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Explore a 28-minute conference talk from CPP 2025 where researchers Anne Baanen, Alain Chavarri Villarello, and Sander R. Dahmen present their work on formalizing the certification of rings of integers in number fields using Lean 4. Learn how they developed computational data types and formalized key mathematical concepts including resultants, discriminants, and methods for proving polynomial irreducibility over finite fields and rational numbers. The presentation demonstrates how they formally verified entries from the L-functions and modular forms database (LMFDB) by creating SageMath code that generates Lean proofs to verify integral bases and discriminants of number fields. This talk showcases the intersection of formalized mathematics, algebraic number theory, and computational verification techniques, with supplementary materials available through Zenodo.
