“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 ...

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near. For ...

A recent entry in the visitor’s book of the James Joyce Tower & Museum in Sandycove, Dublin, perplexed the Friends of Joyce’s Tower, the volunteers who run the museum. The entry, reproduced as the ...

Major reforms and inventions often begin with a line of mathematics. For students, equations can look abstract on a classroom board. Yet some of them reorganised science, engineering and economics.

The cosmos is a unique laboratory for testing the laws of physics, in particular those of Euler and Einstein. Euler described the movements of celestial objects, while Einstein described the way in ...

The 3D Euler equation is a simplification of the Navier–Stokes equations, and a singularity is the point where an equation starts to break down or "blow up," meaning it can suddenly become chaotic ...

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 – ...

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.