Verifiable things, not promises
Results
This page lists what the project has already produced. Every entry links to an external, independent source where the result can be checked: repositories with exact coordinates and verification scripts, or the entry in the On-Line Encyclopedia of Integer Sequences (OEIS). We cannot guarantee the next problem will fall. We can guarantee that everything we find — dead ends included — stays public and belongs to everyone.
■ PROBLEM CLOSED — 2026
Kobon triangles, 14 lines: N(14) = 54
How many non-overlapping triangles can 14 straight lines form? The human record had been stuck at 53; the proven theoretical bound was 54, and nobody knew whether it could be reached. This project found fifteen non-isomorphic arrangements of 14 lines with 54 triangles — the maximum possible. The first historically open case of the sequence is closed.
Exact rational coordinates, no floating point; every arrangement passed two independently written verifiers. The result is recorded in the official OEIS entry of the sequence (contribution: Andrea Maiorana, 2026).
→ OEIS A006066 — the Kobon sequence (a(14)=54)
→ GitHub: kobon_triangles_k14 — the 15 solutions and verification scripts
■ CENSUS PUBLISHED — 2026
Kobon triangles, 18 lines: the atlas
For 18 lines the project censused 2,357 distinct arrangements at the record level, catalogued up to isomorphism: not a single point, but the map of an entire landscape of solutions. It is the method that later opened k=14.
■ IN PROGRESS
The fifth colour (Hadwiger–Nelson)
How many colours does it take to paint the plane so that no two points at distance 1 share a colour? All that is known is that the answer lies between 5 and 7 — since 1950. The project has already built and proved, in-house, a 5-chromatic graph of 1465 points with tools written from scratch, and every night the machine works to shrink it. The research diary is told in the story and drawn in the plates.
No promises here: the world record is 509 points and we may never beat it. That is the normal risk of open mathematics — the same risk k=14 carried before it fell.
If you want these nights of computation to continue, there is the jar.