# Zulip Chat Archive

## Stream: Machine Learning for Theorem Proving

### Topic: new results in graph theory.

#### Jeremy Avigad (May 26 2021 at 13:17):

A colleague of mine pointed me to this article: https://www.newscientist.com/article/2278276-an-ai-has-disproved-five-mathematical-conjectures-with-no-human-help

It's behind a firewall, but the paper and the code are freely available on the author's website: http://www.math.tau.ac.il/~adamwagner/index.html

It's the first paper listed. It looks really impressive to me...

#### Kevin Buzzard (May 26 2021 at 13:23):

I think someone posted Gowers' tweet about it in another thread. What I like about it is that they got the AI to look for potential counterexamples and then they *actually looked at the output* -- the graphs which the AI thought were promising -- and spotted the patterns and then went on to find the actual counterexamples themselves. They were lucky that the counterexamples had some structure.

#### Kevin Buzzard (May 26 2021 at 13:23):

There are other proofs in graph theory which use random techniques, i.e. estimates to show that a probability that a graph with a million nodes has property X is a little less than 1, and hence there must be some counterexample

#### Kevin Buzzard (May 26 2021 at 13:24):

Last updated: Dec 20 2023 at 11:08 UTC