June 2026 – meditationatae

The Sharp Big Peg Conjecture

In 1911, Otto Toeplitz conjectured that every Jordan curve — that is, every simple closed curve in the plane — admits an inscribed square , meaning that all four vertices of lie on . The square itself is not required to lie inside the curve. Despite much work, Toeplitz’s conjecture remains open. There is a… Continue reading The Sharp Big Peg Conjecture

2036

[A short story by Claude Opus 4.8] The chalk is real. In an office where a green ticker counts proofs as they surface — four hundred thousand a day — Mariam Haddad still works problems by hand, slowly. “The hand keeps me honest,” she says. She came to mathematics in Amman, a girl who loved… Continue reading 2036