and so on. It runs in the browser.

[https://wwwf.imperial.ac.uk/~buzzard/xena/natural_number_gam...](https://wwwf.imperial.ac.uk/~buzzard/xena/natural_number_game/)

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faeyanpiraat
The math might not be too complex but it still seems arcane magic to me.

But the premise that a computer simulation solved the problem with a given
reason that is too complicated to understood by humans, and require a separate
computer program to verify is both fascinating and scary at the same time.

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chmod775
>solved the problem _with a given reason_

Edit: I just removed my comment because I failed at parsing this expression,
and ended up replying to something you did not actually say.

