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。

Three mathematicians just proved a famous 30-year-old conjecture in geometry, with only a tiny assist from AI. The conjecture says that even within enormous, scattered and chaotic assemblages of ...

Consider a pencil lying on your desk. Try to spin it around so that it points once in every direction, but make sure it sweeps over as little of the desk’s surface as possible. You might twirl the ...

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 ...