A new arXiv paper asks whether an AI agent can rediscover a geometric formula on its own. The honest answer, buried in its own appendix, is not entirely.
Researchers used generalized Blaschke curves, complex-analysis objects describing the boundary behavior of rational functions, as a sandbox for AI-driven math discovery. For one fixed degree-four Blaschke product, an agent received raw numerical coordinates for six pair-lines across 80 boundary configurations, with the actual target theorem kept hidden. After working through rejected geometric hypotheses, the agent's research log shows it landing on a homogeneous cubic equation fitted to polygon sides. That formula predicted 480 lines from 80 unseen parameter values, with a residual error of about 8.88 x 10^-17.
The catch is in the fine print. A one-configuration control run found insufficient evidence that the pattern was a genuine invariant, and a deterministic degree-search baseline added after peer review matched the agent's cubic without any AI involved. That second result undercuts the premise: if brute-force polynomial fitting gets the same answer, this isn't proof an AI agent reasoned its way to a discovery.
Read it as a methods paper on how to grade AI math claims, not a demo of AI doing math; the authors' own numbers make that case better than any press release would.