Mathematicians Hong Wang and Joshua Zahl have proved the three-dimensional case of the Kakeya conjecture, a famous geometric problem that had remained unsolved for more than a century.
Posed in 1917, the Kakeya problem asks: what is the smallest region in which a needle can be turned through 180 degrees? In the three-dimensional version, the researchers showed that so-called “Kakeya sets” can have arbitrarily small volume while still remaining three-dimensional.
The discovery has already been recognized as one of the most important achievements in modern mathematics. Professor Terence Tao noted its significance, and specialists say the work will open new horizons in geometry, number theory and cryptography.
