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mathematical shapesQuanta Magazine
•79% Informative
Topologists thought they could characterize mathematical shapes by synthesizing local measurements.
But paradoxically curved spaces show that this isn’t always possible.
“Things can be much more wild than what we thought,” says Elia Bruè of Bocconi University in Italy .
In 1968 , mathematician Milnor conjectured that complete manifolds whose Ricci tensor is nonnegative at every point can’t have an infinite number of holes.
In 1978 , a mathematician named Mikhael Gromov showed that if a different, more detailed measure of curvature is always nonnegative, then the manifold must have only a finite number.
In 2013 , Naber ’s conjecture was proved for three -dimensional manifolds.
Naber tried several times to prove the conjecture in full generality — for all possible dimensions.
Three geometers built a strange seven -dimensional manifold.
It had nonnegative Ricci curvature at every point.
The mathematicians ended up with what they called a smooth fractal snowflake.
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