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In Topology, When Are Two Shapes the Same?
As topologists seek to classify shapes, the effort hinges on how to define a manifold and what it means for two of them to be equivalent.
New Math Book Rescues Landmark Topology Proof
Michael Freedman’s momentous 1981 proof of the four-dimensional Poincaré conjecture was on the verge of being lost. The editors of a new book are trying to save it.
How Big Data Carried Graph Theory Into New Dimensions
Researchers are turning to the mathematics of higher-order interactions to better model the complex connections within their data.
Proof Assistant Makes Jump to Big-League Math
Mathematicians using the computer program Lean have verified the accuracy of a difficult theorem at the cutting edge of research mathematics.
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.
A Number Theorist Who Connects Math to Other Creative Pursuits
Jordan Ellenberg enjoys studying — and writing about — the mathematics underlying everyday phenomena.
How Mathematicians Use Homology to Make Sense of Topology
Originally devised as a rigorous means of counting holes, homology provides a scaffolding for mathematical ideas, allowing for a new way to analyze the shapes within data.