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Special Surfaces Remain Distinct in Four Dimensions
For decades mathematicians have searched for a specific pair of surfaces that can’t be transformed into each other in four-dimensional space. Now they’ve found them.
Unimaginable Surfaces Discovered After Decades-Long Search
Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.
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.
Dennis Sullivan, Uniter of Topology and Chaos, Wins the Abel Prize
The American mathematician invented entire new ways to understand shapes and spaces.
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.