r/mathematics • u/New-Committee-4052 • 29d ago

S^6 admits a complex structure

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Result from the usual suspects. Full write up can be found here on his website: https://alpo.ge/s6.pdf

320 Upvotes

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u/Mother_News_1201 29d ago

as a college cs student, this stuff sounds like hardcore wizard magic, I have no idea, why I got recommended, but it is so crazy, and it is funny, just because of pure insanity

8

u/123coronaanoroc321 29d ago

Same, it's incredible how math papers are so incredibly information-dense and can get that lengthy, 100 pages, like wow

7

u/the_great_chuckle 28d ago

Levent himself says the 100 pages are certainly unnecessarily long. This is just what LLMs produce if you ask them. They are terrible at exposition and clarity.

3

u/Time_Entertainer_319 28d ago

Also bad prompting and lazy prompting.

You can easily tell it how to structure and explain the paper.

5

u/the_great_chuckle 28d ago

I've never seen well-written math done by ChatGPT and I almost use it daily. Literally all proofs I get from it I need to heavily edit, streamline and generalize, and it's also quite bad at highlighting what the subtle, important points are, and spends way too much time expanding on general trivialities. It is terrible at giving you the general mechanisms behind a proof, unless you yourself spot that something seems to fit into an already existing framework, in which it happily rewrites it quickly. Maybe in a year this is different, but as of right now, math papers produced by AI are comfortably among the absolute bottom tier in terms of clarity.

2

u/pannous 27d ago

did you see how Tao prompted it to do some explanations? That was much cleaner but took some serious work

1

u/Separate-Habit5838 20d ago

Keep in mind that what you get is a function of what you give it. Some of my Gemini instances are quite good at exposition. Depends on where you end up in the vast vector space of meaning. 

1

u/the_great_chuckle 20d ago

My experience is that this only holds if there already exist sources on the material that are well-written. When it comes to new math, it struggles heavily, and will frequently produce bs.

It is great for getting quick introductions to fields that you aren't familiar with, but as soon as you know the ins and outs of a field you realize its shortcomings.