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19th-century mathematicians thought the “roots of unity” were the key to solving Fermat’s Last Theorem. Then they discovered a fatal flaw.

For centuries, mathematicians tried to solve problems by adding new values to the usual numbers. Now they’re investigating the unintended consequences of that tinkering.

A previously unnoticed property of prime numbers seems to violate a long-standing assumption about how they behave.

Using crowd-sourced and traditional mathematics research, Terence Tao has devised a solution to a long-standing problem posed by the legendary Paul Erdős.

Two years ago, Yitang Zhang was virtually unknown. Now his surprise solution to a major problem in number theory has catapulted him to mathematical stardom. Where does he go from here?

A year after tackling how close together prime number pairs can stay, mathematicians have now made the first major advance in 76 years in understanding how far apart primes can be.

Working on the centuries-old twin primes conjecture, two solitary researchers and a massive collaboration have made enormous advances over the last six months.

A virtually unknown researcher has made a great advance in one of mathematics’ oldest problems, the twin primes conjecture.

All complex correlated systems, from Arctic melt ponds to the Internet, appear to be governed by the same math as a random matrix.

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