In recent decades, a growing number of discoveries in fields of mathematics have been assisted by computer algorithms, primarily for exploring large parameter spaces that humans would take too long to investigate. As computers and algorithms become more powerful, an intriguing possibility arises - the interplay between human intuition and computer algorithms can lead to discoveries of novel mathematical concepts that would otherwise remain elusive. To realize this perspective, we have developed a massively parallel computer algorithm that discovers an unprecedented number of continued fraction formulas for fundamental mathematical constants. The sheer number of formulas discovered by the algorithm unveils a novel mathematical structure that we call the conservative matrix field. Such matrix fields (1) unify thousands of existing formulas, (2) generate infinitely many new formulas, and most importantly, (3) lead to unexpected relations between different mathematical constants, including multiple integer values of the Riemann zeta function. Conservative matrix fields also enable new mathematical proofs of irrationality. In particular, we can use them to generalize the celebrated proof by Ap\'ery for the irrationality of $\zeta(3)$. Utilizing thousands of personal computers worldwide, our computer-supported research strategy demonstrates the power of experimental mathematics, highlighting the prospects of large-scale computational approaches to tackle longstanding open problems and discover unexpected connections across diverse fields of science.

翻译：近几十年来，计算机算法辅助的数学发现日益增多，主要用于探索人类耗时过久的大规模参数空间。随着计算机与算法能力的提升，一种引人入胜的可能性逐渐浮现——人类直觉与计算机算法的相互作用可催生对全新数学概念的发现，这些概念原本将难以被人类所察觉。为实现这一愿景，我们开发了一种大规模并行计算机算法，该算法为基本数学常数发现了数量空前的连分式公式。算法发现的庞大数据集揭示了一种新颖的数学结构，我们称之为保守矩阵场。这类矩阵场能够：（1）统一数千个现有公式，（2）生成无穷多个新公式，更重要的是（3）推导出不同数学常数之间的意外关联，包括黎曼ζ函数的多个整数值。保守矩阵场还能实现无理性的新型数学证明。特别地，借助该结构可推广阿佩里对ζ(3)无理性的著名证明。通过整合全球数千台个人计算机，我们的计算机辅助研究策略展示了实验数学的威力，凸显了大规模计算方法在攻克长期未解难题及发现科学领域间意外关联方面的前景。