Combinatorial geometry and density problems form a dynamic field at the intersection of discrete mathematics and geometric analysis. Research in this area explores the intricate arrangements of points ...

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

Watch out, nerdy high schoolers, AlphaGeometry is coming for your mathematical lunch. Credit...Christian Gralingen Supported by By Siobhan Roberts Reported from Stanford, Calif. For four years, the ...

Eigenvalue problems occupy a central role in Riemannian geometry, providing profound insights into the interplay between geometry and analysis. At their core, these problems involve the study of ...

For all of the recent strides we’ve made in the math world—like a supercomputer finally solving the Sum of Three Cubes problem that puzzled mathematicians for 65 years—we’re forever crunching ...

The original version of this story appeared in Quanta Magazine. In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an ...

If you are interested in learning about the easiest math problems that look hard, then you have come to the right place. Many people consider mathematics to be tough, and if you are one of them, then ...