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 ...

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 ...

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 ...

The prime counting function π can be written in terms of another step function, J. The function J can be written in terms of Riemann’s zeta function ζ. You take the point. If you’re not a ...

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 ...

The Basel problem 25 is named from the Swiss city in whose university two of the Bernoulli brothers successively served as professor of mathematics (Jakob, 1687–1705, Johann, 1705–1748). I mentioned ...