Related papers: Teaching "Foundations of Mathematics" with the Lea…
We present a study of the implementation of the Electronic Preparatory Test for beginning undergraduates reading mathematics. The Test comprises two elements: diagnostic and self-learning. The diagnostic element identifies gaps in the…
The aim of this study is to investigate the decisions and reasoning of undergraduate students when choosing simple measurement instruments in an introductory physics laboratory course. For this study, we have developed a questionnaire and…
Leveraging mathematical Large Language Models (LLMs) for proof generation is a fundamental topic in LLMs research. We argue that the ability of current LLMs to prove statements largely depends on whether they have encountered the relevant…
Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…
The combination of verifiable languages and LLMs has significantly influenced both the mathematical and computer science communities because it provides a rigorous foundation for theorem proving. Recent advancements in the field provide…
This work discusses an approach to teach to mathematicians the importance and effectiveness of the application of Interactive Theorem Proving tools in their specific fields of interest. The approach aims to motivate the use of such tools…
We evaluate the effectiveness of LLM-Tutor, a large language model (LLM)-powered tutoring system that combines an AI-based proof-review tutor for real-time feedback on proof-writing and a chatbot for mathematics-related queries. Our…
Nowadays, formal theorem provers have made monumental progress on high-school and competition-level mathematics, but few of them generalize to more advanced mathematics. In this paper, we present REAL-Prover, a new open-source stepwise…
Proof Blocks is a software tool that provides students with a scaffolded proof-writing experience, allowing them to drag and drop prewritten proof lines into the correct order instead of starting from scratch. In this paper we describe a…
Traditional language model-based theorem proving assumes that by training on a sufficient amount of formal proof data, a model will learn to prove theorems. Our key observation is that a wealth of informal information that is not present in…
The study of propositional logic -- fundamental to the theory of computing -- is a cornerstone of the undergraduate computer science curriculum. Learning to solve logical proofs requires repeated guided practice, but undergraduate students…
Studying Mathematics requires a synthesis of skills from a multitude of academic disciplines; logical reasoning being chief among them. This paper explores mathematical logical preparedness of students entering first year university…
Mathematical theorem proving is an important testbed for large language models' deep and abstract reasoning capability. This paper focuses on improving LLMs' ability to write proofs in formal languages that permit automated proof…
A step-by-step presentation of the code for a small theorem prover introduces theorem-proving techniques. The programming language used is Standard ML. The prover operates on a sequent calculus formulation of first-order logic, which is…
Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research. A mitigation is using LLMs to generate formal proofs in languages like Lean. We perform the…
Advances in large language models (LLMs) enable many new innovations in education. However, evaluating the effectiveness of new technology requires real students, which is time-consuming and hard to scale up. Therefore, many recent works on…
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…
Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for…
Recent advances in large language models (LLMs) for mathematical reasoning have largely focused on tasks with easily verifiable final answers while generating and verifying natural language math proofs remains an open challenge. We identify…
Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…