AI-Verified in Lean: Polynomials Can Be Evaluated With Half the Multiplications, Decades-Old Proof Finally Published
thomasahle · x · 2026-09-11
thomasahle shares a purely mathematical result: with rational preprocessing, a monic polynomial of degree n can be evaluated in ⌊n/2⌋+1 multiplications (one more for general polynomials), beating Horner's method — e.g. a quartic needs just two multiplications. The 100-page proof sat unpublished for years until AI verified it in Lean. Now shipped with an online chain compiler, paper (arXiv:2609.06022) and GitHub code; useful for approximating exp/sin/cos and for cryptography, hashing and coding theory.
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