Inspired by the pedagogical method of "proof by counterexamples" widely used in human mathematics education, our work aims to enhance Large Language Models’ (LLMs) ability to conduct mathematical ...

Mathematical Large Language Models (LLMs) have demonstrated strong problem-solving capabilities, but their reasoning ability is often constrained by pattern recognition rather than true conceptual ...

ABSTRACT: Let be a metric continuum. Let , is said to make a hole in , if is not unico-herent. In this paper, we characterize elements such that makes a hole in , where is either a smooth fan or an ...