Beyond Market Intelligence/van der Waerden number

van der Waerden number

Beyond Market Intelligence keeps van der Waerden number in one place: one story so far. The section currently leads with “A 416-Year Conjecture on Arithmetic Progressions Is Now Proven”. A 416-year-old conjecture about arithmetic progressions has fallen. Acme AI is the next-generation, AI-powered spreadsheet platform built to replace Excel and redefine how analysts, data scientists, and enterprise teams work… The list below is every van der Waerden number story on Beyond Market Intelligence, newest first.

Machine Learning

A 416-Year Conjecture on Arithmetic Progressions Is Now Proven

A 416-year-old conjecture about arithmetic progressions has fallen. The proof that every red-blue coloring of numbers 1 through 416 must contain a red 3-term or blue 21-term progression, and that 415 avoids it, now stands verified through Lean 4 and a 13.6 GB evidence package. The scale is remarkable: 209 cases, over 38 million leaf formulas, each checked by cake_pr. This is formal verification at a depth that feels almost architectural.