Arithmetic geometry is a vibrant field at the intersection of number theory and algebraic geometry, focussing on the study of polynomial equations and the distribution of their rational solutions.

This article proposes the "Coherence-Point Principle" as a unified framework for understanding multiplicative number-theoretic inequalities, most notably the ABC conjecture. When three distinct number ...

On its surface, the Kakeya conjecture is a simple statement about rotating needles. But it underlies a wealth of mathematics. In mathematics, a simple problem is often not what it seems. Earlier this ...

Alexandru Ghitza receives funding from the Australian Research Council. A couple of months ago, Japanese mathematician Shinichi Mochizuki posted the latest in a series of four papers claiming the ...