The most interesting tool of all: Discussion Partner: A tool which “empowers Claude Code with the ability to ’seek assistance’ during Lean formalization: when encountering obstacles—such as proof bottlenecks, dilemmas in strategy selection, or ambiguities in intermediate lemmas—the primary model can proactively initiate discussions with other LLMs”.
Discovering math together: Along with the Putnam demonstration, the authors also used the software as an active partner in some math work, specifically formalizing Brascamp Lieb (I will not pretend to be able to explain what this means). “Over a period of less than two weeks of intermittent collaboration, the two human experts and the agent completed the formalization of more than 8,000 lines of Lean code. During this process, the agent autonomously introduced approximately 70 new definitions, lemmas, and theorems, illustrating its ability to actively extend the formal library and participate in large-scale, sustained formalization efforts,” the authors write.
Why this matters - capability overhangs and AI ecologies: Numina-Lean-Agent neatly demonstrates two important things about contemporary AI: 1) AI systems are far more capable than people think and the creation of some specialized frameworks and tools often lets us elicit dramatically better capabilities from our systems (here, math, but it has been demonstrated in many domains )
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