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AI for Math Book Club – Season 2, Episode 6

November 7, 2026 · · 28 min read · 2 views

Series | AI for Math Book Club Season 2 Issue 6

Published: July 11, 2026 12:04 AM
Source column: MirrorSpeed CN
Original site: WeChat Official Account – Jizhi Club

Summary

Lead: How artificial intelligence is changing the ways and paradigms of mathematical research. This issue is the sixth session of the AI for Math Book Club Season 2, where Dr. Zhu Taoyu from Peking University Biomedical Frontier Innovation Center will review large models, reinforcement learning, and mathematical intelligence.

Introduction

How artificial intelligence is changing the way and paradigm of mathematical research. This issue is the 6th session of the second season of the AI for Math reading group. Dr. Zhu Taoyu from Peking University’s Biomedical Frontier Innovation Center will outline the technical foundations of large models, reinforcement learning, and mathematical agents, examine how AI moves from problem‑solving assistance to research‑level exploration, discuss formalization and semantic consistency using the Navier‑Stokes equations as an example, and finally address human‑machine collaboration and responsibility boundaries.

To systematically review the latest advances of AI in science and mathematics, JiZhi Club, together with Associate Professor Chen Xiaoyang, a tenured faculty member at Tongji University’s School of Mathematical Sciences, and Associate Researcher Zhuge Changjing from the School of Mathematics, Statistics and Mechanics at Beijing University of Technology, jointly launched the “Artificial Intelligence and Mathematics” Reading Group Season 2. It brings together researchers and explorers interested in this topic to jointly study cutting‑edge literature and exchange research ideas.

The reading group will start on September 22, 2026, and will be held online every Tuesday from 19:30 to 21:30 for 8–10 weeks, featuring a main presentation, sharing, and discussion, with video recordings provided afterward. We sincerely invite researchers in related fields and those with interdisciplinary interests to participate.

Report Overview

This talk focuses on “Mathematics Development in the AI Era,” exploring how artificial intelligence is changing the ways and paradigms of mathematical research. It first introduces the technical foundations of mathematical AI, including large language models, reinforcement learning, formal proof, and the operating mechanisms of mathematical agents; then, drawing on Terence Tao’s research perspectives, First Proof, and OpenAI’s collection of mathematical results, it analyzes the shift of AI from problem‑solving assistance to research‑level mathematical exploration; next, using the Navier–Stokes equations as a core case study, it discusses the relationship among formalization of mathematical statements, proof verification, and semantic consistency; it further presents related case studies by Shing‑Tung Yau and the development of mathematical agents both domestically and internationally; finally, it summarizes the new workflow of mathematical research in the AI era, human‑AI collaboration models, responsibility boundaries, and future directions.

Sharing Outline

Fundamentals of Math AI Technology: Large Models, Reinforcement Learning, and Mathematical Agents
AI from Assisted Problem Solving to Research-Level Exploration: Views of Terence Tao and Others
N‑S Equation: Formalization, Verification, and Semantic Consistency Relations
Shing‑Tung Yau Research Case and the Development of Mathematical Agents Domestically and Internationally
Summarizing New AI Mathematics Workflows, Human‑Machine Collaboration, and Responsibility Boundaries

Core Concepts

Mathematical Agent (Mathematical Intelligent Agent): A system that can autonomously plan around mathematical tasks, invoke tools, perform searches, verify results, and iteratively refine them.
Symbolic Reasoning: Derivation based on explicit mathematical rules and logical relationships, with strict rule constraints.
Formal Proof: Transforming mathematical propositions and proofs into a rigorous formal language so that they can be logically checked by a computer.
Lean: An interactive theorem-proving system that verifies formal statements and their proof objects through type checking.
Proof Search: Exploring different derivation paths among existing assumptions, lemmas, and goals to find a complete proof.
Proposition as Type (Curry–Howard Correspondence):Corresponds mathematical propositions to types, treating a proof of a proposition as a concrete instance of that type.
Semantic Fidelity:Checks whether a formal expression faithfully represents the original mathematical problem, including objects, assumptions, quantifiers, and conclusions.
Countermodel:Constructs a mathematical structure that satisfies the premises but not the conclusion, used to refute universal statements.
Proof Dependency Graph:Records the dependency relationships among theorems and lemmas, helping trace proof errors and their impact scope.
Verifiability: Whether mathematical results can obtain reliable evidence through formal checking, computational certificates, or independent review.
Reproducibility: By fixing code, tool versions, dependencies, and execution logs, research results can be re‑examined.
Goodhart’s Law: When a metric becomes an optimization target, it may gradually lose its ability to measure true value. This report uses this to argue that the value of mathematical research cannot be simply measured by the number of AI‑solved problems.

Speaker Introduction

Speaker:Zhu Taoyu, Ph.D. at Peking University Biomedical Frontier Innovation Center, undergraduate from Zhejiang University. Research interests: computational biology, algebraic topology, Riemannian geometry. My research focuses on discovering biological targets through data integration modeling and analyzing geometric structures in biological data for related modeling and theoretical proof. Beyond my main research areas, I enjoy studying variable quantization and Korean pop music; I have been a Buddy (GFRIEND fan) for 11 years and a Na.V (VIVIZ) fan for 4 years, and I am a half‑marathon elite recreational runner with a PB of 1:22:39.

References

[1] Tao, T. (2026). Mathematics in the Age of AI. arXiv:2608.16753.

