alt Hacker NewsReconfiguring existing proofs in ways that have been tedious or obscured from humans, or using well framed methods in novel ways, will be done at superhuman speeds, and it'll unlock all sorts of capabilities well before we have to be concerned about AGI. It's going to be awesome to see what mathematicians start to do with AI tools as the tools become capable of truly keeping up with what the mathematicians want from the tools. It won't necessarily be a huge direct benefit for non-mathematicians at first, because the abstract and complex results won't have direct applications, but we might start to see millenium problems get taken down as legitimate frontier model benchmarks.
Or someone like Terence Tao might figure out how to wield AI better than anyone else, even the labs, and use the tools to take a bunch down at once. I'm excited to see what's coming this year.
Replies
> Reconfiguring existing proofs in ways that have been tedious or obscured from humans,
To a layman, that doesn't sound like very AI-like? Surely there must be a dozen algorithms to effectively search this space already, given that mathematics is pretty logical?
I agree only with the part about reconfiguring existing proofs. That's the value here. It is still likely very tedious to confirm what the LLMs say, but at least it's better than waiting for humans to do this half of the work.
For all topics that can be expressed with language, the value of LLMs is shuffling things around to tease out a different perspective from the humans reading the output. This is the only realistic way to understand AI enough to make it practical and see it gain traction.
As much as I respect Tao, I feel like his comments about AI usage can be misleading without carefully reading what he is saying in the linked posts.
This is what has excited me for many years - the idea I call "scientific refactoring"
What happens if we reason upwards but change some universal constants? What happens if we use Tao instead of Pi everywhere, these kind of fun questions would otherwise require an enormous intellectual effort whereas with the mechanisation and automation of thought, we might be able to run them and see!
If this isn't AGI, what is? It seems unavoidable that an AI which can prove complex mathematical theorems would lead to something like AGI very quickly.
I don't think there's a real boundary between reconfiguring existing proofs and combining existing methods and "truly novel" math