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?

A long-standing puzzle seems to constrain how addition and multiplication relate to each other. A graduate student has gone further than anyone else in establishing the connection. In 1983 the ...