PS2 retweeted
日本語だと「未然形」「連用形」「終止形」「連体形」「仮定形」「命令形」の6種類ある上に五段活用、下一段活用、上一段活用、カ変、サ変と少なくとも(ネイティブでないと区別につかなさそうな)32種類の変化の仕方があるわけだが……
the (人名)'s theorem←誤り
the (人名) theorem←その人の代表的な定理
(人名)'s theorem←普通はこれ
(人名) theorem←通常誤りだが、人名が性質名に転用されている場合結果的にこの形になることがある
This quoted post is unavailable.
新着に4つ目の例が
A Borsuk-Ulam theorem for adaptive continuous measurements
Mario Ullrich
arxiv.org/abs/2610.33781 [𝚖𝚊𝚝𝚑.𝙵𝙰 𝚌𝚜.𝙲𝙲]
ALT We prove a Borsuk-Ulam theorem for adaptive measurements: if 2ⁿ≤ m, then any n adaptively chosen continuous functionals take identical values at two antipodal points of any sphere in ℝᵐ. Consequently, at least ⌈log₂(m+1)⌉ adaptive continuous measurements are needed to learn the vectors of a ball in ℝᵐ with an error smaller than its radius, which matches the recently obtained upper bound up to one measurement. The bound extends to Bernstein widths in Banach spaces. The main idea of the proof was found by Claude Fable 5, an AI model developed by Anthropic, and we document the development in a last section.
PS2 retweeted
Local smoothing conjectureの証明の概要をChatGPTに聞いてみたところ、時空変数を複素方向に移すとか四元数Monge–Ampère型方程式とか言ってて意味がわからない...。