I am as upset as the slew of math slop from OpenAI as the next guy, but I do not understand this article. Are they saying that this was not a true improvement because the algorithm is _galactic_? Human algorithm researchers have been publishing those sorts of results for decades now

A lot of people are emphatically NOT upset about the OpenAI math dump.

I think it's reasonable to give the benefit of the doubt to humans, but not LLMs, that their galactic constants are not just attempts to "hack" the problem description. If LLMs are going to turn up a bunch of them, we have to develop a better version of complexity theory that accounts for them.

> “The model uses exact complex arithmetic.” That means it assumes you can store and multiply complex numbers at arbitrary precision. Indeed, the algorithm requires you to multiply complex numbers whose magnitudes grow superpolynomially with n.

This in particular is the kind of thing that I'd expect a human would at least pause on and ideally note as a severe caveat to any claimed asymptotic improvement. I don't know off the top of my head if the story is as simple as "you can tuck part of the asymptote into your presumed constant arithmetic", but it sounds kinda plausible?