What is the general design of these new math solving systems? [D]
Our take
The recent wave of AI-driven mathematical proof systems, as elegantly outlined by /u/tough-dance, represents a fascinating and rapidly evolving frontier in both AI and formal mathematics. The core concept—leveraging large language models like Aster to generate LEAN code, iteratively compiling and refining it until a complete proof emerges—is surprisingly straightforward in its description, yet incredibly complex in its execution. The observation that these systems can produce proofs spanning hundreds of pages suggests a level of orchestration far beyond simply stuffing statements into a context window. It implies a sophisticated management system for "facts," intelligently piecing together smaller logical steps into a cohesive whole. We've seen similar explorations of AI's potential in code generation previously, such as the comparative analysis of Astra and Fable in Astra vs. Fable 5.1 on real ML tasks -- tradeoffs, strengths, shortcomings, highlighting the subtle but crucial differences in their capabilities. This current development builds on that foundation, pushing the boundaries of what AI can demonstrably achieve in a rigorous, logically structured domain.
What’s particularly compelling about this approach is its potential to unlock new avenues of mathematical discovery. While the challenge of composing larger ideas from smaller ones—as /u/tough-dance notes—remains significant, the iterative, compiler-driven feedback loop offers a powerful mechanism for exploration. The reliance on LEAN, a dependently typed programming language specifically designed for formal verification, provides a robust and unambiguous framework for expressing and validating mathematical statements. This contrasts sharply with the often-opaque reasoning processes of traditional AI systems. The question of hardware requirements is a valid one; training and running these models undoubtedly demands substantial computational resources. However, the potential payoff – automating aspects of mathematical reasoning and potentially uncovering new theorems – justifies continued investigation. The conversation around reproducibility in machine learning, as discussed in Reproducibility seems to be headed towards irrelevance in ML research. Is it too late?, also has implications here; ensuring the transparency and verifiability of these AI-generated proofs will be crucial for their acceptance within the mathematical community. The recent paper commitment results for AACL-IJCNLP 2026, detailed in IJCNLP-AACL 2026: Paper Commitment Results (ARR May 2026 Cycle), might offer some insight into the broader acceptance and scrutiny these types of contributions are receiving.
The significance extends beyond pure mathematics. The underlying techniques—large language models generating formal code, iterative refinement based on compiler feedback—have broad applicability to other domains requiring rigorous verification and automated reasoning. Imagine applying similar principles to software development, where AI could generate and verify code segments, or to scientific modeling, where AI could construct and validate complex simulations. The ability to translate abstract concepts into formal, verifiable representations is a powerful tool, and these mathematical proof systems represent a crucial step in that direction. The focus on the “management of facts” is particularly interesting; it suggests a need for AI systems that can not only generate content but also maintain a coherent and consistent understanding of that content over extended interactions. This is a core challenge in building truly intelligent agents, and the successes of these proof systems offer valuable lessons.
Ultimately, the question isn’t whether this is a “fool’s errand,” but rather how we can best harness this technology to augment human intelligence and accelerate the pace of discovery. The open invitation from /u/tough-dance to experiment and share ideas is a testament to the collaborative spirit driving this field. As these systems become more sophisticated, it will be crucial to develop robust methods for evaluating their outputs—not just in terms of correctness, but also in terms of originality and insight. How will we distinguish between a truly novel mathematical discovery made by an AI and a clever recombination of existing knowledge? That’s a question worth watching closely as this field continues to evolve, and one that will shape the future of both AI and mathematics.
From what I've seen online so far, the description of these systems is roughly:
They asked the model (often Aster) to generate statements in LEAN and then submit those to a LEAN compiler to be checked. Based on the results of attempting the LEAN compilation, they somehow add those statements as fact. When the full proof in LEAN compiles, the system is finished.
I can imagine trying to jam as much of a proof as possible into the context window but some of the papers these systems have produced are hundreds of pages. To me this would indicate that somehow the paper is being built piece by piece and being assembled before being submitted to LEAN. This resonates with the part of my understanding that after checking LEAN compilation there's some kind of management of "facts."
I would like to try to implement my own janky version and see if it can answer a question I have about higher dimensional geometry. I'm struggling to find a meaningful way to compose larger ideas from smaller ones. I can imagine it's relatively simple if you know what to do.
What things have you seen? Do you have any ideas you haven't seen that might be interesting to try? Is this a fool's errand because you really need huge amounts of hardware to do anything meaningful? I would welcome any thoughts or links on the matter, cheers
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