The Greatest Unsolved
Questions in Mathematics
Explore rigorous editorial content, speculative theoretical frameworks, and reproducible computational experiments—all in one place.
The Remaining Six
P vs NP Problem
Is every problem whose solution can be quickly verified also quickly solvable?
Yang–Mills Existence and Mass Gap
Prove that quantum Yang–Mills theory exists and has a positive mass gap.
Navier–Stokes Existence and Smoothness
Do smooth, globally defined solutions exist for the 3D incompressible Navier–Stokes equations?
Hodge Conjecture
Are certain cohomology classes on smooth projective varieties representable by algebraic cycles?
Birch and Swinnerton-Dyer Conjecture
Is the rank of an elliptic curve determined by the behavior of its L-function at s = 1?
Poincaré Conjecture
Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.
Theories & Hypotheses
The Mann Theory
The Mann Theory is presented as a speculative framework exploring analogies between the analytic structure of zeta functions and spectral phenomena encountered in mathematical physics. It does not propose a proof of the Riemann Hypothesis.
The Kaufmann Theory
The Kaufmann Theory investigates the Riemann Hypothesis from a strictly mathematical and structural perspective. It does not rely on physical interpretation or numerical coincidence.
Experiments
Mann Theory — Experiment Runner
Run computational experiments with adjustable parameters. Explore toy zeta functions, compare solvers, and download reproducible results.
Transparent & Reproducible
Every experiment exposes its full parameter set, solver diagnostics, and numerical output. Results can be downloaded as JSON and independently verified.
Browse all experimentsOur Books
The Mann Theory
Spectral Gravity and the Critical Line
Hilbert’s Eighth Problem, Zeta Functions, and the Quantum Geometry of Black Holes. A speculative framework exploring analogies between zeta function zeros and spectral phenomena in mathematical physics.
The Kaufmann Theory
Stability Constraints and the Structure of the Riemann Hypothesis
A structural stability framework for the Riemann Hypothesis. This book investigates whether admissible configurations can be categorically excluded by stability conditions, offering a new perspective on the critical-line conjecture.
Our Methodology
Separation
We clearly distinguish between established theory and speculative proof attempts, so readers always know where they stand.
Transparency
All parameters, assumptions, and data sources are openly documented and available for independent verification.
Clarity
Complex mathematics is presented in accessible language without sacrificing rigour, making deep ideas approachable.
Scholarship
Every claim is grounded in the literature with proper attribution to the researchers whose work we build upon.
Disclaimer: This website does not claim to prove any Millennium Prize Problem. All theories presented here are speculative frameworks. Computational experiments are heuristic explorations, not formal proofs.