I don't repost mathematics if I do not personally feel sure of its correctness, so I did not yet comment on the purported construction of a complex structure on S^6. However, I wanted to add some contextualization because I don't agree with the social media narrative that is developing. 0. Of the AI breakthroughs so far it's the closest to my interests, although still pretty far. I am not grieving, I am interested to learn more about it! I don't know if it's correct but on cursory glance it seems quite plausible. 1. If correct, this would be a major development. I believe it is a central problem in its field (complex differential geometry), like the Unit Distance Conjecture was for combinatorial geometry. Perhaps even more famous names are attached to this field, leading some people to say it's even more prestigious, but I prefer not to think in such terms. 2. There are two writeups, a 2-page one and a 100+-page one. Both are terrible and seem deliberately constructed to be inhumane. Fortunately, one can fight AI with AI: I asked Claude/GPT/Gemini to collaborate on making a more readable and enlightening version, which you can find at To make this, I prompted the models to write a document in the style of one of my own surveys. I haven't checked the mathematics, but it seems less forbidding than the original document at least. 3. 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. 4. 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. 5. There are some intriguing differences with the previous artifacts from Claude. The announcement seems coy about the provenance of the solution - there is a vague allusion to Claude, but which model(s) did it come from, and what was the human involvement? Why is it hosted on a personal website instead of the Anthropic one? We have seen some instances of AI results that are so good, the human authors seem to begrudge credit. I keep a list of such instances. The standard should be to disclose the role of AI clearly and transparently. Better to be honest than go through life under a cloud of suspicion. 6. Although this may solve one of the more famous problems of mathematics, there are still whole fields that are only just starting to feel acceleration. I'm not aware of any AI breakthroughs in my areas of research, for example. When those come, as I suspect they will before long, I look forward to studying the insights!