A cap set, the new proofs establish, can be at most (2.756/3) n as large as the whole deck. Mathematicians are now scrambling to figure out the implications of the new proof.

Measured against that, the Kakeya conjecture – a problem stemming from a 1917 thought experiment by Japanese mathematician ...

A 125-page proof posted to arXiv may represent a huge breakthrough in geometric measure theory. This problem has implications in fields like encryption, computer science, and number theory.

Simple Set Game Proof Stuns Mathematicians. By Erica Klarreich. May 31, ... mathematicians translate the game into geometry. ... it’s possible to create a polynomial that evaluates to zero at all ...

Basic Books. 368 pages. ... Today, for example, we have computerized proofs by exhaustion, ... Yet politics is messier than geometry; ...

Mathematicians Wrote a Proof for a 100-Year-Old ... that’s one example of a thought exercise from geometric ... In their proof, Wang and Zahl consider tubes instead of simple lines or ...

As he was brushing his teeth on the morning of July 17, 2014, Thomas Royen, a little-known retired German statistician, suddenly lit upon the proof of a famous conjecture at the intersection of ...