Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Claim. The Lean 4 theorem Erdos521.erdos_521_negative in the
lean-proofs repository states, in the repository's index, that it is not
almost surely true that for the distinct real roots of a
random polynomial, which is the negative answer to
Problem 521 for that reading. The
index credits the proof to Colin Snyder (starfleetmath.com) and records that
the repository's continuous integration builds the file against a pinned
Mathlib and checks that the headline theorem
uses no sorry and no axiom beyond propext, Classical.choice and
Quot.sound. The files were hosted in the repository on 2026-07-23, the
date this page carries, and the formal-conjectures statement of the problem
has linked the file at the repository's revision of 2026-07-30 as its formal
proof since 2026-08-07 (the record link is pinned at the catalog's commit of
that day), marking the problem solved with answer false; the
catalog's docstring says the result was first obtained by others, who
deserve the credit, and that the link is to an independent machine-checked
proof. The imports of the development name a cone criterion, records, the
Kochen–Stone lemma and a fourth-moment analysis, so its route appears
related to the cone-record arguments of the other claims.
Depends on. No page of this wiki.
Standing. Claimed. This corpus has not built, replayed or audited the development, no write-up accompanies it, and the catalog's tag links a proof without refereeing it; the hosting repository's verdicts file records a term-by-term faithfulness read by its maintainers (521: faithful, the negation proved through an event of positive measure) beside its CI build and axiom check, and says neither replaces peer review; this corpus has not examined the statement's fidelity. The site labels the problem OPEN (page last edited 19 October 2025). The written arguments for the same conclusion are on Kovač 2026, Kwon–Zou 2026, Sneiderman 2026 and An–Lin 2026; a second Lean development, in Boris Alexeev's repository, is on Alexeev 2026.