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# topology

## Latest Articles

### Mathematicians Transcend Geometric Theory of Motion

More than 30 years ago, Andreas Floer changed geometry. Now, two mathematicians have finally figured out how to extend his revolutionary perspective.

### How Tadayuki Watanabe Disproved a Major Conjecture About Spheres

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.

### Major Quantum Computing Strategy Suffers Serious Setbacks

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.

### 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.