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arxiv 2311.00007 v2 pith:YWRN4WZ5 submitted 2023-10-31 math.HO math.LO

Mathematics and the formal turn

Jeremy Avigad This is my paper
classification math.HO math.LO
keywords formalmathematicalmathematicssystemsarticleassistantsbeenbuilding
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof assistants now make it possible to encode mathematical knowledge in digital form. This article enumerates some of the ways that these and related technologies can help us do mathematics.

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  1. Axioms for physical reasoning: codifying the Seiberg--Witten solution in Lean

    hep-th 2026-07 conditional novelty 8.0

    The Seiberg–Witten SU(2) solution is formalized in Lean 4 with physical assumptions as named predicates and mathematical consequences as sorry-free theorems, demonstrating a method for auditing non-rigorous physics arguments.