AI Mathematician: Towards Fully Automated Frontier Mathematical Research

• URL: http://arxiv.org/abs/2505.22451v1
• Date: Wed, 28 May 2025 15:10:37 GMT
• Title: AI Mathematician: Towards Fully Automated Frontier Mathematical Research
• Authors: Yuanhang Liu, Yanxing Huang, Yanqiao Wang, Peng Li, Yang Liu,
• Abstract summary: Large Reasoning Models (LRMs) have made significant progress in mathematical capabilities in recent times.<n>We propose AI Mathematician framework, which harnesses the reasoning strength of LRMs to support frontier mathematical research.
• Score: 7.510563191984209
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Large Reasoning Models (LRMs) have made significant progress in mathematical capabilities in recent times. However, these successes have been primarily confined to competition-level problems. In this work, we propose AI Mathematician (AIM) framework, which harnesses the reasoning strength of LRMs to support frontier mathematical research. We have identified two critical challenges of mathematical research compared to competition, {\it the intrinsic complexity of research problems} and {\it the requirement of procedural rigor}. To address these challenges, AIM incorporates two core strategies: an exploration mechanism to foster longer solution paths, and the pessimistic reasonable verification method to ensure reliability. This early version of AIM already exhibits strong capability in tackling research-level tasks. We conducted extensive experiments across several real-world mathematical topics and obtained promising results. AIM is able to autonomously construct substantial portions of proofs and uncover non-trivial insights within each research area. These findings highlight the potential of LRMs in mathematical discovery and suggest that LRM-based agent systems could significantly accelerate mathematical research in the future.

