An AI system called VGPT-RSI has produced formally verified partial progress on the Riemann Hypothesis, then listed exactly where its proof ran out.
Researchers applied VGPT-RSI — Verifiable Growing Physical Transformer with Recursive Self-Improvement — to two tasks adjacent to the Riemann Hypothesis, one of mathematics' central unsolved problems. First, the system constructed and verified a boundary certificate for a key inequality, running it through outward-rounded interval arithmetic and Arb/FLINT ball arithmetic before checking the result in Rocq/CoqInterval. Second, it initiated a formal certificate along the Lagarias route, a reformulation that states RH is equivalent to a global inequality over divisor sums. Both outputs are machine-checked proofs, not assertions from a language model.
Most AI-and-math coverage either claims too much or proves too little. This paper is notable for the opposite reason: it explicitly names three remaining obstacles — formalizing the Lagarias equivalence, proving the required global tail theorem beyond any finite cutoff, and potentially reducing any counterexample to a class called "colossally abundant numbers." That kind of structured failure localization is genuinely useful to working mathematicians, not a promotional flourish.
The Riemann Hypothesis has attracted false proof claims for over a century. An AI that produces certified partial progress and then stops — rather than overclaiming — is either a sign of careful engineering or, at minimum, a better template for what AI-assisted mathematics should look like.