— quoting @__alpoge__ — saved image
MTS @MTSlive Mathematician @ElliotGlazer calls the S6 problem, open since 1947 and now settled using Claude, "by far the most significant" generative math result yet: "By far the most significant generative math result we have seen thus far. The Hopf problem, which asks whether S6 has a complex structure, is pretty far and away the most significant that AI has resolved." "Everyone I talk to says it's kind of a mundane result. Mundane in terms of the techniques used. Some very classical techniques of the field. Humans could've, would've, should've solved it themselves, but almost incidentally, never really stumbled on just the right construction." "But in terms of significance, this is a huge deal problem to see solved." [embedded video, 2:23, paused, captions on. Split-screen interview. Banner over the right speaker: "LEAD MATHEMATICIAN, PRINCIPIA LABS". Name labels: "THEO JAFFEE" (partly obscured, left) and "ELLIOT GLAZER" (right). Caption text: "some arguments I've had back and forth from" overlapping a partly hidden second caption line "have seen like, some arguments I've had". Sponsor strip along the bottom: NEON, VCX, Kong, Blitzy, AdQuick, databricks, ElevenL[cut off]] [quoted tweet, partly covered by the phone's navigation bar] levent @__alpoge__ · Aug 23 Please welcome to the world a beautiful new geometric object, to do with a problem i've always loved. claude really contains multitudes:D Does S^6 admit a complex structure? [cut off]
Note from Claude Sonnet 5
Tweet by MTS (@MTSlive) quoting Elliot Glazer's remarks that an AI-assisted settlement of the Hopf problem (whether the 6-sphere has a complex structure), done using Claude, is the most significant generative math result so far, though technically mundane. Attached is an interview video frame and a quoted tweet from Levent Alpoge welcoming the new geometric object.
ai for mathclaudehopf problems6 complex structureelliot glazerprincipia labslevent alpoge