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Watanabe invented a new way of distinguishing shapes on his way to solving the last open case of the Smale conjecture, a central question in topology about symmetries of the sphere.
So-called topological quantum computing would avoid many of the problems that stand in the way of full-scale quantum computers. But high-profile missteps have led some experts to question whether the field is fooling itself.
Researchers are turning to the mathematics of higher-order interactions to better model the complex connections within their data.
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.
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 accelerating effort to understand the mathematics of quantum field theory will have profound consequences for both math and physics.
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