计算数学研究者终于有了能自动跑实验、找反例的 AI 助手——Iteris 直接参与开放问题攻关，做数值算法或优化理论的团队值得关注。
Iteris 是一个专为计算数学开放问题设计的智能体研究系统，能自动生成数值实验、构造反例和证明草稿。在 Simons Workshop 的两个开放问题上，Iteris 产出了经专家验证的成果：一是共轭梯度法与随机坐标下降法在幂律谱下的渐近比较相图，二是证明 QR 分解列主元法在低相干性下仍可能失败。研究表明，智能体系统可参与计算数学研究流程，但人类验证仍不可或缺。
Iteris: Agentic Research Loops for Computational Mathematics
Recent advances in large language models and agentic AI systems have enabled significant progress in mathematical discovery, from solving competition problems to tackling research-level conjectures. However, open problems in computational mathematics have received comparatively less attention: research in this area often requires not only proofs but also numerical experimentation, adversarial constructions, and algorithm design. In this paper, we introduce an agentic research system, Iteris, designed for open problems in computational mathematics. We apply Iteris to two open problems from a recent Simons Workshop collection (arXiv:2602.05394). In these case studies, Iteris generated numerical evidence, constructions, and proof drafts that led, after expert review and correction, to verified results. The first result is a phase diagram for the asymptotic comparison between conjugate gradient and randomized coordinate descent on power-law spectra; the second is a counterexample showing that QR factorization with column pivoting can fail to select well-conditioned submatrices even under low coherence. These case studies suggest that agentic AI systems can participate meaningfully in research workflows for open problems in computational mathematics, while human validation remains essential.