- The dual agent AI system independently solved Anderson’s 2014 conjecture
- Rethlas explores problem-solving strategies as a human mathematician would
- Archon turns potential evidence into projects for the Lean 4 verifier
A research team led by Peking University developed a dual-agent AI system capable of solving advanced mathematical problems while verifying its own results.
The system solved a conjecture proposed in 2014 by Dan Anderson, completing the process within 80 hours of driving.
“Using this framework, we successfully solved an open problem in commutative algebra and automatically formalized the proof with essentially no human intervention,” the researchers wrote in a preprint paper published on arXiv.
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How the dual-agent framework actually works
The AI tool uses a reasoning system called Rethlas, which draws from a mathematical theorem search engine called Matlas to explore problem-solving strategies.
When Rethlas produces a potential proof, another system called Archon uses another search engine called LeanSearch to turn that proof into a project for an interactive theorem prover.
The theorem prover, Lean 4, is also a programming language with a community-maintained library containing hundreds of thousands of theorems and definitions.
The researchers noted that no mathematical judgment was required from the human operator during the problem-solving process.
The AI system performed mathematical tasks faster than any human, including independently doing work that would normally require collaboration between experts in different fields.
However, the team also found that a mathematician could speed up the process by guiding the Archon when needed.
“This work provides a concrete example of how mathematical research can be significantly automated using AI,” the researchers said.
Mathematical proofs require complete rigor, but even expertly written proofs can contain subtle errors.
Similarly, proofs produced by large language models are prone to hallucinating and are far less reliable than formal verification methods.
The Chinese team’s framework bridges the gap between natural language reasoning and formal machine verification, enabling the AI system to both solve problems and verify its own results.
“Our work illustrates a promising paradigm for mathematical research in which informal and formal reasoning systems work in tandem to produce verifiable results,” the researchers noted.
The paper has not yet been peer-reviewed by experts, so independent verification is still pending.
Anderson’s conjecture was a relatively obscure problem in commutative algebra, which makes the AI’s achievement remarkable.
However, this feat does not compare to solving a millennium premium level challenge like the Riemann Hypothesis or the P vs NP problem.
Whether this approach scales to more difficult mathematical problems remains to be seen.
That said, for a field that has resisted automation for centuries, this represents a remarkable milestone.
Via The independent
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