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 ...

We give a simple proof that the solution of the Allen-Cahn equation converges to Brakke's motion by mean curvature, by utilizing the recent results of Röger and Schätzle in space dimension 2 and 3.

The Standard Model is far more than elementary particles arranged in a table. The Standard Model of particle physics is often visualized as a table, similar to the periodic table of elements, and used ...

Many of the world's most important systems, such as the atmosphere, turbulent fluids, and even the motion of planets, behave ...

ChatGPT, Photomath, Symbolab, and other artificial intelligence-powered platforms can solve a complicated math equation in just seconds—and provide a step-by-step explanation of the answer. That power ...