For a long time, the Kakeya conjecture, which involves rotating an infinitely narrow needle, kept mathematicians guessing—until now
It is rare to read about "spectacular progress" or a "once-in-a-century" result in mathematics. That's for good reason: if a problem has not had a solution for many years, then completely new approaches and ideas are usually needed to tackle it. This is also the case with the innocent-looking "Kakeya conjecture," which relates to the question of how to rotate a needle in such a way that it takes up as little space as possible. Experts have been racking their brains over the associated problems since 1917. But in a preprint paper posted in February, mathematician Hong Wang of New York University and her colleague Joshua Zahl of the University of British Columbia finally proved the three-dimensional version of the Kakeya conjecture. "It stands as one of the top mathematical achievements of the 21st century," said mathematician Eyal Lubetzky of N.Y.U. in a recent press release. Suppose there is an infinitely narrow needle on a table. Now you want to rotate it 360 degrees so that the tip of the needle points once in each direction of the plane. To do this, you can hold the needle in the middle and rotate it. As it rotates, the needle then covers the surface of a circle. On supporting science journalism If you're enjoying this article, consider supporting our award-winning journalism by subscribing. By purchasing a subscription you are helping…