alt Hacker NewsA complex structure on S^6 [pdf]
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It seems the trend for AI math is:
>Proofs which fewer and fewer people are able to understand
>Those who do understand, the rate at which models make discoveries exceed the amount of time those humans have in a day
>As a result, we will increasingly use other AI models to validate the proofs AI make for us
I don't see a future where this doesn't apply to everything. Let's say you're an evil CEO, you could ask an AI model to run for days cooking up every possible nefarious scheme to get out of a class-action lawsuit scott-free, to avoid taxes via complex financial engineering, etc. The plans will be far more complex than any human can understand. There simply aren't enough humans with the mental bandwidth to oppose you, so it's just machine vs machine, and if you have more money to pay for more compute, you win.
This kind of papers go way over my head, but recently I was surprised that ChatGTP (free) found the proof for an expression had a square value for some variables. It dug up a relationship from a paper from 2009 and correctly applied it to the case.
The chat: https://chatgpt.com/share/6a7f1b08-b9dc-83ea-b911-aaf8b65f1c...
LGTM
I skimmed through it. Looks fine. Had a bit of trouble following step 5 of theroem 10.5 (page 89), but after a second look it became all too obvious.
Is this a proof a human could have come up with? Is it elegant? How significant was the human contribution?
I’ve been turning the handle on GPT for weeks, feeding in toy models of physics and seeing what pops out the other end.
It’s mostly this type of mathematics: classifying what high dimensional spaces can and can’t do.
Maths like this is where the AIs will be most useful in the next few years: tirelessly grinding through every possibility on the edge of human knowledge, filling in gaps and completing maps of no-go regions in the theory space.
And in other news (elliptic curve of rank 31): https://news.ycombinator.com/item?id=49412774
Announced by the same people, basically at the same time.
100 pages of dense mathematics created by Claude. It doesn't even have an abstract or a summary. What are we looking at here? Has anyone read this? Please explain like I'm not a math PhD.