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# Mathematical physics

## Latest Articles

### For His Sporting Approach to Math, a Fields Medal

With Hugo Duminil-Copin, thinking rarely happens without moving. His insights into the flow-related properties of complex networks have earned him the Fields Medal.

### Wheel Made of ‘Odd Matter’ Spontaneously Rolls Uphill

Physicists have solved a key problem of robotic locomotion by revising the usual rules of interaction between simple component parts.

### Mathematicians Coax Fluid Equations Into Nonphysical Solutions

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.

### Deep Learning Poised to ‘Blow Up’ Famed Fluid Equations

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.

### A New Theory for Systems That Defy Newton’s Third Law

In nonreciprocal systems, where Newton’s third law falls apart, “exceptional points” are helping researchers understand phase transitions and possibly other phenomena.

### How Wavelets Allow Researchers to Transform, and Understand, Data

Built upon the ubiquitous Fourier transform, the mathematical tools known as wavelets allow unprecedented analysis and understanding of continuous signals.

### 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 Prove Symmetry of Phase Transitions

A group of mathematicians has shown that at critical moments, a symmetry called rotational invariance is a universal property across many physical systems.

### Nathan Seiberg on How Math Might Complete the Ultimate Physics Theory

Even in an incomplete state, quantum field theory is the most successful physical theory ever discovered. Nathan Seiberg, one of its leading architects, talks about the gaps in QFT and how mathematicians could fill them.