Besides the satisfaction of cracking this long-lasting problem, proving the Kakeya conjecture will also help mathematicians solve related problems using the mathematical tools developed by Zahl and Wang. “In my subfield of analysis, it’s certainly the biggest advance in 10 years,” says Tao. “This conjecture is part of this whole family of problems that seemed impossible.”

Answering those problems could in turn help unpick some of the biggest questions in areas like general relativity or harmonic analysis, the mathematical study of how waves behave, says Guth. The proof could even help reveal the origin of prime numbers by tackling one of the most infamous unsolved problems in maths, the Riemann hypothesis.

“The Kakeya conjecture is just one tiny component of what’s going on with the [Riemann hypothesis], but it was one of many obstacles, and so now that’s gone, lots of things are now unlocked,” says Tao. “I foresee years and years of activity now on this whole tree of harder problems in number theory, partial differential equations, combinatorics and so forth, which were just considered hopeless, now they seem just very difficult.”