Related papers: Aristotle: IMO-level Automated Theorem Proving
The need for formal definition of the very basis of mathematics arose in the last century. The scale and complexity of mathematics, along with discovered paradoxes, revealed the danger of accumulating errors across theories. Although,…
Theorem proving serves as a major testbed for evaluating complex reasoning abilities in large language models (LLMs). However, traditional automated theorem proving (ATP) approaches rely heavily on formal proof systems that poorly align…
Undergraduate students of artificial intelligence often struggle with representing knowledge as logical sentences. This is a skill that seems to require extensive practice to obtain, suggesting a teaching strategy that involves the…
Debate has been widely adopted as a strategy to enhance critical thinking skills in English Language Arts (ELA). One important skill in debate is forming effective argumentation, which requires debaters to select supportive evidence from…
We propose a minimal agentic baseline that enables systematic comparison across different AI-based theorem prover architectures. This design implements the core features shared among state-of-the-art systems: iterative proof refinement,…
Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis,…
Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…
Proprietary AI systems have recently demonstrated impressive capabilities on complex proof-based problems, with gold-level performance reported at the 2025 International Mathematical Olympiad (IMO). However, the training pipelines behind…
As large language models (LLMs) reach high scores on established mathematical benchmarks, such as GSM8K and MATH, the research community has turned to International Mathematical Olympiad (IMO) problems to push the evaluation frontier.…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…
In the domain of education, the integration of,technology has led to a transformative era, reshaping traditional,learning paradigms. Central to this evolution is the automation,of grading processes, particularly within the STEM domain…
Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…
We present Prover Agent, a novel AI agent for automated theorem proving that integrates large language models (LLMs) with a formal proof assistant, Lean. Prover Agent coordinates an informal reasoning LLM, a formal prover model, and…
The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. This paper focuses on formal verification,…
Formal mathematical reasoning remains a critical challenge for artificial intelligence, hindered by limitations of existing benchmarks in scope and scale. To address this, we present FormalMATH, a large-scale Lean4 benchmark comprising…
Background & Objectives: In the last decade, Machine learning research has grown rapidly, but large models are reaching their soft limits demonstrating diminishing returns and still lack solid reasoning abilities. These limits could be…
The evolution of Artificial Intelligence (AI) has been significantly accelerated by advancements in Large Language Models (LLMs) and Large Multimodal Models (LMMs), gradually showcasing potential cognitive reasoning abilities in…
During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical…