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# topology

## Latest Articles

### How Complex Is a Knot? New Proof Reveals Ranking System That Works.

“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.

### Untangling Why Knots Are Important

Steven Strogatz explores the mysteries of knots with the mathematicians Colin Adams and Lisa Piccirillo.

### Dennis Sullivan, Uniter of Topology and Chaos, Wins the Abel Prize

The American mathematician invented entire new ways to understand shapes and spaces.

### The Year in Math and Computer Science

Mathematicians and computer scientists answered major questions in topology, set theory and even physics, even as computers continued to grow more capable.

### 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.