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 ...

But now, two mathematician friends have used their quarantine time to crack a variation of the age-old geometry problem. They analyzed a set of loopy shapes called smooth, continuous curves to prove ...

The computer scientist Erik Demaine and his artist and computer scientist father, Martin Demaine, have been pushing the limits of paper folding for years. Their intricate origami sculptures are part ...

Mathematicians have finally solved a geometry problem that has puzzled the field for decades. The question was proposed by Japanese mathematician Sōichi Kakeya in 1917. It sounds simple: How can you ...

This video shows how to solve algebra problems using geometry, offering a visual approach that makes abstract equations ...

Hong Wang, an associate professor at NYU’s Courant Institute of Mathematical Sciences, presenting her work on the Kakeya conjecture on March 10, 2025. Credit: David Song/NYU. Mathematicians from New ...

A research team led by Maxim Kontsevich, a professor at the French Institute of Advanced Scientific Studies (IHES) and a 1998 ...

Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong. One of the oldest and simplest ...