“... the KLS conjecture (named after its creators, Ravi Kannan, László Lovász and Miklós Simonovits) asks a simple question: Suppose you want to cut a convex shape — maybe an apple without dimples — into two equal-size portions, and you’re planning to put one aside for later. The exposed surface is going to turn brown and unappetizing, so you want to make it as small as possible. Among all the possible cuts, which will minimize the exposed surface?

“It’s not too hard to answer this question, at least approximately, if you are limited to straight cuts. But if you’re allowed to make curved cuts, all bets are off. In dimension two, mathematicians know that the best cut will always be a straight line or an arc of a circle.…