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A pair of researchers has shown that trying to classify groups of numbers called “torsion-free abelian groups” is as hard as it can possibly be.
For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.
A two-player game can reveal whether the universe has an infinite amount of complexity.
Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.
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