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partial differential equations
Mathematician Proves Huge Result on ‘Dangerous’ Problem
Mathematicians regard the Collatz conjecture as a quagmire and warn each other to stay away. But now Terence Tao has made more progress than anyone in decades.
Black Hole Singularities Are as Inescapable as Expected
For the first time, physicists have calculated exactly what kind of singularity lies at the center of a realistic black hole.
Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
A founder of modern geometric analysis who produced “some of the most dramatic advances in mathematics in the last 40 years,” Uhlenbeck is the first woman to be awarded this top honor.
A Traveler Who Finds Stability in the Natural World
The mathematician Alessio Figalli is rarely in one place for very long. But his work has established the stability of everything from crystals to weather fronts by using concepts derived from Napoleonic fortifications.
Mathematicians Tame Turbulence in Flattened Fluids
By squeezing fluids into flat sheets, researchers can get a handle on the strange ways that turbulence feeds energy into a system instead of eating it away.