A question mathematicians have not been able to answer since 1948 was answered on Sunday, in a 108-page file posted to X
Levent Alpoge, a junior fellow at Harvard's Society of Fellows who also works with Anthropic, posted a 108-page paper on 23 August claiming to construct a complex structure on the six-dimensional sphere. The question — known as the Hopf problem — has been open since the late 1940s, and Alpoge says the work took about three days with Claude. One other mathematician, Qiaochu Yuan, has read through it. Important caveat: this is a first-party claim, not a settled result. There is no peer review yet, and the field has been burned before — Michael Atiyah announced a proof of the opposite conclusion in 2016 and it did not survive scrutiny.
Why it mattersThe same researcher used Claude in July to produce a counterexample that disproved the Jacobian Conjecture, open since 1939. Two problems of that age from one person-and-model pairing inside five weeks is a different sort of claim than a benchmark score: it argues that in some corners of pure mathematics the bottleneck has shifted from insight to search speed. If the proof holds, the slow step in mathematics is now peer review, which takes months and cannot be accelerated the same way.
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