Every pure mathematician has experienced that awkward moment when asked, “So what’s your research good for?” There are standard responses: a proud “Nothing!”; an explanation that mathematical research is an art form like, say, Olympic gymnastics (with a much smaller audience); or a stammered response that so much of pure math has ended up finding application that maybe, perhaps, someday, it will turn out to be useful. That last possibility is now proving itself to be dramatically true in the case of category theory, perhaps the most abstract area in all of mathematics. Where math is an abstraction of the...