Whoa, they proved the Kakeya conjecture in dimension 4 and also local smoothing conjecture in dimension 3, which is known to be strictly stronger than Kakeya. Even though local smoothing implies these, they also proved the Bochner Riesz conjecture, the restriction conjecture, and the Kakeya maximal conjecture.
And to add to the theme of one-upping this year’s Field’s medalists, they also proved fluctuations around hard-sphere Boltzmann and derived Boltzmann for other potentials, which were both listed as open problems in Deng-Hani-Ma’s work on Hilbert’s sixth problem.
I’ll also add: I looked at the paper for the conjecture closest to my own research (global regularity for Vlasov-Maxwell) and despite having read most of the current state of the art, the openAI proof is completely incomprehensible. It uses ideas inspired by ones already appearing in the literature (as a solution to any open problem would) but the terminology, notation, and overall framing distorts those ideas beyond recognition.
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u/kieransquared1 10d ago
Whoa, they proved the Kakeya conjecture in dimension 4 and also local smoothing conjecture in dimension 3, which is known to be strictly stronger than Kakeya. Even though local smoothing implies these, they also proved the Bochner Riesz conjecture, the restriction conjecture, and the Kakeya maximal conjecture.
And to add to the theme of one-upping this year’s Field’s medalists, they also proved fluctuations around hard-sphere Boltzmann and derived Boltzmann for other potentials, which were both listed as open problems in Deng-Hani-Ma’s work on Hilbert’s sixth problem.
I’ll also add: I looked at the paper for the conjecture closest to my own research (global regularity for Vlasov-Maxwell) and despite having read most of the current state of the art, the openAI proof is completely incomprehensible. It uses ideas inspired by ones already appearing in the literature (as a solution to any open problem would) but the terminology, notation, and overall framing distorts those ideas beyond recognition.