挑战AI数学推理能力，用高深公式评测其证明与发现新恒等式的能力。
The Ramanujan Challenge For AI
- 设计可精确验证的数学常数公式，用于评估AI的数学推导能力。
- 包含已知证明但暂加密的公式，以及尚未证明的开放问题。
- 适合研究符号计算、自动证明和数学发现的AI研究人员参考。
为评估当前AI系统的数学能力，我们提出一组用于基本数学常数的公式。这些问题适合AI评估，因为它们具体明确，可任意精度数值验证，但证明可能需要非平凡的数学技巧。π、e、Catalan常数及黎曼ζ函数的特殊值一直是数学家们几世纪以来的研究对象。寻找能计算这些常数的公式，催生了该领域最优美的数学成果，尤其在产生无理性证明或快速收敛率方面。拉马努金的遗产正是这一传统的典范。我们提供的列表包含两类问题：作者已知证明但短期内加密的公式；以及尚未被证明的公式。我们期待观察AI在这两类问题上的表现。
原文摘要 · Abstract (English)
To help evaluate the mathematical skills of current AI systems, we present a set of formulas for fundamental mathematical constants. These problems are attractive for AI evaluation because they are concrete and can be checked numerically to arbitrary precision, yet proving them may require non-obvious mathematics. Mathematical constants such as $π$, $e$, Catalan's constant, and special values of the Riemann zeta function have fascinated mathematicians for centuries. The search for formulas evaluating mathematical constants has produced some of the most beautiful mathematics in the field, especially in cases that yield irrationality proofs or fast convergence rates. Ramanujan's legacy is emblematic of this tradition. The list we provide contains two types of problems: formulas whose proofs are known to the authors but will remain encrypted for a short initial period; and formulas that are not yet proven. We are curious to see the achievements of AI in both cases.
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