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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.
Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.
The result could help researchers answer a larger question about flattening objects from the fourth dimension to the third dimension.
Three mathematicians show, for the first time, how to form a square with the same area as a circle by cutting them into interchangeable pieces that can be visualized.
More than 30 years ago, Andreas Floer changed geometry. Now, two mathematicians have finally figured out how to extend his revolutionary perspective.
Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.
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