9 papers · 1 filter
An AI-Assisted Formalization of the Poincaré Conjecture
Zhiyuan Zhang, Axel Delaval, Leheng Chen +6
We present an AI-assisted Lean 4 formalization of the Poincaré conjecture. The project began with limited reusable formal infrastructure for the geometric analysis behind the proof…
Constructing Rational Curves via Jets on Projective Varieties with Non-Nef Canonical Bundle
Bin Dong, Guoxiong Gao, Bin Guo +3
We give an algebraic proof in characteristic zero of the Miyaoka--Mori criterion: every point of a curve of negative canonical degree on a smooth projective variety lies on a ratio…
Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory
Jihao Liu, Guoxiong Gao, Zeming Sun +8
Recent LLM-based mathematical reasoning agents have begun to tackle research-level problems and, in several cases, have contributed to the resolution of open problems. However, sca…
From Search to Synthesis: Training LLMs as Zero-Shot Workflow Generators
Gan Luo, Zihan Qin, Bin Dong +1
Large language models (LLMs) excel across a wide range of tasks, yet their instance-specific solutions often lack the structural consistency needed for reliable deployment. Workflo…
Hilbert-Geo: Solving Solid Geometric Problems by Neural-Symbolic Reasoning
Ruoran Xu, Haoyu Cheng, Bin Dong +1
Geometric problem solving, as a typical multimodal reasoning problem, has attracted much attention and made great progress recently, however most of works focus on plane geometry w…
Automated Conjecture Resolution with Formal Verification
Haocheng Ju, Guoxiong Gao, Jiedong Jiang +13
Recent advances in large language models have significantly improved their ability to perform mathematical reasoning, extending from elementary problem solving to increasingly capa…
LeanSearch v2: Global Premise Retrieval for Lean 4 Theorem Proving
Guoxiong Gao, Zeming Sun, Jiedong Jiang +5
Proving theorems in Lean 4 often requires identifying a scattered set of library lemmas whose joint use enables a concise proof -- a task we call global premise retrieval. Existing…
Matlas: A Semantic Search Engine for Mathematics
Haocheng Ju, Leheng Chen, Peihao Wu +2
Retrieving mathematical knowledge is a central task in both human-driven research, such as determining whether a result already exists, finding related results, and identifying his…
AI for Mathematics: Progress, Challenges, and Prospects
Haocheng Ju, Bin Dong
AI for Mathematics (AI4Math) has emerged as a distinct field that leverages machine learning to navigate mathematical landscapes historically intractable for early symbolic systems…