数学前沿

The EWM has released a statement on ‘[AI and the profession](https://www.europeanwomeninmaths.org/ewm-statement-on-ai-and-the-profession/)‘. They are welcoming anyone who would like to help to join working groups, and urge the need for better representation in the current debates on AI and mathematics.

In [this essay,](https://vislumbres.github.io/#/post/raw-mathematics) Rivera advocates for ‘raw mathematics’, a culture that is more collaborative and is driven by genuine understanding and curiosity rather than prestige and productivity. Rivera draws inspiration from [Art Brut](https://artbrut.ch/en/what-is-raw-art), whose artists “forge a universe for their own use”. This is the first post on a new communal blog ‘[Vislumbres](https://vislumbres.github.io/#/)‘, which will not be exclusively focused only on AI and Mathematics, but will include accessible expositions across different fields about themes that usually don’t make it beyond academic circles.

[Tim Gehrunger](https://people.math.ethz.ch/~timge/) has created this [GitHub repository](https://github.com/GTimG/QuasiRiemannTracker) and [website](https://gtimg.github.io/QuasiRiemannTracker/) to track the best known zero-free region for the Riemann Zeta Function. The fact that there are no zeroes for $\operatorname{Im}(z) > 1$ is classical; OpenAI’s big breakthrough was reducing this to $\frac{7}{8}$, which has since been reduced slightly. We’re waiting for $\frac{1}{2}$, get to work everyone! Similarly, [OpenAI provided](https://github.com/openai/math/blob/main/preprints/Integer-multiplication-below-n-log-n-September-23-2026/paper.pdf) a deterministic algorithm to multiply two $n$\-bit integers in $O(n(\log n)^{1-\kappa})$ steps, with an absurdly small $\kappa$. [This website](https://beyond-n-log-n.netlify.app/) and [GitHub](https://github.com/CrocSwap/integer-mult-bounds) track the best improvements on $\kappa$ (at least in some instances).

[This website](https://curticapean.net/math-notes/) documents OpenAI’s claimed solutions, and related activities in the mathematical community at the time. Ir provides related preprints, comments by researches, and additional discussion; and anyone can comment contributions. A related initiative is the website [citedbyagi.com](https://citedbyagi.com/), which tracks every human author cited across [OpenAI’s Maths GitHub](https://openai.com/index/sharing-ai-progress-in-mathematics/) manuscripts.

To celebrate Ada Lovelace day, we've spoken to some of the brilliant women honoured at the International Congress of Mathematicians.

To celebrate Ada Lovelace day, we've spoken to some of the brilliant women honoured at the International Congress of Mathematicians.

How do you adjust your approach when new information is coming in all the time? The answer lies with Bayes Theorem.

How do you adjust your approach when new information is coming in all the time? The answer lies with Bayes Theorem.

This research was carried out by Antrhopic’s Red Team and is titled ‘[AI models may be capable of self-replicating without access to a datacenter](https://www.anthropic.com/research/self-replicating-ai)‘. As the discourse in the wider tech spheres about potential catastrophic loss-of-control scenarios escalates, expect to see more research of this sort.

OpenAI publishes new results on open problems in mathematics from an internal frontier model and shares Lean proof formalizations and research details on GitHub.

OpenAI is working with an independent Advisory Group on Mathematics and Artificial Intelligence to guide the review and communication of emerging AI results.

Acknowledgments of AI use in arXiv math preprints rose from 4% in April 2026 to 25% in August, with 6% crediting AI with a substantial research contribution.

数控插补将离散刀位点转化为机床可执行的运动轨迹，其生成质量直接影响加工效率与运动稳定性。传统方法通常采用“先平滑几何路径，再规划进给速度”的两阶段策略，难以实现拐角几何形状与运动速度的最优匹配；联合优化方法能够改善这一问题，但往往面临数值求解耗时过长的瓶颈。因此，如何在满足几何公差和运动学约束的前提下，兼顾轨迹质量与规划效率，成为数控加工领域亟待解决的重要问题。 针对上述问题，计算机数学研究中心副研究员赵明阳与合作者提出了一种基于人工智能的内嵌运动学信息的强化学习框架（ Kinematics-Informed Reinforcement Learning ，简称 KIRL ）。该框架将几何平滑与进给速度规划整合为一个连续的运动状态决策过程。其核心机制是提取前瞻路径信息，预测相邻路径段交点处的位置、速度和加速度，并采用时间参数化的五次多项式作为运动基元进行平滑连接，从而在统一框架内实现了路径形状与运动速度的协同优化。 该工作将运动学信息内嵌进轨迹构造与可行性校验中，通过一维时长搜索生成满足约束的轨迹段，并以最小化总加工时间作为学习目标，引导策略减少在拐角处不必要的减速与停顿。仿真结果表明，在所测试的平面路径上，相较于经典的两阶段方法，基于该框架逐路径训练的策略可缩短 8.0% 至 22.4% 的加工时间，并显著降低了加加速度（ Jerk ）的均方根值。此外，该工作还提出一种通用训练策

OpenAI's GPT-6 Astra tops the Epoch Capabilities Index (ECI) with a score of 166, ahead of Claude Fable 5.1 at 164 and GPT-5.6 Sol at 162. Its Math-ECI of 170 sets a new record, but on software engineering benchmarks its SWE-ECI of 164 still lags behind Fable 5.1's 167.

9月15日 数学四大顶刊之一的《 Inventiones Mathematicae 》（数学新进展）又更新上线了一篇文章， 中国科学院数学与系统科学研究院的简旺键与北京大学的田刚院士、美国罗格斯大学‌宋剑合作发表了题为“ Finite time singularities of the Kähler–Ricci flow （凯勒–里奇流的有限时间奇点）”的最新重要研究成果。 该研究建立了标量曲率和距离的一致有界性结果，将 Perelman （佩雷尔曼）关于 Fano （法诺） Kähler–Ricci 流的工作推广到了 Kähler–Ricci 流的一般有限时间解。这些有界性结果是通过三位作者对 Kähler–Ricci 流的加权 Ricci 势函数所建立的 Li–Yau （李伟光-丘成桐）型估计和 Harnack 估计得到的。 研究进一步证明，在选取合适的基点后，该有限时间解的I型爆破（ blow-ups ）总是在 Gromov–Hausdorff 意义下子收敛到一族解析正规簇上的一个古老解。作为推论，对于该纤维化的正则底流形上每个相对紧开子集上的纤维，都满足I型直径界。研究还应用这些估计证明，所有具有 Calabi 对称性的 Kähler–Ricci 流，必然会演化出I型奇点，包括高余维收缩和纤维塌缩两种情形。 该研究通过发展的新估计工具，首次将法诺 Kähler-Ricci