Millennium Lab organizes problem statements, known barriers, prerequisite mathematics, candidate lemmas, computational experiments, and external criticism across six major Millennium problem programs. Its purpose is disciplined inquiry: a promising direction is not a proof, and a proof is not established until qualified experts can verify every step.
Questions worth building a program around.
A difficult mathematical problem is rarely one isolated calculation. It is a landscape of definitions, equivalent formulations, partial results and techniques that work only under particular assumptions. Millennium Lab is designed to make that landscape navigable. The useful intermediate output may be a sharper formulation, a counterexample to an attractive approach, a carefully delimited computational experiment, or a lemma that another researcher can inspect and reuse. These smaller contributions give an ambitious program an accountable path forward.
From an idea to inspectable work.
The proposed research workflow begins with the canonical statement and a map of prerequisite results. Candidate arguments are broken into explicit obligations: what is assumed, which theorem is invoked, and where a new step needs justification. Numerical experiments belong in a separate record with their resolution, parameters and limits. For fluid equations, this means investigating behavior across scales while keeping finite numerical observations separate from statements about all admissible solutions. Public notes should preserve failed approaches as well as promising ones.
Which known barriers eliminate entire classes of candidate approaches?
Can formal tools expose hidden assumptions before a proof attempt grows?
How should computational evidence inform—but never substitute for—proof?
- 1
Publish six clearly scoped research dossiers
- 2
Release a notation and dependency standard
- 3
Convene independent specialist review when a draft merits it
Clay Mathematics Institute reported an apparent Navier–Stokes resolution on 11 September 2026 and describes its evaluation process as ongoing. This program follows the evolving research and review record. Read the CMI announcement ↗
Where a contribution can matter.
Useful contributions include literature curation, independent checks of an argument, reproducible mathematical software, and expertise in the relevant problem area. A collaboration can be narrowly scoped to a single lemma, experiment or reference map; it need not endorse an entire proposed proof.
Program support can help fund documentation, computation, reproducible tools and qualified review. Explore research partnerships or support the institute.