Tools such as AlphaEvolve are giving mathematicians very useful new capabilities. For optimization problems in particular, we can now quickly test potential inequalities for counterexamples, or to confirm our beliefs in what the extremizers are, which greatly improves our intuition about these problems and allows us to find rigorous proofs more readily.
大多数人认为数学证明需要人类直觉和创造力,但作者认为AI工具可以显著加速数学发现过程,甚至帮助人类找到更严谨的证明。这挑战了数学研究作为纯粹人类智力活动的传统观念,暗示AI可能成为数学家的真正合作伙伴而非简单工具。