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: This letter reveals the incorrect argumentation, erroneous mathematical calculations, and misleading observations reported in the article titled “Counterexample to Passivity Preservation for ...

Counterexample- and proof-based refinement are complementary approaches to iterative abstraction. In the former case, a single abstract counterexample is eliminated by each refinement step, while in ...

This is a preview. Log in through your library . Abstract Consider first-passage percolation on the square lattice. Hammersley and Welsh, who introduced the subject in 1965, conjectured that the ...

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 ...

School of Biomedical Engineering, Shenzhen Key Laboratory for Nano-Biosensing Technology, Guangdong Key Laboratory of Biomedical Measurements and Ultrasound Imaging, Marshall Laboratory of Biomedical ...