Papers

Before an AI system is trusted to find new space-filling solids, it should first be able to find one that a person found recently, the way software must pass a regression test (a known answer it has to reproduce) before a change ships. Here the system had to rebuild the Josehedron, a solid Mathias Bernhard described this spring, from only the twelve points that determine it, and pass checks that were written down before the run started. The paper's final version also reports that the solid's shape had already appeared, unnamed, in M. W. Schmitt's 2016 survey of space-filling solids.

I keep a record of every error that the checks in my AI-assisted math work have caught. This paper goes through that record: for each error, who made it, what caught it, and how far it had spread first. Over 52 days the record held 58 errors. No single kind of check caught a majority of them. None of the six that got as far as a submission was caught by the agent that made it rereading its own work; those were caught by an editor, a referee, me, a check against a live public database, or a separate agent auditing the work. The record itself is described in The record I keep of errors my checks caught, and two that changed how I work.