The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true.

Have you ever sat in a math classroom and wondered, “When will I ever use this?” You might have asked yourself this question when you first encountered “imaginary” numbers, and with good reason: What ...

For the first time, physicists have built a working version of quantum mechanics without complex numbers — numbers that have been considered essential to the theory for nearly a century. Complex ...