AI models advanced in pure mathematics faster than in theoretical physics because math offers self-contained verification methods. This immediate, objective feedback loop makes mathematical proof search ideal for reinforcement learning, whereas evaluating theoretical physics requires external, less formalized criteria.

Languages like Lean allow mathematical proofs to be automatically verified. This provides a perfect, binary reward signal (correct/incorrect) for a reinforcement learning agent. It transforms the abstract art of mathematics into a well-defined environment, much like a game of Go, that an AI can be trained to master.

Unlike natural language proofs that require human verification, formal systems like Lean allow for automated, verifiable rewards. This could enable an AI to endlessly extend a mathematical library like Mathlib, exploring a vast tree of logic and potentially discovering novel theories without any human check-ins, similar to how AlphaGo trained itself by playing millions of games.

Reinforcement learning with verifiable rewards allows models to achieve super-human mathematical and coding performance rapidly, because outcomes can be objectively checked in simulated environments. In contrast, progress in non-verifiable domains advances much slower because improvement remains tethered to human data generation bottlenecks. The resulting jagged intelligence frontier creates super-intelligence within narrow formal environments while general capabilities lag behind.

AI is excelling at solving formal math problems because they are "clean" and lack real-world complexities. This success may not translate directly to fields like biomedicine or material science, which are hampered by messy data, measurement uncertainty, and necessary simplifications—challenges that abstract mathematics doesn't face.

Current AI models struggle to reliably verify their own mathematical steps. To establish trustworthy proofs, researchers now pair large language models with separate formal software like the Lean language, which verifies the logical validity of generated code against strict mathematical axioms.

Unlike medicine or biology, which require messy, expensive real-world experiments, pure mathematics offers a cost-effective and prestigious arena for AI labs to demonstrate their models' abstract reasoning power. A proof is a proof, requiring no lab work or physical trials to validate.

Friedberg and Sacks explain that AI advances much faster in mathematics and software engineering because their reasoning loops are completely testable in software. Unlike biology or logistics, these disciplines require no physical lab testing or human-in-the-loop validation, enabling continuous automated reinforcement learning.

Unlike math or code with cheap, fast rewards, clinically valuable biology problems lack easily verifiable ground truths. This makes it difficult to create the rapid reinforcement learning loops that drive explosive AI progress in other fields.