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Mathematics formalisation is the task of writing mathematics (i.e., definitions, theorem statements, proofs) in natural language, as found in books and papers, into a formal language that can then be checked for correctness by a program. It…

As automated reasoning systems advance rapidly, there is a growing need for research-level formal mathematical problems to accurately evaluate their capabilities. To address this, we present Formal Conjectures, an evolving benchmark of…

Formal theorem-proving benchmarks enable mechanically verifiable evaluation of mathematical reasoning in large language models. However, existing benchmarks mainly focus on Olympiad-style problems and algebraic domains, leaving…

The task of Critical Questions Generation (CQs-Gen) aims to foster critical thinking by enabling systems to generate questions that expose underlying assumptions and challenge the validity of argumentative reasoning structures. Despite…

The challenge of formal proof generation has a rich history, but with modern techniques, we may finally be at the stage of making actual progress in real-life mathematical problems. This paper explores the integration of ChatGPT and basic…

Retrieval-augmented generation (RAG) improves knowledge-intensive question answering by incorporating external evidence. However, existing RAG methods still suffer from hallucinations and subtle reasoning errors. Recent studies introduce…

Autoformalization, the process of transforming informal mathematical language into formal specifications and proofs remains a difficult task for state-of-the-art (large) language models. Existing works point to competing explanations for…

Automatic translation of natural language mathematics into faithful Lean 4 code is hindered by the fundamental dissonance between informal set-theoretic intuition and strict formal type theory. This gap often causes LLMs to hallucinate…

As the world becomes increasingly saturated with AI-generated content, disinformation, and algorithmic persuasion, critical thinking - the capacity to evaluate evidence, detect unreliable claims, and exercise independent judgment - is…

The critique capacity of Large Language Models (LLMs) is essential for reasoning abilities, which can provide necessary suggestions (e.g., detailed analysis and constructive feedback). Therefore, how to evaluate the critique capacity of…

AI for Mathematics (AI4Math) is not only intriguing intellectually but also crucial for AI-driven discovery in science, engineering, and beyond. Extensive efforts on AI4Math have mirrored techniques in NLP, in particular, training large…

Training large language models (LLMs) to spend more time thinking and reflection before responding is crucial for effectively solving complex reasoning tasks in fields such as science, coding, and mathematics. However, the effectiveness of…

Autoformalization aims to translate natural-language mathematical statements into a formal language. While LLMs have accelerated progress in this area, existing methods still suffer from low accuracy. We identify two key abilities for…

Tool-Integrated Reasoning (TIR) with search engines enables large language models to iteratively retrieve up-to-date external knowledge, enhancing adaptability and generalization in complex question-answering tasks. However, existing search…

Large Language Models (LLMs) show strong potential for automating model generation from natural-language descriptions. A common approach begins with an initial model generation, followed by an iterative critique-refine loop in which the…

Code generation with large language models often relies on multi-stage human-in-the-loop refinement, which is effective but very costly - particularly in domains such as frontend web development where the solution quality depends on…

Large language models (LLMs) primarily rely on supervised fine-tuning (SFT) as a key method to adapt pre-trained models to domain-specific tasks such as mathematical reasoning. However, standard SFT uniformly penalizes all tokens,…

Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as…

Automated formalization of mathematics enables mechanical verification but remains limited to isolated theorems and short snippets. Scaling to textbooks and research papers is largely unaddressed, as it requires managing cross-file…

Reinforcement Learning (RL) has emerged as a popular training paradigm, particularly when paired with reasoning models. While effective, it primarily focuses on generating responses and lacks mechanisms to explicitly foster critique or…