The Surprising Simple Math Behind Puzzling Matchups — Quanta Magazine

My latest column for Quanta Magazine is about one of my all-time favorite mathematical ideas: transitivity. Well, technically it’s about intransitivity, a subtly complex mathematical situation which any sports fan knows all about.

It’s the championship game of the Imaginary Math League, where the Atlanta Algebras will face the Carolina Cross Products. The two teams haven’t played each other this season, but earlier in the year Atlanta defeated the Brooklyn Bisectors by a score of 10 to 5, and Brooklyn defeated Carolina by a score of 7 to 3. Does that give us any insight into who will take the title?

Well, here’s one line of thought. If Atlanta beat Brooklyn, then Atlanta is better than Brooklyn, and if Brooklyn beat Carolina, then Brooklyn is better than Carolina. So, if Atlanta is better than Brooklyn and Brooklyn is better than Carolina, then Atlanta should be better than Carolina and win the championship.

Sports fan knows things are never this simple, and in my column I explore some of the surprising mathematical reasons why it may be the case that A is better than B and B is better than C, but C is better than A. You can read the full column for free here.