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Partial differential equations
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Latest Neural Nets Solve World’s Hardest Equations Faster Than Ever Before
Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster.
In Violation of Einstein, Black Holes Might Have ‘Hair’
A new study shows that extreme black holes could break the famous “no-hair” theorem, and in a way that we could detect.
Symbolic Mathematics Finally Yields to Neural Networks
After translating some of math’s complicated equations, researchers have created an AI system that they hope will answer even bigger questions.
New Math Proves That a Special Kind of Space-Time Is Unstable
Einstein’s equations describe three canonical configurations of space-time. Now one of these three — important in the study of quantum gravity — has been shown to be inherently unstable.
Mathematicians Prove Universal Law of Turbulence
By exploiting randomness, three mathematicians have proved an elegant law that underlies the chaotic motion of turbulent systems.
For Fluid Equations, a Steady Flow of Progress
A startling experimental discovery about how fluids behave started a wave of important mathematical proofs.
Famous Fluid Equations Spring a Leak
Researchers have spent centuries looking for a scenario in which the Euler fluid equations fail. Now a mathematician has finally found one.
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.