Fuchen Shen

Yuliang Ji, Fuchen Shen, Jian Wu et al.

To comprehensively evaluate the mathematical reasoning capabilities of Large Language Models (LLMs), researchers have introduced abundant mathematical reasoning datasets. However, most existing datasets primarily focus on linear reasoning, neglecting other parts such as proof by contradiction and proof by cases, which are crucial for investigating LLMs' reasoning abilities. To address this limitation, we first introduce a novel first-order logic (FOL) dataset named PC-FOL, annotated by professional mathematicians, focusing on case-based reasoning problems. All instances in this dataset are equipped with a manually written natural language proof, clearly distinguishing it from conventional linear reasoning datasets. Our experimental results over leading LLMs demonstrate a substantial performance gap between linear reasoning and case-based reasoning problems. To further investigate this phenomenon, we provide a theoretical analysis grounded in graphical model, which provides an explanation for the observed disparity between the two types of reasoning problems. We hope this work can reveal the core challenges in the field of automated natural language mathematical proof generation, paving the way for future research.

Qiujie Xie, Yixuan Weng, Minjun Zhu et al.

The emergence of large language models (LLMs) is propelling automated scientific discovery to the next level, with LLM-based Artificial Intelligence (AI) Scientist systems now taking the lead in scientific research. Several influential works have already appeared in the field of AI Scientist systems, with AI-generated research papers having been accepted at the ICLR 2025 workshop, suggesting that a human-level AI Scientist capable of uncovering phenomena previously unknown to humans, may soon become a reality. In this survey, we focus on the central question: How far are AI scientists from changing the world and reshaping the scientific research paradigm? To answer this question, we provide a prospect-driven review that comprehensively analyzes the current achievements of AI Scientist systems, identifying key bottlenecks and the critical components required for the emergence of a scientific agent capable of producing ground-breaking discoveries that solve grand challenges. We hope this survey will contribute to a clearer understanding of limitations of current AI Scientist systems, showing where we are, what is missing, and what the ultimate goals for scientific AI should be.