Contrary to the "inhuman intelligence" narrative, a top mathematician observes that AI-generated proofs and their reasoning processes are very recognizable and similar to how a human mathematician would think. They are not producing incomprehensible "move 37" style solutions that are common in games like Go.

Generative AI can produce the "miraculous" insights needed for formal proofs, like finding an inductive invariant, which traditionally required a PhD. It achieves this by training on vast libraries of existing mathematical proofs and generalizing their underlying patterns, effectively automating the creative leap needed for verification.

A significant but underappreciated strength of AI in math is its ability to perfectly execute the minute details of an idea. While humans get lost in the 'epsilon smaller than delta' complexities, AI systems consistently and correctly handle these finicky arguments, which is often the primary barrier to proving a result.

Reinforcement learning incentivizes AIs to find the right answer, not just mimic human text. This leads to them developing their own internal "dialect" for reasoning—a chain of thought that is effective but increasingly incomprehensible and alien to human observers.

An OpenAI model, without any specific mathematical training, solved a famous 80-year-old math problem. This proves general-purpose AI can autonomously produce landmark scientific results, not just accelerate human research. It signals a new era for discovery where AI is a primary research agent.

A common fear is that AIs will produce billion-line proofs of theorems without offering human insight. However, an alternative and perhaps more likely future is that their superhuman capabilities will be applied to explanation. They could take complex, human-incomprehensible proofs and find novel ways to make them intuitive and easy to understand.

Contrary to fears of AI producing thousand-page, unreadable proofs, its current mathematical breakthroughs are often short, elegant, and human-like. The reasoning traces read like a colleague's thought process, making the solutions understandable and building confidence that the AI is not just guessing but reasoning cogently.

Unlike human mathematicians who give up on ideas after weeks of tedious work, AI models are relentlessly dogged. They will execute on a given approach without the human bias of judging it as unlikely or not worth the time, leading to breakthroughs in problems where the solution required immense, finicky detail work.

An internal, general-purpose OpenAI model solved a famous combinatorial geometry problem without specialized training or scaffolding. Unlike task-specific AIs, this achievement demonstrates a significant advance in abstract reasoning, suggesting models are progressing towards more general intelligence faster than anticipated.