The Entropy Formula for the Ricci Flow and Its Geometric Applications
TL;DR — Perelman’s first Ricci-flow paper — posted to arXiv, never submitted to a journal, and it proved the Poincaré conjecture.
⬇ Download the archived copy — kept here so the document survives its source going dark. arXiv preprint (author distribution licence).
arXiv:math/0211159v1 [math.DG], 11 November 2002.
The first of three preprints in which Perelman completed Hamilton’s Ricci flow programme and proved the Poincaré conjecture — the only one of the seven Millennium Prize Problems yet solved.
The publication is as remarkable as the mathematics. He posted it to arXiv, gave a short lecture tour, answered questions, and then declined both the Fields Medal and the million-dollar prize, withdrawing from mathematics entirely. It was never submitted to a journal; verification took teams of mathematicians several years.
Thirty-nine pages that are the strongest argument for the preprint server ever made.
Where this came from
39 pages. A copy is archived locally against link rot; the header links the original source.