The mathematical physics underpinning electromagnetic fields and wave equations provides a rigorous framework for understanding the behaviour of electric and magnetic phenomena in both classical and ...

This post originally appered in Business Insider. Mathematics is all around us, and it has shaped our understanding of the world in countless ways. 1) The Pythagorean theorem: This theorem is ...

Proposed 15 years ago, the bounded L2 curvature conjecture has finally been proved by a group of three researchers at the Laboratoire Jacques-Louis Lions (CNRS / UPMC / Université Paris Diderot) and ...

As artificial intelligence (AI) takes on increasingly critical roles—from managing power grids to piloting autonomous vehicles—making sure these systems are safe has never been more important. But how ...

Speaking of mathematics, the catchy EqWorld site, hosted in Russia, aims to provide an interface for all things mathematical. The stated aims of the site are to “help the widest possible audience of ...

A relationship between natural or manmade elements that is used in every discipline except circuit logic. Algebraic and geometric equations are at the heart of scientific research and practice from ...

Methods for solving linear, ordinary, and partial differential equations of mathematical physics. Green's functions, distribution theory, integral equations, transforms, potential theory, diffusion ...

Beauty, they say, is in the eye of the beholder, and neurobiology, it turns out, supports this idiom. While some people might be moved by the beauty of an artistic or musical work, others experience ...

At the frontiers of theoretical physics, many of the most popular ideas have one thing in common: they begin from a mathematical framework that seeks to explain more things than our currently ...