Recent advancements in large language models, such as GPT -4, have demonstrated remarkable capabilities in processing standard queries.

Large language models have demonstrated impressive capabilities across various natural language processing tasks, especially in solving mathematical problems. However, large language models are not good at math theorem proving using formal languages like Lean. A significant challenge in this area is the scarcity of training data available in these formal languages. To address this issue, we propose a novel pipeline that iteratively generates and filters synthetic data to translate natural language mathematical problems into Lean 4 statements, and vice versa. Our results indicate that the synthetic data pipeline can provide useful training data and improve the performance of LLMs in translating and understanding complex mathematical problems and proofs. Our final dataset contains about 57K formal-informal question pairs along with searched proof from the math contest forum and 21 new IMO questions.

Recent advancements in large language models, such as GPT-4, have demonstrated remarkable capabilities in processing standard queries. Despite these advancements, their performance substantially declines in advanced mathematical problems requiring complex, multi-step logical reasoning. To enhance their inferential capabilities, current research has delved into prompting engineering, exemplified by methodologies such as the Tree of Thought and Graph of Thought.Nonetheless, these existing approaches encounter two significant limitations. Firstly, their effectiveness in tackling complex mathematical problems is somewhat constrained. Secondly, the necessity to design distinct prompts for individual problems hampers their generalizability.In response to these limitations, this paper introduces the Multi-Agent System for conditional Mining (MACM) prompting method. It not only resolves intricate mathematical problems but also demonstrates strong generalization capabilities across various mathematical contexts.With the assistance of MACM, the accuracy of GPT-4 Turbo on the most challenging level five mathematical problems in the MATH dataset increase from $\mathbf{54.68\\%}

Although demonstrating remarkable performance on reasoning tasks, Large Language Models (LLMs) still tend to fabricate unreliable responses when confronted with problems that are unsolvable or beyond their capability, severely undermining the reliability. Prior studies of LLM reliability have primarily focused on knowledge tasks to identify unanswerable questions, while mathematical reasoning tasks have remained unexplored due to the dearth of unsolvable math problems. To systematically investigate LLM reliability in mathematical reasoning tasks, we formulate the reliability evaluation for both solvable and unsolvable problems. We then develop a ReliableMath dataset which incorporates open-source solvable problems and high-quality unsolvable problems synthesized by our proposed construction workflow with human evaluations. Experiments are conducted on various LLMs with several key findings uncovered. LLMs fail to directly identify unsolvable problems and always generate fabricated responses. When instructing LLMs to indicate unsolvability using a reliable prompt, the reliability of larger-sized LLMs remains on solvable problems, but notably improves on unsolvable problems yet still falls short of solvable problems. However, small LLMs rarely show any progress despite employing reliable prompts. Therefore, we further propose an alignment strategy to enhance small LLMs' reliability, which can significantly improve LLM reliability performances on both in-domain and out-of-domain tasks.

Recent advancements in large language models, such as GPT -4, have demonstrated remarkable capabilities in processing standard queries.

Large language models (LLMs) have recently shown strong performance on mathematical benchmarks. At the same time, they are prone to hallucination and sycophancy, often providing convincing but flawed proofs for incorrect mathematical statements provided by users. This significantly limits the applicability of LLMs in theorem proving, as verification of these flawed proofs must be done manually by expert mathematicians. However, existing benchmarks that measure sycophancy in mathematics are limited: they focus solely on final-answer problems, rely on very simple and often contaminated datasets, and construct benchmark samples using synthetic modifications that create ill-posed questions rather than well-posed questions that are demonstrably false. To address these issues, we introduce BrokenMath, the first benchmark for evaluating sycophantic behavior in LLMs within the context of natural language theorem proving. BrokenMath is built from advanced 2025 competition problems, which are perturbed with an LLM to produce false statements and subsequently refined through expert review. Using an LLM-as-a-judge framework, we evaluate state-of-the-art LLMs and agentic systems and find that sycophancy is widespread, with the best model, GPT-5, producing sycophantic answers 29% of the time. We further investigate several mitigation strategies, including test-time interventions and supervised fine-tuning on curated sycophantic examples. These approaches substantially reduce, but do not eliminate, sycophantic behavior.

