Breaking the high-degree barrier in Lehmer's problem with a human-AI discovery loop

arXiv cs.AIOctober 23, 2026en

arXiv:2610.30277v1 Announce Type: new Abstract: While artificial intelligence has made rapid progress in mathematical reasoning, many open problems depend on structure that is revealed only through large-scale computational exploration and analytical synthesis. One such example is Lehmer's problem from 1933. It asks whether the Mahler measure of an integer polynomial, which measures how far its roots stray from the unit circle, can be made arbitrarily small. Previously, constructing irreducible polynomials with integer coefficients and small Mahler measure has been carried out systematically only for even degrees $d \le 180$. At higher degrees, Boyd's analytical one-parameter family frequent

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