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    Hironaka’s resolution of singularities theorem autoformalized in Lean

    A contributor says Resolution’s downstream Lean work no longer needs to treat the theorem as an axiom.

    Geoffrey IrvingGI
    2 Sources, 2h ago, first seen 2h ago

    TLDR

    The team says it autoformalized Hironaka’s 1964 resolution of singularities theorem in Lean. A contributor says Resolution had treated it as an axiom in its learning theory work, but the formal proof now makes downstream work unconditional. They also say downstream agents can examine the full proof.

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    2 Sources, first seen 2h ago

    Combined views

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    2 Sources, first seen 2h ago

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    2 Sources

    Geoffrey Irving@geoffreyirvingResolution of singularities is one of the major algebraic geometry tools behind the rest of Resolution's learning theory work. We've been doing Lean formalization treating it as an axiom, but a pile of tokens later it's a Lean theorem and the downstream work is unconditional. 🧵2h

    2 Sources

    Geoffrey Irving@geoffreyirvingResolution of singularities is one of the major algebraic geometry tools behind the rest of Resolution's learning theory work. We've been doing Lean formalization treating it as an axiom, but a pile of tokens later it's a Lean theorem and the downstream work is unconditional. 🧵2h