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A New Proof Smooths Out the Math of Melting
A powerful mathematical technique is used to model melting ice and other phenomena. But it has long been imperiled by certain “nightmare scenarios.” A new proof has removed that obstacle.
A Tower of Conjectures That Rests Upon a Needle
On its surface, the Kakeya conjecture is a simple statement about rotating needles. But it underlies a wealth of mathematics.
New Proof Threads the Needle on a Sticky Geometry Problem
A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures.
Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations
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.
Mathematicians Prove Melting Ice Stays Smooth
After decades of effort, mathematicians now have a complete understanding of the complicated equations that model the motion of free boundaries, like the one between ice and water.
Mathematicians Identify Threshold at Which Shapes Give Way
A new proof establishes the boundary at which a shape becomes so corrugated, it can be crushed.
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.