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AI is discovering patterns in pure mathematics that have never been seen before

sciencealert.com

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Re: AI is discovering patterns in pure mathematics that have never been seen before

#2
That’s actually pretty cool (and not the hyperbole that articles about use of AI in science usually are.)

Current-gen Deep Leaning systems are really good at “riffing on” text inputs. So feed them a bunch of known math conjectures, and new conjectures should fall out.

Not that this is a new thing — mathematicians have been using various procedural generation methods to formulate conjectures since Prolog was invented. But the Deep Learning text AIs make this much easier — you don’t need to model the domain, the syntax of a mathematical conjecture; these AIs discover that much for you. So you can more quickly and cheaply apply these modern methods to exploring conjecture-space in new subdisciplines.

And of course, this still has nothing to do with what futurists were expecting ML to eventually do for math (generating proofs, putting mathematicians out of a job); instead, something a lot less obvious as “useful work”, but useful nevertheless!

Re: AI is discovering patterns in pure mathematics that have never been seen before

#4
I'm a fan of deepmind and all, but this story has been way overblown based on what I saw in the actual code. There's nothing particularly new about mathematicians using computers to investigate and make conjectures, even if you add ML into it.

Re: AI is discovering patterns in pure mathematics that have never been seen before

#5
post #4

I'm a fan of deepmind and all, but this story has been way overblown based on what I saw in the actual code. There's nothing particularly new about mathematicians using computers to investigate and make conjectures, even if you add ML into it.

As is typical in most AI coverage. The amount of white lies and fake news in scientific journalism is insane

Re: AI is discovering patterns in pure mathematics that have never been seen before

#7
> "While mathematicians have used machine learning to assist in the analysis of complex data sets, this is the first time we have used computers to help us formulate conjectures or suggest possible lines of attack for unproven ideas in mathematics."

This is not true. Doron Zeilberger has long used Shalosh Ekhad to formulate conjectures: https://www.wired.com/2013/03/computers-and-math .

Re: AI is discovering patterns in pure mathematics that have never been seen before

#8
post #4

I'm a fan of deepmind and all, but this story has been way overblown based on what I saw in the actual code. There's nothing particularly new about mathematicians using computers to investigate and make conjectures, even if you add ML into it.

> but this story has been way overblown based on what I saw in the actual code.

Could you expand on this? What code did you see, where, and doing what? Were you part of this team?

> There's nothing particularly new about mathematicians using computers to investigate and make conjectures, even if you add ML into it.

I think you're being needlessly reductive here. The article itself explicitly states that "using computers" is not what's new.

Re: AI is discovering patterns in pure mathematics that have never been seen before

#9
I don't normally complain about this, but that result has been at least four times on the front page in the last two weeks:

https://news.ycombinator.com/item?id=29514642

https://news.ycombinator.com/item?id=29424749

https://news.ycombinator.com/item?id=29405380

https://news.ycombinator.com/item?id=29208141

Finding mathematical patterns and relations by fitting expressive functions has actually been a common technique in experimental mathematics (https://en.wikipedia.org/wiki/Experimental_mathematics) for a while.

In the last few years, neural networks in particular have been used a lot in areas of math related to string theory, where one tries to find structures on certain topological spaces that preserve or generate symmetries of the resulting physics. Here's a review that might be interesting:

https://arxiv.org/abs/2101.06317

Unfortunately, none of these mathematicians have the marketing prowess of a multi-billion dollar company...

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