AI is discovering patterns in pure mathematics that have never been seen before
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Re: AI is discovering patterns in pure mathematics that have never been seen before
#2Current-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
#3Re: AI is discovering patterns in pure mathematics that have never been seen before
#4Re: AI is discovering patterns in pure mathematics that have never been seen before
#5I'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
#6Re: AI is discovering patterns in pure mathematics that have never been seen before
#7This 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
#8I'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.
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
#9https://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...