arXiv subjects

Wenze Su

Publications and source records attributed to Wenze Su.

3 recordsLinked to original sources

arXiv2026

Code2Math: Can Your Code Agent Effectively Evolve Math Problems Through Exploration?

As large language models (LLMs) advance their mathematical capabilities toward the IMO and research level, the scarcity of challenging, high-quality problems has become a significant bottleneck for training, evaluation and self-evolution of LLMs. Simultaneously, recent code agents have demonstrated sophisticated skills in agentic coding and reasoning, suggesting that code execution can serve as a scalable environment for mathematical experimentation. In this paper, we investigate the potential of code agents to autonomously evolve existing math problems into more complex variations. We introduce a multi-agent framework designed to perform problem evolution while validating the solvability and increased difficulty of the generated problems. Our experiments demonstrate that, given sufficient test-time exploration, code agents can synthesize new, solvable problems that are structurally distinct from and more challenging than the originals. This work provides empirical evidence that code-driven agents can serve as a viable mechanism for synthesizing high-difficulty mathematical reasoning problems within scalable computational environments. Code and data is available at https://github.com/TarferSoul/Code2Math.

cs.CL↗

arXiv2025

Shock Formation for Compressible Euler Equations on $\mathbb{S}^2$

In this paper, we prove the finite-time shock formation for the compressible Euler equations on the two-dimensional sphere $\mathbb{S}^2$. In contrast to the flat Euclidean case $\mathbb{R}^2$, the geometry of $\mathbb S^2$ imposes new difficulties, and the fluid dynamics are affected by the curved background. To overcome these challenges, we modify the existing modulation method and employ a set of carefully constructed, time-dependent coordinates that precisely track the shock formation on $\mathbb{S}^2$. In particular, we first perform a time-dependent rotation of $\mathbb S^2$, then apply the stereographic projection to the sphere, straighten the steepening shock front, and finally construct shock-adapted coordinates. In the shock-adapted coordinates, the compressible Euler equations on $\mathbb{S}^2$ can be recast into a form suitable for self-similar analysis. Within this framework, we implement a detailed bootstrap argument and establish global well-posedness for the self-similar system. After transferring these results back to the original physical system, we thereby demonstrate the finite-time shock formation on $\mathbb{S}^2$.

math.AP↗

arXiv2023

Shock formation for 2D Isentropic Euler equations with self-similar variables

We study the 2D isentropic Euler equations with the ideal gas law. We exhibit a set of smooth initial data that give rise to shock formation at a single point near the planar symmetry. These solutions are associated with non-zero vorticity at the shock and have uniform-in-time 1/3-Hölder bound. Moreover, these point shocks are of self-similar type and share the same profile, which is a solution to the 2D self-similar Burgers equation. Our proof, following the 3D shock formation result of Buckmaster, Shkoller and Vicol, is based on the stable 2D self-similar Burgers profile and the modulation method.

math.AP↗