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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.
How readers used their geometry skills to survive a dangerous puzzle.
Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.
Laurent Fargues and Peter Scholze have found a new, more powerful way of connecting number theory and geometry as part of the sweeping Langlands program.
A group of mathematicians has shown that at critical moments, a symmetry called rotational invariance is a universal property across many physical systems.
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