Prime numbers are maddeningly capricious. They clump together like buddies on some regions of the number line, but in other areas, nary a prime can be found. So number theorists can’t even roughly ...

I. The 1859 paper “On the Number of Prime Numbers Less Than a Given Quantity” was Bernhard Riemann’s only publication on number theory, and the only one of his productions that contained no ...

WHEN Andrew Wiles, a British mathematician working at Princeton University, announced a decade ago that he had solved Fermat's last theorem, his discovery was reported on front pages around the world.

Universality theorems occupy a central role in analytic number theory, demonstrating that families of analytic functions—including the prototypical Riemann zeta-function—can approximate an extensive ...