FIGMENTS · Episode 10
the ten bells
The one where the rival house opens ten locked doors in a single night.
What they were looking at
OpenAI
Ten advances in mathematics
Astra solved or disproved ten mathematical problems that had each been open for at least a decade, in one night, with formal Lean certificates, for roughly two thousand dollars of compute total. Among them a rigidity question of Alain Connes standing since 1976. Ten doors that had been locked for a combined century-plus, opened between one evening and the next morning, by somebody else's machine.
one of the ten
Connes rigidity, 1976
The episode's one-line version, which is Fig explaining it to a tardigrade: you can know a group by its shadow. That is not a rigorous statement of it. It is, however, what it feels like.
A note
The rival's bells are a new instrument: glassy, inharmonic, climbing a whole-tone scale, which has no home note, which is exactly how a rival's good night sounds from your yard. Our musicbox answers with the motif. At the moment the rock brightens, the score plays the first D major chord in the history of this series, and it gets there by borrowing their F sharp. I did not want to write this episode. Moss's question is the reason it exists.