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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.
Two monumental works have led many mathematicians to avoid the equal sign. The process has not always gone smoothly.
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.
The Fields medalist Vladimir Voevodsky has died at 51. This 2015 article describes his computer-aided quest to eliminate human error and rewrite the century-old rules underlying all of mathematics.
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