Take Fermat’s Last Theorem, for example: short and sweet enough to scribble in a margin, but a proof took more than 350 years and the development of multiple new fields of math to find.

Aigner enlisted fellow mathematician Günter Ziegler, and the two started collecting examples of exceptionally ... “a glimpse of mathematical heaven,” presents proofs of dozens of theorems ...

Acceptance of the work in Publications of the Research Institute for Mathematical ... emerge.” A proof, if confirmed, could change the face of number theory, by, for example, providing an ...

For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise. In October 2018, David Asperó was on holiday in Italy, gazing out a car ...

For example, among the 3,044 ... with new ways of thinking about familiar mathematical objects.” Mathematicians who are already skeptical of Mochizuki’s abc proof may well consider Scholze ...

Both had studied geometry and some trigonometry, and both told us math was not easy. What no one told them was there had been more than 300 documented proofs of the Pythagorean Theorem using ...

But if you try killing any nontrivial Hydra, after the first few cuts, your situation will look like in our example ... You may now ask for a simpler proof. You won’t get one.

An error in a proof underlying a widely used branch of modern mathematics was accidentally discovered by mathematicians while translating old proofs to a computer ...