The Riemann zeta function, a central object in analytic number theory, has long intrigued mathematicians and physicists alike. Its non-trivial zeros not only encapsulate the distribution of prime ...

Multiple zeta functions extend the classical Riemann zeta function to several complex variables by involving multiple summations with distinct exponents. These functions not only encapsulate deep ...

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 ...

Numbers like pi, e and phi often turn up in unexpected places in science and mathematics. Pascal's triangle and the Fibonacci sequence also seem inexplicably widespread in nature. Then there's the ...

Prime numbers, the indivisible atoms of arithmetic, seem to be strewn haphazardly along the number line, starting with 2, 3, 5, 7, 11, 13, 17 and continuing without pattern ad infinitum. But in 1859, ...

It’s been 162 years since Bernhard Riemann posed a seminal question about the distribution of prime numbers. Despite their best efforts, mathematicians have made very little progress on the Riemann ...

The Millennium Prize Problems, announced in 2000 by the Clay Mathematics Institute in the United States, are problems with a prize of $1 million (approximately 160 million yen). One of these problems ...

Did a team of mathematicians just take a big step toward answering a 160-year-old, million-dollar question in mathematics? Maybe. The crew did solve a number of other, smaller questions in a field ...

The Riemann hypothesis is the most important open question in number theory—if not all of mathematics. It has occupied experts for more than 160 years. And the problem appeared both in mathematician ...

William Ross does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their ...