There is a purported AI construction of a complex structure on S^6. The file contains two writeups, a 2-page one and a 100+-page one. Both are hard to digest, but with a few short prompts to an LLM one can easily convert them into more readable formats, e.g. this. This was made by feeding the original file into Claude/GPT/Gemini with the prompt below, then having them make a couple rounds of revisions. I have not checked the mathematical details of this document and cannot vouch for their correctness at this time. This page is just meant to share a possible workflow which could speed up understanding of the mathematics, in the hopes that someone will get to the bottom of this, and start explaining it to people!

Prompt:

In s6.tex there is a claimed construction of a complex structure on S^6. The writeup is AI generated and not comprehensible. Our goal is to write a more readable, insightful, and enlightening account. Technical details and computations can be omitted in favor of intuition and insight, and a precise citation to the original document. A model example is a survey I personally wrote, in the AMS Survey subfolder. This length (20-30) pages is the target length. Images, visuals, analogies, metaphors, and intuitions are appreciated. Historical context, placing the ideas of the proof in relation to the literature, and clarifying how the claimed solution situates relative to prior work, are welcome.

The survey referred to in the prompt is (https://arxiv.org/abs/2602.15629); I do not know to what extent including this document actually had any benefit.

Stepping back, the following comments reflect my opinion about this and all future AI generated breakthroughs.

• This is a great opportunity for an expert to write an illuminating account of the construction, explain the key ideas and their proper historical context, and summarize the takeaways and lessons learned for the mathematics community.
• If I see such an account, I would be happy to arrange for the author to give a lecture series in Berkeley. If this lecture series is also wonderful, I would go further and advocate for the author to have a position at Berkeley (if desired). For contrast, I see little value in having colleagues who are good at being the first to prompt AI for a solution.