“Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don’t know what it means. But we have proved it, and therefore we know it must be the truth.” —Benjamin ...

For centuries, mathematicians have sought to understand and model the motion of fluids. The equations that describe how ripples crease the surface of a pond have also helped researchers to predict the ...

The Euler equations constitute a fundamental set of hyperbolic partial differential equations that describe the motion of an inviscid fluid. In gas dynamics, these equations are instrumental in ...

The compressible Euler equations form the cornerstone of fluid dynamics, describing the conservation of mass, momentum and energy in a compressible fluid. When augmented by damping effects, these ...

What is it that makes Euler's identity, e]iPi + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most ...

Mathematical equations aren't just useful -- many are quite beautiful. And many scientists admit they are often fond of particular formulas not just for their function, but for their form, and the ...

Scientific progress is not usually straightforward. Researchers pursue and abandon lines of inquiry. Results languish. Theories take decades to cohere. But sometimes the accumulation of scientific ...