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What's up in

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.

A new proof establishes the boundary at which a shape becomes so corrugated, it can be crushed.

Playing with numbers can lead to deep mathematical and scientific insights.

Jordan Ellenberg enjoys studying — and writing about — the mathematics underlying everyday phenomena.

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them.

A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections.

A mathematical shortcut for analyzing black hole collisions works even in cases where it shouldn’t. As astronomers use it to search for new classes of hidden black holes, others wonder: Why?