Anyone who's ever tried tiling a floor, a backsplash or even an arts-and-crafts project probably knows the emotional frustration of working with pieces whose shapes don't perfectly complement each ...

A 125-page proof posted to arXiv may represent a huge breakthrough in geometric measure theory. This problem has implications ...

A geometry problem over a century old has just found its definitive answer. Mathematicians have confirmed that the solution ...

A new proof solves the “Kakeya conjecture” in three dimensions, opening up a new set of possibilities for mathematics, from computer science to cryptography ...

Professors from NYU and the University of British Columbia have resolved the Kakeya set conjecture in three dimensions.

As it unfurls, the saga of Mahmoud Khalil—the Columbia agitator picked up by immigration enforcement last week—looks less like a complicated immigration-law dispute and more like something out of a ...