In 1986 Belgian mathematician Jean Bourgain posed a seemingly simple question that continued to puzzle researchers for decades. No matter how you deform a convex shape—consider shaping a ball of clay into a watermelon, a football or a long noodle—will you always be able to slice a cross section bigger than a certain size? A paper by Bo’az Klartag of the Weizmann Institute of Science in Rehovot, Israel, and Joseph Lehec of the University of Poitiers in France, posted to the preprint site arXiv.org , has finally provided a definitive answer: yes.

Bourgain’s slicing problem asks whether every convex shape in n dimensions has a “slice” such that the cross section is bigger than some fixed value. For three-dimensional objects, this is like asking whether an avocado of a given size, no matt

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