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The emergence of large language models (LLMs) has revolutionized machine learning and related fields, showcasing remarkable abilities in comprehending, generating, and manipulating human language. However, their conventional usage through…
Large Language Models (LLMs) are increasingly used in math education not only as problem solvers but also as assessors of learners' reasoning. However, it remains unclear whether stronger math problem-solving ability is associated with…
Recent advances in mathematical reasoning and the long-term planning capabilities of large language models (LLMs) have precipitated the development of agents, which are being increasingly leveraged in business operations processes. Decision…
Large Reasoning Models (LRMs) demonstrate remarkable problem-solving capabilities through extended Chain-of-Thought (CoT) reasoning but often produce excessively verbose and redundant reasoning traces. This inefficiency incurs high…
Recent advancements in large language models (LLMs) have revitalized philosophical debates surrounding artificial intelligence. Two of the most fundamental challenges - namely, the Frame Problem and the Symbol Grounding Problem - have…
Artificial intelligence (AI) has achieved human-level performance in specialized tasks such as Go, image recognition, and protein folding, raising the prospect of an AI singularity-where machines not only match but surpass human reasoning.…
While LLMs have shown impressive capabilities in solving math or coding problems, the ability to make scientific discoveries remains a distinct challenge. This paper proposes a "Turing test for an AI scientist" to assess whether an AI agent…
The growing ubiquity of artificial intelligence (AI), in particular large language models (LLMs), has profoundly altered the way in which learners gain knowledge and interact with learning material, with many claiming that AI positively…
Large language models (LLMs) have seen considerable advancements in natural language understanding tasks, yet there remains a gap to bridge before attaining true artificial general intelligence, especially concerning shortcomings in…
Governments around the world aspire to ground decision-making on evidence. Many of the foundations of policy making - e.g. sensing patterns that relate to societal needs, developing evidence-based programs, forecasting potential outcomes of…
We present TuringQ, the first benchmark designed to evaluate the reasoning capabilities of large language models (LLMs) in the theory of computation. TuringQ consists of 4,006 undergraduate and graduate-level question-answer pairs,…
The evolution of Large Language Models (LLMs) from passive text generators to autonomous, goal-driven systems represents a fundamental shift in artificial intelligence. This chapter examines the emergence of agentic AI systems that…
Recent large language models (LLMs) have demonstrated versatile capabilities in long-context scenarios. Although some recent benchmarks have been developed to evaluate the long-context capabilities of LLMs, there is a lack of benchmarks…
Large language models have recently demonstrated advanced capabilities in solving IMO and Putnam problems; yet their role in research mathematics has remained fairly limited. The key difficulty is verification: suggested proofs may look…
Effective math tutoring requires not only solving problems but also diagnosing students' difficulties and guiding them step by step. While multimodal large language models (MLLMs) show promise, existing benchmarks largely overlook these…
This essay examines the relationship between artificial intelligence and the historical evolution of modern Mathematics. Rather than viewing AI as an external rupture, we argue that its effectiveness reveals a structural tendency already…
Large Language Models (LLMs) achieve impressive performance in a wide range of tasks, even if they are often trained with the only objective of chatting fluently with users. Among other skills, LLMs show emergent abilities in mathematical…
Large language models (LLMs), a recent advance in deep learning and machine intelligence, have manifested astonishing capacities, now considered among the most promising for artificial general intelligence. With human-like capabilities,…
The rapid advancement of large language models (LLMs) has enabled the generation of coherent essays, making AI-assisted writing increasingly common in educational and professional settings. Using large-scale empirical data, we examine and…
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…