Limits RegistryArticles
Explainers on the boundaries.
Plain-language write-ups of the open problems, proven bounds, and reference constants cataloged in the Registry — each tied to a real record with its own evidence trail.
A 70-year-old coloring problem, narrowed to 5, 6, or 7 — and still open.
Mathematics · Open problemsWhat Is the Beal Conjecture?A $1,000,000 prize for a one-line generalization of Fermat's Last Theorem.
Mathematics · Open problemsWhat Are the Millennium Prize Problems?Seven $1,000,000 problems named in 2000. One is solved. Six are still open.
Mathematics · Open problemsWhy Are Physical Constants Known to So Many Decimal Places?Inside CODATA 2022, the internationally adjusted reference values behind every precision measurement.
Physics · ConstantsWhat Is RSA Factoring, and Why Is It Hard?The factoring challenge that underwrites internet cryptography — and the exact number where the record currently stands.
Cryptography · ComputingWhat Is a Mersenne Prime?Primes of the form 2^p − 1, and the volunteer computing project still finding new ones.
Mathematics · Number theoryWhat Is the Theoretical Limit of Lossless Data Compression?Shannon's source-coding theorem sets a hard floor on file size — no cleverer algorithm can beat it.
Information theory · ComputingWhat Is a Ramsey Number?Why R(5,5) — a single unknown integer between 43 and 46 — might never be found by brute force.
Mathematics · CombinatoricsWhat Is a Kissing Number?The surprising geometry of how many equal spheres can touch one central sphere without overlap.
Mathematics · GeometryWhat Is the No-Cloning Theorem?Why quantum mechanics forbids a universal machine from making a perfect copy of an unknown quantum state.
Quantum information · ImpossibilityHow Do Upper and Lower Bounds Work?The two-sided language researchers use to describe exactly what is known when the final answer is still out of reach.
Methodology · Open problemsWhat Is Channel Capacity?The hard ceiling on reliable communication through a noisy channel — and why more clever coding cannot erase noise for free.
Information theory · Computing