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Impossible-Seeming Surfaces Confirmed Decades After Conjecture | Quanta Magazine | Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.

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Impossible-Seeming Surfaces Confirmed Decades After Conjecture | Quanta Magazine | Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.
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Can someone give a more rigorous ELIU, and I have one more important question at a high level what camps does mathematical research normally fall into ?
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