J. R. Brown, Philosophy of mathematics: an introduction to the world of proofs and pictures, Routledge (1999). 2. R. B. Nelsen, Proofs without words I: exercises in ...

Mathematicians have broken through a long-standing barrier in the study of “minimizing surfaces,” which play an important role in both math and physics. In the mid-19th century, the Belgian physicist ...

"Hearst Magazines and Yahoo may earn commission or revenue on some items through these links." A 125-page proof posted to arXiv may represent a huge breakthrough in geometric measure theory. This ...

Though pictures are often used to present mathematical arguments, they are not typically thought to be an acceptable means for presenting mathematical arguments rigorously. With respect to the proofs ...

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 ...