Sebastien Bubeck of OpenAI says “yes, nonsofic groups exist”—as an example of “many new beautiful results” from Astra, next major OpenAI model. OpenAI published a page and PDF detailing ten advances ...

Alpöge’s discovery is the latest in a string of high-profile mathematical breakthroughs made by large language models. Recent examples include OpenAI’s disproof of the unit distance conjecture, and ...

Joan Birman popularized the Burau representation problem decades ago. Now she and two colleagues have a proof that reveals ...

Artificial intelligence promises clear answers from complex data. Yet new research suggests there are limits that no amount ...

It is common understanding that as quantum computing gets its feet under itself, it will work hand-in-hand with classical supercomputers and leverage what rapidly evolving AI tools can offer to begin ...

Mathematicians are still trying to understand fundamental properties of the Fourier transform, one of their most ubiquitous and powerful tools. A new result marks an exciting advance toward that goal.

You are free to share (copy and redistribute) this article in any medium or format and to adapt (remix, transform, and build upon) the material for any purpose, even commercially within the parameters ...

MPSpack is a user-friendly and fully object-oriented MATLAB toolbox that implements the method of particular solutions (aka Trefftz or nonpolynomial FEM, including the method of fundamental solutions, ...

This course focuses on three-dimensional geometry processing, while simultaneously providing a first course in traditional differential geometry. Our main goal is to show how fundamental geometric ...