“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 ...

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 ...

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 ...

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 ...

Purdue faculty dedicate countless hours to exploring the frontiers of their respective fields, pushing the boundaries of knowledge and contributing to the ever-evolving landscape of academia. To ...

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 ...

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 – ...

Many people find complex math puzzling, including some mathematicians. Recently, a mathematician has found solutions to a puzzle that has been around for centuries. They have found a way to generate ...