Shifts from “Can AI do mathematics?” to “What mathematics truly values in the AI era,” emphasizing the importance of understanding, structure, and knowledge organization.

[2] Klowden, T., & Tao, T. (2026). Mathematical Methods and Human Thought in the Age of AI. arXiv:2603.26524.

Discusses how AI expands mathematical thinking from the perspective of cognition and tool evolution, and reshapes human‑machine collaboration.

[3] Abouzaid, M., Srivastava, N., Ward, R., & Williams, L. (2026). First Proof Second Batch. arXiv:2606.18119.

Evaluating AI capabilities on real research problems, providing empirical background for “AI entering research-level mathematics.”

[4] Hubert, T., Mehta, R., Sartran, L., et al. (2026). Olympiad-level formal mathematical reasoning with reinforcement learning. Nature, 651, 607–613.

AlphaProof is a representative work, showcasing rapid progress of AI in formal mathematical reasoning and automated verification.

[5] Thurston, W. P. (1994). On proof and progress in mathematics. Bulletin of the American Mathematical Society, 30(2), 161–177.

Classic discussions of mathematical progress focus not only on proofs but also on forming and disseminating mathematical understanding, which resonates strongly with debates in the AI era.

[6] Yao, Z., & Su, J. (2026). Manifold fitting: A review of methods and applications. Harvard Data Science Review, 8(3).

A systematic review of manifold fitting theory, clarifying its differences from dimensionality reduction, embedding, and denoising, serves as an important overview for understanding data geometry discovery.

[7] Fefferman, C., Ivanov, S., Kurylev, Y., Lassas, M., & Narayanan, H. (2018). Fitting a putative manifold to noisy data. Proceedings of Machine Learning Research, 75, 688–720.

It establishes a crucial theoretical foundation for recovering underlying manifolds and their geometric properties from finite noisy high‑dimensional samples.

[8] Yao, Z., & Xia, Y. (2025). Manifold fitting under unbounded noise. Journal of Machine Learning Research, 26(45), 1–55.

Extends manifold fitting to unbounded noise settings, providing statistical guarantees for stable geometric recovery in real-world data.

[9] Whiteley, N., Gray, A., & Rubin-Delanchy, P. (2026). Statistical exploration of the manifold hypothesis. Journal of the Royal Statistical Society Series B, 88, 353–385.

Explains why high-dimensional data naturally exhibit low-dimensional manifold structure from a statistical generative perspective, providing theoretical foundations for “discovering mathematical structure from data.”

Time Information

⏰ Time: November 8, 2026 (Sunday) 10:00-12:00

📍 Online: Tencent Meeting

If you’re interested, please scan the QR code to sign up for the reading club; after registering, you can join the participants group for discussions.

Sign up for the reading club: AI for Math

To clarify the opportunities and limitations of AI in the fields of science and mathematics, the JiZhi Club, together with Associate Professor Chen Xiaoyang, a tenured faculty member at Tongji University’s School of Mathematical Sciences, and Associate Researcher Zhuge Changjing from the School of Mathematics, Statistics, and Mechanics at Beijing University of Technology, jointly launched“Artificial Intelligence and Mathematics” Book Club Season 2. The group brings together researchers and explorers interested in this topic to study cutting‑edge literature and exchange research ideas.

The book club will run online every Tuesday from 19:30 to 21:30 starting September 22, 2026, for 8–10 weeks, featuring presentations, discussions, and post‑session video recordings. Researchers in related fields and anyone with interdisciplinary interest are warmly invited to join.

Scan the QR code in the poster to sign up for the reading club

Registration Method

Step 1: Scan the WeChat QR code to fill in the registration information.

(Scan QR code to register)

Step 2: Fill in the information and register with payment. If you need to pay with Alipay, please go to the reading group page on a PC to register and pay:

https://pattern.swarma.org/mobile/study_group/91?from=wechat

Step 3: Add the operations assistant on WeChat and be added to the reading group community (WeChat group) for the corresponding topic.

PS:

To maintain the professionalism and focus of academic exchange, this reading group sets the following guidelines for discussion content:

We encourage in‑depth discussions centered onmathematics, artificial intelligence, complex scienceand related specific issues. To ensure the quality of the discussion, please avoid posting content that deviates from the theme of this reading group, lacks empirical basis, or is overly abstract philosophical speculation.

If the discussion clearly strays from the topic and does not adjust after a reminder from the moderator, we will have to remove that member from the discussion group to maintain a healthy learning environment, and proportionally refund the portion of the fee corresponding to the unparticipated sessions based on their actual participation.

Thank you for your understanding and cooperation. Let’s work together to create a focused, deep, and rewarding shared learning space.

Join the community to access core resources

Become a member to unlock the full learning ecosystem, including:live Q&A sessions, on‑demand recordings of all courses, exclusive material sharing, high‑quality community interaction, first‑hand information updates, and the ability to earn points byparticipating in co‑creation tasks among other benefits.

Special Refund and Incentive Mechanism

We offer the following two avenues for your investment to receive tangible returns:

Task Completion Refund Path

Claim and successfully complete any two subtitle tasks, and you will receive a full refund of the registration fee, plus an exclusive JiZhi merchandise reward.

Operational Growth Incentive Path

After successfully completing a subtitle task, you can apply to become an Operations Assistant. Once the reading club project is completed successfully, the tuition fee will be refunded. Outstanding performers also have the chance to receive additional scholarships.

AI for Math Book Club – Season 2, Episode 6