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 ...

On a mild autumn day in 2016, the Hungarian mathematician Gábor Domokos arrived on the geophysicist Douglas Jerolmack’s doorstep in Philadelphia. Domokos carried with him his suitcases, a bad cold, ...

Researchers have discovered a hidden quantum geometry inside materials that subtly steers electrons, echoing how gravity warps light in space. Once thought to exist only on paper, this effect has now ...

Geometry may be one of the oldest branches of mathematics, but it’s much more than a theoretical subject. It’s part of our everyday lives, says Professor Jennifer Taback, and key to understanding many ...

When two mathematicians raised pointed questions about a classic proof that no one really understood, they ignited a years-long debate about how much could be trusted in a new kind of geometry. In the ...

A 150-year-old rule in geometry has been proven wrong. Mathematicians found two different doughnut-shaped surfaces that look identical when measured locally but are actually different overall. For ...

When you purchase an independently reviewed book through our site, we earn an affiliate commission. “Girls can’t do Euclid: can they, sir?” “The Mill on the Floss” contains one of George Eliot’s ...

Quantum geometry describes quantum states in systems with changing system parameters, such as an electron spinning in a magnetic field whose direction is slowly changing. The state of the electron ...