Numbers like π, e and φ 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 ...

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 ...

Analytic number theory continues to serve as a cornerstone of modern mathematics through its probing study of zeta functions and their applications. At the heart of this discipline is the classical ...

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 ...

This article is more than 8 years old. So what? Riemann was interested in the distribution of prime numbers and he discovered a formula for the number of primes less than or equal to a given integer ...

I. There should actually be a lot of algebra in this book, much more than I have been able to present. My focus has been on Bernhard Riemann and his work on prime numbers and the zeta function. That ...

The original version of this story appeared in Quanta Magazine. Sometimes mathematicians try to tackle a problem head on, and sometimes they come at it sideways. That’s especially true when the ...

A famed mathematical enigma is once again in the spotlight. The Riemann hypothesis, posited in 1859 by German mathematician Bernhard Riemann, is one of the biggest unsolved puzzles in mathematics. The ...

Over the past few days, the mathematics world has been abuzz over the news that Sir Michael Atiyah, the famous Fields Medalist and Abel Prize winner, claims to have solved the Riemann hypothesis. If ...

Yitang Zhang, a number theorist at the University of California, Santa Barbara, has posted a paper on arXiv that hints at the possibility that he may have solved the Landau-Siegel zeros conjecture.