It’s final: a pyramid over a crate

I didn’t read this week’s NYT science article (here) until today. I once fancied myself as being mathematically-inclined (it seems, in retrospect, that I have fancied myself inclined in very many ways over the years…hmmmm..) and so I read the article with greater care than I normally would read a piece from under the “science” rubric.

It appears that one of the oldest problems of math has been conclusively solved (as demonstrated by the acceptance of the proof by a leading mathematics journal). No, don’t stop reading! You may want to know, even if you have no interest in math. The problem is all about the most efficient ways to pack oranges (originally stated as a problem of stacking cannonballs): the pyramid holds more than the crate. Why? The Times gives this simple layperson’s explanation: “(the pyramid) allows each layer of oranges to sit lower, in the hollows of the layer below, and take up less space than if the oranges sat directly on top of each other.”

The article explains how the computer-assisted proof initially raised eyebrows (checking issues arose). It is a fascinating story of how mathematics can no longer rely on the human brain to solve its remaining puzzles (but neither can it simply feed the problems to the computer, for understandable reasons). But I am still stuck on this very basic truth: pyramid over crate. So easy, so logical, but I would have never guessed.