“There are five fundamental operations in mathematics,” the German mathematician Martin Eichler supposedly said. “Addition, subtraction, multiplication, division and modular forms.” Part of the joke, ...

Bilinear forms and character sums have emerged as pivotal tools in analytic number theory, offering robust frameworks for investigating sums wherein variables interact multiplicatively. Bilinear forms ...

The Markov numbers reveal the secrets of irrational numbers and the patterns of the Fibonacci sequence. But there’s one question about them that has resisted proof for over a century. Most people are ...