Euler’s identity is an equality found in mathematics that has been compared to a Shakespearean sonnet and described as "the most beautiful equation." It is a special case of a foundational equation in ...

We introduce a dyadic model for the Euler equations and the Navier-Stokes equations with hyper-dissipation in three dimensions. For the dyadic Euler equations we prove finite time blow-up. In 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 ...

This video explores one of Leonhard Euler’s most elegant ideas, showing how factorials can be used to connect π, square roots ...

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 ...

For more than 250 years, mathematicians have wondered if the Euler equations might sometimes fail to describe a fluid’s flow. A new computer-assisted proof marks a major breakthrough in that quest.

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 ...

“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 ...