This summer, battle lines were drawn over a simple math problem: 8 ÷ 2(2 + 2) = ? If you divide 8 by 2 first, you get 16, but if you multiply 2 by (2 + 2) first, you get 1. So, which answer is right?

Long considered solved, David Hilbert’s question about seventh-degree polynomials is leading researchers to a new web of mathematical connections. Success is rare in math. Just ask Benson Farb. “The ...