Existing methods usually leverage a fixed strategy, such as natural language reasoning, code-augmented reasoning, tool-integrated reasoning, or ensemble-based reasoning, to guide Large Language Models (LLMs) to perform mathematical reasoning. Our analysis reveals that the single strategy cannot adapt to problem-specific requirements and thus overlooks the trade-off between effectiveness and efficiency. To address these issues, we propose Planning and Routing through Instance-Specific Modeling (PRISM), a novel framework that decouples mathematical reasoning into two stages: strategy planning and targeted execution. Specifically, we first curate a multi-strategy preference dataset, which we call MathStrat, capturing correctness, process quality, and computational efficiency for each problem--strategy pair. Then, we train a lightweight Strategy Adapter based on the dataset to obtain confidence distributions over the mentioned four reasoning strategies. At inference time, an adaptive routing policy dynamically tailors the reasoning approach based on predictor confidence. It directs the model to use single-strategy execution for high-confidence predictions, dual-strategy verification for competitive scenarios, or comprehensive multi-strategy exploration for uncertain cases. Extensive experiments across five mathematical reasoning benchmarks demonstrate that PRISM consistently outperforms individual strategies and ensemble baselines, achieving improvements ranging from 0.9% to 7.6% across different base models. The adaptive routing approach shows particularly strong benefits for mathematical reasoning tasks across diverse model architectures. Our code is released at https://github.com/reml-group/PRISM.

Mathematical reasoning poses significant challenges for Large Language Models (LLMs) due to its demand for multi-step reasoning and abstract conceptual integration. While recent test-time scaling techniques rely heavily on high-quality, challenging problems, the scarcity of Olympiad-level math problems remains a bottleneck. We introduce CogAtom, a novel cognitive atom-based framework for synthesizing mathematically rigorous and cognitively diverse problems. Unlike prior approaches, CogAtom models problem construction as a process of selecting and recombining fundamental reasoning units, cognitive atoms, extracted from human-authored solutions. A diversity-promoting random walk algorithm enables exploration of the cognitive atom space, while a constraint-based recombination mechanism ensures logical soundness and structural validity. The combinatorial nature of the graph structure provides a near-infinite space of reasoning paths, and the walk algorithm systematically explores this space to achieve large-scale synthesis of high-quality problems; meanwhile, by controlling the number of cognitive atoms, we can precisely adjust problem difficulty, ensuring diversity, scalability, and controllability of the generated problems. Experimental results demonstrate that CogAtom outperforms existing methods in accuracy, reasoning depth, and diversity, generating problems that closely match the difficulty of AIME while exceeding it in structural variation. Our work offers a cognitively grounded pathway toward scalable, high-quality math problem generation.Our code is publicly available at https://github.com/Icarus-1111/CogAtom.

Multi-agent systems (MAS) have emerged as a powerful paradigm for orchestrating large language models (LLMs) and specialized tools to collaboratively address complex tasks. However, existing MAS frameworks often require manual workflow configuration and lack native support for dynamic evolution and performance optimization. In addition, many MAS optimization algorithms are not integrated into a unified framework. In this paper, we present EvoAgentX, an open-source platform that automates the generation, execution, and evolutionary optimization of multi-agent workflows. EvoAgentX employs a modular architecture consisting of five core layers: the basic components, agent, workflow, evolving, and evaluation layers. Specifically, within the evolving layer, EvoAgentX integrates three MAS optimization algorithms, TextGrad, AFlow, and MIPRO, to iteratively refine agent prompts, tool configurations, and workflow topologies. We evaluate EvoAgentX on HotPotQA, MBPP, and MATH for multi-hop reasoning, code generation, and mathematical problem solving, respectively, and further assess it on real-world tasks using GAIA. Experimental results show that EvoAgentX consistently achieves significant performance improvements, including a 7.44% increase in HotPotQA F1, a 10.00% improvement in MBPP pass@1, a 10.00% gain in MATH solve accuracy, and an overall accuracy improvement of up to 20.00% on GAIA. The source code is available at: https://github.com/EvoAgentX/EvoAgentX

The challenges of solving complex university-level mathematics problems, particularly those from MIT, and Columbia University courses, and selected tasks from the MATH dataset, remain a significant obstacle in the field of artificial intelligence. Conventional methods have consistently fallen short in this domain, highlighting the need for more advanced approaches. In this paper, we introduce a language-based solution that leverages zero-shot learning and mathematical reasoning to effectively solve, explain, and generate solutions for these advanced math problems. By integrating program synthesis, our method reduces reliance on large-scale training data while significantly improving problem-solving accuracy. Our approach achieves an accuracy of 90.15%, representing a substantial improvement over the previous benchmark of 81% and setting a new standard in automated mathematical problem-solving. These findings highlight the significant potential of advanced AI methodologies to address and overcome the challenges presented by some of the most complex mathematical courses and datasets.