Mathematical physics occupies the fertile borderland between pure mathematics and theoretical physics, developing precise frameworks to formulate and solve the laws governing nature. It embraces the ...

Turbulence is one of the least understood phenomena of the physical world. Long considered too hard to understand and predict mathematically, turbulence is the reason the Navier-Stokes equations, ...

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 ...

Black holes exist in our universe. That’s widely accepted today. Physicists have detected the X-rays emitted when black holes feed, analyzed the gravitational waves from black hole collisions and even ...

Artificial intelligence (AI) systems, particularly artificial neural networks, have proved to be highly promising tools for uncovering patterns in large amounts of data that would otherwise be ...

This article is the first part of a series about quantum field theory published by Quanta Magazine. Other stories in the series can be found here. Over the past century, quantum field theory has ...

Maxwell’s equations of electromagnetism and the Euler equation top a poll to find the greatest equations of all time. Robert P Crease discusses the results of his reader survey First among equals – ...

The original version of this story appeared in Quanta Magazine. At the turn of the 20th century, the renowned mathematician David Hilbert had a grand ambition to bring a more rigorous, mathematical ...

In a new open-access study that I published with my late colleague Kostya Trachenko from Queen Mary University of London, I propose a surprisingly simple nonlinear mathematical equation that unifies ...