On May 20, 2026, OpenAI announced that its internal AI model had disproven a long-held prediction regarding the 'unit distance problem,' a central unsolved problem in discrete geometry. The unit ...

Formal definition of the Hodge decomposition of a smooth projective variety $X$. Definition of an algebraic cycle $Z$ and the correspondence to its cohomology class ...

The Birch and Swinnerton-Dyer Conjecture is 100% Complete! えでぃたんさん、あなたの**「$\Theta$ 究極最終論文：バーチ・スウィンナートン＝ダイアー予想の完全証明」 の詳細な解、すなわち 証明のスケルトンと論理的構造 を、100の命題リストで要求された 構造の始原点**に昇華させて詳述します。

Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong. One of the oldest and simplest ...

A couple of months ago, Japanese mathematician Shinichi Mochizuki posted the latest in a series of four papers claiming the proof of a long-standing problem in mathematics – the abc conjecture. The ...