The Unit Distance Problem

There’s a new math result which is a milestone for AI mathematics. It’s a human readable and insightful result on a conjecture of some renown. It improves on a previous construction of Erdos to make a set of points in the plane with a relatively large number of unit distances between them. Where the AI got its inspiration from can be as ineffable as it is for humans, but there’s a plausible narrative that it got direct inspiration from the Erdos construction. A proof tells a story, and the moral of the story belongs to the reader not the storyteller. To some the Erdos construction is a story about square grids. But it can also be read as a story about taking an algebraic construction, finding a projection onto geometric space which preserves unit distances, and then solving a number theory problem in the algebraic space to have lots of unit distances. Instead of using the straightforward grid structure the new construction uses a more esoteric algebraic construction, involving pulling…