AI could soon spew out hundreds of mathematical proofs that look "right" but contain hidden flaws, or proofs so complex we ...

George Pólya’s random walk theorem absolved him of being a lurker and revealed how the laws of chance interact with physical ...

Abstract: A new proof of the direct part of the quantum channel coding theorem is shown based on a standpoint of quantum hypothesis testing. A packing procedure of ...

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 ...

Large language models struggle to solve research-level math questions. It takes a human to assess just how poorly they perform. By Siobhan Roberts A few weeks ago, a high school student emailed Martin ...

The goal of the book is to provide insight into many enjoyable and fascinating aspects of geometry, and to reveal interesting geometrical properties. The emphasis is on the practical applications of ...

Abstract: This paper introduces the formal proof of the three mean value theorems of differentiation in detail. The differential mean value theorem is the core theorem of differential calculus, an ...