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.
Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program.
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.
The accelerating effort to understand the mathematics of quantum field theory will have profound consequences for both math and physics.
A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections.
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