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 ...