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Statistics Postdoc Tames Decades-Old Geometry Problem

The Quanta Podcast

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Borgon's Conjecture on High Dimensional Geometry

High dimensional shapes often behave in ways that defy our human low dimension intuition. In dimensions ten and up, it's possible to build a cube and a ball such that the cube has larger volume than the ball. The paper doesn't quite prove borgon's full conjecture, but it does prove a version so close that it puts a strict limit on high dimensional weirdness for all practical purposes.

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