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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 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.
Mathematicians Prove 2D Version of Quantum Gravity Really Works
In three towering papers, a team of mathematicians has worked out the details of Liouville quantum field theory, a two-dimensional model of quantum gravity.
The Mystery at the Heart of Physics That Only Math Can Solve
The accelerating effort to understand the mathematics of quantum field theory will have profound consequences for both math and physics.
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.