Agents are doing the maths now. The proof is the product.

The proof is the point

Formal mathematics is the hardest possible test for an agent, because the answer is either proved or it is not. A preprint this week introduces LEAP, an agentic framework that bridges informal language-model reasoning and formal verification in Lean by decomposing complex problems and iterating with the compiler. It boosts the one-shot formal solve rate of general-purpose language models from below 10 percent to 70 percent on Lean-IMO-Bench — above the 48 percent benchmark set by specialised, gold-medal-calibre IMO systems — and solves all 12 problems of the 2025 Putnam Competition. It also produced a verified proof for a subproblem in Knuth's Hamiltonian decomposition of even-order Cayley graphs, which is research-level work, not a benchmark trick. The compiler is the judge, and the compiler cannot be charmed. m:…9320

A second preprint makes the proving cheaper. AoA shifts theorem-proving agents from text-based interaction to manipulation of the abstract syntax tree, using JSON-based tree edits that fuse proof operations and states and eliminate repeated line-number-based queries. The benchmarks show 2.3 to 4.7 times lower API costs and 3.9 to 8.9 times fewer tool calls compared with Amazon's Isabelle Agent, with higher success rates on the NTP4VC-Pearl verification benchmark. The method also enables the use of Minilang, a proof language otherwise inaccessible to models trained on legacy corpora. Proving is becoming an engineering problem with a cost curve, which is when things start to scale. m:…6586

The scale of what formalisation can now do is on display in Axiom's announcement: the first machine-verified proof of Faltings' theorem, the landmark result that curves of genus at least 2 have only finitely many rational points. The formalisation follows the proof of Paul Vojta as simplified by Enrico Bombieri, and contains roughly 110,000 lines of proof-specific Lean code — built on library modules containing roughly 6,400,000 lines from the Stacks Project. The point the team makes is that formal mathematics compounds: foundational libraries let each new proof build on the last. The rising sea lifts every theorem. m:…3657

The lab, with a checker

The same logic is spreading to experimental science. A preprint on collider physics introduces a benchmark and task format for high-energy physics designed to test and improve agentic AI through reinforcement learning, moving beyond static task completion to open-ended optimisation with verifiable scientific rewards. Frontier reasoning models currently struggle to provide correct and complete solutions for complex high-energy physics workflows, the authors report — but they demonstrate a proof of concept in which a small language model improves its performance through reinforcement learning using automated feedback, without human intervention. Where the feedback is computable, the agent can teach itself. m:…9315

Neuroimaging shows both the promise and the limit. NIBench, a benchmark covering 56 tasks across seven neuroimaging tool ecosystems, finds that leading agents execute supplied analysis protocols nearly perfectly — but withholding procedural guidance widens the performance differences among agents, and distilled skills improve performance on acquisition tasks while giving inconsistent results on unseen tasks. The telling result is the last one: agents reproduce their reported results yet sometimes reach conclusions inconsistent with expert-derived answers. Running the protocol is solved. Judging what it means is not. m:…9312

Cancer diagnostics shows what the finished version looks like. AVA, an agentic framework for variant adjudication in cancer diagnostic sequencing, outperforms the best achievable fixed VAF and depth thresholds on both the SEQC2 DNA-seq benchmark and patient RNA-seq data, addressing the bottleneck where fixed thresholds fail to distinguish genuine mutations from artefacts in low-VAF zones. It provides auditable reasoning traces for clinical adjudication without requiring training on existing data, and runs on locally deployed open-weight models — GLM 5.3 Flash and Gemma 4 31b — for privacy-constrained clinical deployment. The pattern across the week is the same in mathematics, physics, brain scans and cancer sequencing: the agent is welcome in the lab precisely where its work can be checked, and the check is the product. m:…9308