A complex structure on S^6 [pdf]

mr_mitm•about 2 hours ago

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.

cmenge•about 2 hours ago

There's an abstract on page 3. But it's quite ... abstract.

By the end of the first sentence I'm pretty sure it would take me quite some time to understand what it's about (the first sentence of the abstract, not the whole paper)

robinhouston•about 2 hours ago

I’m pretty sure no one (except perhaps Anthropic insiders who had prior access, and probably not even them) has properly digested this paper yet, and some caution is warranted given the notoriety of this problem and the history of claimed solutions that did not stand up to scrutiny. But if it stands up, it’s a really big deal.

Background: https://mathoverflow.net/questions/1973/is-there-a-complex-s...

scuppernong•about 2 hours ago

https://xcancel.com/__alpoge__/status/2091639597193368014#m

bad_haircut72•about 2 hours ago

LGTM

scuppernong•about 3 hours ago

christ

gerdesj•about 2 hours ago

I'm with you. That is quite a dense paper.

I nearly made it through the first line, OK, sentence of what looks like the Intro, which doesn't bother introducing itself and isn't actually the introduction which occurs later.

I can only describe pages one and two as some sort of foreplay. If you manage to hang on until P108 you can dispense with a safe word in future.

esafak•about 2 hours ago

Is this a proof a human could have come up with? Is it elegant? How significant was the human contribution?

jiggawatts•about 2 hours ago

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.

frozenseven•about 2 hours ago

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.

dinga•about 2 hours ago

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.

cmenge•about 2 hours ago

I was more confused by the application of Nakayama’s lemma in the following paragraph, but then it suddenly became clear to me.

_zoltan_•about 2 hours ago

basically trivial.

A complex structure on S^6 [pdf]

⚡ Community Insights

Discussion (13 Comments)Read Original on HackerNews