This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American This blog is called "Roots of Unity" because ...

19th-century mathematicians thought the “roots of unity” were the key to solving Fermat’s Last Theorem. Then they discovered a fatal flaw. Sometimes the usual numbers aren’t enough to solve a problem.

If you’ve ever taken an algebra or physics class, then you’ve met a parabola, the simple curve that can model how a ball flies through the air. The most important part of a parabola is the vertex — ...