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 ...

Topological relations such as inside, outside, or intersection are ubiquitous to our spatial thinking. Here, we examined how people reason deductively with topological relations between points, lines, ...

Abstract: Generative large language models (LLMs) can follow human-provided instruction prompts and generate human-like responses. Apart from natural language responses, they have been found to be ...

This is a preview. Log in through your library . Abstract We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the ...

In our project (topology-toolkit) we wanted to use Boost instead of Qhull to have fewer third party libraries. We had some bug appearing when using Boost implemantation for convex hull, and after some ...