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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.