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fluid dynamics

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2022 in Review

The Year in Math

By Konstantin Kakaes
December 22, 2022
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Four Fields Medals were awarded for major breakthroughs in geometry, combinatorics, statistical physics and number theory, even as mathematicians continued to wrestle with how computers are changing the discipline.

A GIF of a spinning vortex made up of fluid equations
fluid dynamics

Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations

By Jordana Cepelewicz
November 16, 2022
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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.

A ring of bubbles in blue water.
fluid dynamics

Mathematicians Coax Fluid Equations Into Nonphysical Solutions

By Leila Sloman
May 2, 2022
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The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.

Simulated water particles swirl in an upward vortex.
mathematical physics

Deep Learning Poised to ‘Blow Up’ Famed Fluid Equations

By Jordana Cepelewicz
April 12, 2022
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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.

Fluorescent purple liquid splashes.
fluid dynamics

An Injection of Chaos Solves Decades-Old Fluid Mystery

By Adam Mann
January 4, 2022
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In the 1960s, drillers noticed that certain fluids would firm up if they flowed too fast. Researchers have finally explained why.

A GIF of ice melting in a glass of water
mathematical physics

Mathematicians Prove Melting Ice Stays Smooth

By Mordechai Rorvig
October 6, 2021
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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.

A GIF showing increasingly more twists being added to the curves on a sphere.
geometry

Mathematicians Identify Threshold at Which Shapes Give Way

By Mordechai Rorvig
June 3, 2021
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A new proof establishes the boundary at which a shape becomes so corrugated, it can be crushed.

An animation showing chaotic swirls of purple coalesce into a single line
Abstractions blog

New Quantum Algorithms Finally Crack Nonlinear Equations

By Max G. Levy
January 5, 2021
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Two teams found different ways for quantum computers to process nonlinear systems by first disguising them as linear ones.

Mathematician Lauren Williams standing in front of a whiteboard that has mathematics written on it.
combinatorics

A Mathematician’s Unanticipated Journey Through the Physical World

By Kevin Hartnett
December 16, 2020
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Lauren Williams has charted an adventurous mathematical career out of the pieces of a fundamental object called the positive Grassmannian.


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