Related papers

• Accelerating Scientific Research with Gemini: Case Studies and Common Techniques [105.15622072347811]
  Large language models (LLMs) have opened new avenues for accelerating scientific research.<n>We present a collection of case studies demonstrating how researchers have successfully collaborated with advanced AI models.
  arXiv  Detail & Related papers  (2026-02-03T18:56:17Z)
• Long-horizon Reasoning Agent for Olympiad-Level Mathematical Problem Solving [65.02106674311908]
  This paper introduces Intern-S1-MO, a long-horizon math agent that conducts multi-round hierarchical reasoning.<n>By maintaining a compact memory in the form of lemmas, Intern-S1-MO can more freely explore the lemma-rich reasoning spaces.<n> Experiments show that Intern-S1-MO can obtain 26 out of 35 points on the non-geometry problems of IMO2025, matching the performance of silver medalists.
  arXiv  Detail & Related papers  (2025-12-11T15:26:28Z)
• ATLAS: A High-Difficulty, Multidisciplinary Benchmark for Frontier Scientific Reasoning [118.46980291324148]
  ATLAS is a large-scale, high-difficulty, and cross-disciplinary evaluation suite composed of approximately 800 original problems.<n>Its key features include: High Originality and Contamination Resistance, with all questions newly created or substantially adapted to prevent test data leakage.<n>Preliminary results on leading models demonstrate ATLAS's effectiveness in differentiating their advanced scientific reasoning capabilities.
  arXiv  Detail & Related papers  (2025-11-18T11:13:06Z)
• AI Mathematician as a Partner in Advancing Mathematical Discovery - A Case Study in Homogenization Theory [6.856242640393325]
  We investigate how the AI Mathematician (AIM) system can operate as a research partner rather than a mere problem solver.<n>We reveal how human intuition and machine computation can complement one another.<n>The approach leads to a complete and verifiable proof, and more broadly, demonstrates how systematic human-AI co-reasoning can advance the frontier of mathematical discovery.
  arXiv  Detail & Related papers  (2025-10-30T11:22:15Z)
• The Mathematician's Assistant: Integrating AI into Research Practice [0.0]
  This paper explores the current landscape of publicly accessible large language models (LLMs) in a mathematical research context.<n>We propose a framework for integrating AI into the research workflow, centered on the principle of the augmented mathematician.<n>We conclude that the primary role of AI is currently augmentation rather than automation.
  arXiv  Detail & Related papers  (2025-08-27T19:33:48Z)
• Revisiting Multi-Agent Debate as Test-Time Scaling: A Systematic Study of Conditional Effectiveness [50.29739337771454]
  Multi-agent debate (MAD) approaches offer improved reasoning, robustness, and diverse perspectives over monolithic models.<n>This paper conceptualizes MAD as a test-time computational scaling technique, distinguished by collaborative refinement and diverse exploration capabilities.<n>We conduct a comprehensive empirical investigation comparing MAD with strong self-agent test-time scaling baselines on mathematical reasoning and safety-related tasks.
  arXiv  Detail & Related papers  (2025-05-29T01:02:55Z)
• RealMath: A Continuous Benchmark for Evaluating Language Models on Research-Level Mathematics [21.453837660747844]
  Existing benchmarks for evaluating mathematical reasoning in large language models (LLMs) rely primarily on competition problems, formal proofs, or artificially challenging questions.<n>We introduce RealMath, a novel benchmark derived directly from research papers and mathematical forums that assesses LLMs' abilities on authentic mathematical tasks.
  arXiv  Detail & Related papers  (2025-05-18T23:32:46Z)
• A Survey of Efficient Reasoning for Large Reasoning Models: Language, Multimodality, and Beyond [88.5807076505261]
  Large Reasoning Models (LRMs) have demonstrated strong performance gains by scaling up the length of Chain-of-Thought (CoT) reasoning during inference.<n>A growing concern lies in their tendency to produce excessively long reasoning traces.<n>This inefficiency introduces significant challenges for training, inference, and real-world deployment.
  arXiv  Detail & Related papers  (2025-03-27T15:36:30Z)
• Challenging the Boundaries of Reasoning: An Olympiad-Level Math Benchmark for Large Language Models [86.45058529521258]
  OlymMATH is a novel Olympiad-level mathematical benchmark designed to rigorously test the complex reasoning capabilities of LLMs.<n>OlymMATH features 200 meticulously curated problems, each manually verified and available in parallel English and Chinese versions.
  arXiv  Detail & Related papers  (2025-03-27T11:20:17Z)
• Evaluating Mathematical Reasoning Across Large Language Models: A Fine-Grained Approach [15.960271016276447]
  We present a systematic evaluation of mathematical reasoning abilities across eight leading Large Language Models (LLMs)<n>Our analyses reveal several key findings: DeepSeek-R1 performs competitively with o1 across most domains and achieves the highest accuracy on the MMLU Formal Logic benchmark.<n>We explore how architectural choices, training paradigms, and optimization strategies contribute to variation in reasoning performance.
  arXiv  Detail & Related papers  (2025-03-13T17:23:45Z)
• Large Language Models Post-training: Surveying Techniques from Alignment to Reasoning [185.51013463503946]
  Large Language Models (LLMs) have fundamentally transformed natural language processing, making them indispensable across domains ranging from conversational systems to scientific exploration.<n>These challenges necessitate advanced post-training language models (PoLMs) to address shortcomings, such as restricted reasoning capacities, ethical uncertainties, and suboptimal domain-specific performance.<n>This paper presents the first comprehensive survey of PoLMs, systematically tracing their evolution across five core paradigms: Fine-tuning, which enhances task-specific accuracy; Alignment, which ensures ethical coherence and alignment with human preferences; Reasoning, which advances multi-step inference despite challenges in reward design; Integration and Adaptation, which
  arXiv  Detail & Related papers  (2025-03-08T05:41:42Z)
• Mathematics and Machine Creativity: A Survey on Bridging Mathematics with AI [14.825293189738849]
  This paper presents a comprehensive overview on the applications of artificial intelligence (AI) in mathematical research.<n>Recent developments in AI, particularly in reinforcement learning (RL) and large language models (LLMs), have demonstrated the potential for AI to contribute back to mathematics.<n>This survey aims to establish a bridge between AI and mathematics, providing insights into the mutual benefits and fostering deeper interdisciplinary understanding.
  arXiv  Detail & Related papers  (2024-12-21T08:58:36Z)
• Formal Mathematical Reasoning: A New Frontier in AI [60.26950681543385]
  We advocate for formal mathematical reasoning and argue that it is indispensable for advancing AI4Math to the next level.<n>We summarize existing progress, discuss open challenges, and envision critical milestones to measure future success.
  arXiv  Detail & Related papers  (2024-12-20T17:19:24Z)
• A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challenges [25.82535441866882]
  This survey provides the first comprehensive analysis of mathematical reasoning in the era of multimodal large language models (MLLMs)<n>We review over 200 studies published since 2021, and examine the state-of-the-art developments in Math-LLMs.<n>In particular, we explore multimodal mathematical reasoning pipeline, as well as the role of (M)LLMs and the associated methodologies.
  arXiv  Detail & Related papers  (2024-12-16T16:21:41Z)
• Assessing the Creativity of LLMs in Proposing Novel Solutions to Mathematical Problems [9.162206328913237]
  This study explores the creative potential of Large Language Models (LLMs) in mathematical reasoning. We introduce a novel framework and benchmark, CreativeMath, which encompasses problems ranging from middle school curricula to Olympic-level competitions. Our experiments demonstrate that, while LLMs perform well on standard mathematical tasks, their capacity for creative problem-solving varies considerably.
  arXiv  Detail & Related papers  (2024-10-24T00:12:49Z)
• OlympicArena: Benchmarking Multi-discipline Cognitive Reasoning for Superintelligent AI [73.75520820608232]
  We introduce OlympicArena, which includes 11,163 bilingual problems across both text-only and interleaved text-image modalities.<n>These challenges encompass a wide range of disciplines spanning seven fields and 62 international Olympic competitions, rigorously examined for data leakage.<n>Our evaluations reveal that even advanced models like GPT-4o only achieve a 39.97% overall accuracy, illustrating current AI limitations in complex reasoning and multimodal integration.
  arXiv  Detail & Related papers  (2024-06-18T16:20:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.