Junyi Zhang

Eric Jiang, Xiao Liang, Yikai Zhang et al.

Recent developments in AI for Mathematics (AI4Math), especially Large Language Model (LLM)-driven theorem provers, has achieved remarkable success in formal proof generation for well-defined mathematical problems through Interactive Theorem Proving (ITP) languages. However, current systems remain fundamentally limited in tackling frontier research mathematics, such as discovering new theorems or resolving open conjectures, which are often open-ended, under-specified, and involve multiple layers of abstraction. We argue that the next leap in AI4Math systems requires a decisive shift from predefined problem-solvers to research agents that can address frontier mathematical challenges with rigorous formal mathematical reasoning. In this position paper, we provide a systematic review of the field, covering datasets, auto-formalization, and proof synthesis. More importantly, we identify core limitations of existing systems in serving as mathematical research agents, examining issues across datasets, relational structure, mathematical exploration, tool ecosystem, and human-AI collaboration, outlining a strategic road-map for the future of AI4Math.

Zhangqian Bi, Yao Wan, Zhaoyang Chu et al.

Pre-training a language model and then fine-tuning it has shown to be an efficient and effective technique for a wide range of code intelligence tasks, such as code generation, code summarization, and vulnerability detection. However, pretraining language models on a large-scale code corpus is computationally expensive. Fortunately, many off-the-shelf Pre-trained Code Models (PCMs), such as CodeBERT, CodeT5, CodeGen, and Code Llama, have been released publicly. These models acquire general code understanding and generation capability during pretraining, which enhances their performance on downstream code intelligence tasks. With an increasing number of these public pre-trained models, selecting the most suitable one to reuse for a specific task is essential. In this paper, we systematically investigate the reusability of PCMs. We first explore three intuitive model selection methods that select by size, training data, or brute-force fine-tuning. Experimental results show that these straightforward techniques either perform poorly or suffer high costs. Motivated by these findings, we explore learning-based model selection strategies that utilize pre-trained models without altering their parameters. Specifically, we train proxy models to gauge the performance of pre-trained models, and measure the distribution deviation between a model's latent features and the task's labels, using their closeness as an indicator of model transferability. We conduct experiments on 100 widely-used opensource PCMs for code intelligence tasks, with sizes ranging from 42.5 million to 3 billion parameters. The results demonstrate that learning-based selection methods reduce selection time to 100 seconds, compared to 2,700 hours with brute-force fine-tuning, with less than 6% performance degradation across related tasks.

Alexander K Taylor, Junyi Zhang, Ethan Ji et al.

Automated theorem proving (ATP) benchmarks largely consist of problems formalized in MathLib, so current ATP training and evaluation are heavily biased toward MathLib's definitional framework. However, frontier mathematics is often exploratory and prototype-heavy, relying on bespoke constructions that deviate from standard libraries. In this work, we evaluate the robustness of current ATP systems when applied to a novel definitional framework, specifically examining the performance gap between standard library problems and bespoke mathematical constructions. We introduce TaoBench, an undergraduate-level benchmark derived from Terence Tao's Analysis I, which formalizes analysis by constructing core mathematical concepts from scratch, without relying on standard Mathlib definitions, as well as by mixing from-scratch and MathLib constructions. For fair evaluation, we build an agentic pipeline that automatically extracts a compilable, self-contained local environment for each problem. To isolate the effect of definitional frameworks, we additionally translate every problem into a mathematically equivalent Mathlib formulation, yielding paired TaoBench-Mathlib statements for direct comparison. While state-of-the-art ATP models perform capably within the MathLib framework, performance drops by an average of roughly 26% on the definitionally equivalent Tao formulation. This indicates that the main bottleneck is limited generalization across definitional frameworks rather than task difficulty. TaoBench thus highlights a gap between benchmark performance and applicability, and provides a concrete foundation for developing and testing provers better aligned with research mathematics.