“You don’t have to believe in God, but you have to believe in The Book,” the Hungarian mathematician Paul Erdős once said. The Book, which only exists in theory, contains the most elegant proofs of ...

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The basic building blocks of the whole numbers remain mysterious.

19th-century mathematicians thought the “roots of unity” were the key to solving Fermat’s Last Theorem. Then they discovered a fatal flaw. Sometimes the usual numbers aren’t enough to solve a problem.