Sean Carroll in Preposterous Universe:
There are some problems for which it’s very hard to find the answer, but very easy to check the answer if someone gives it to you. At least, we think there are such problems; whether or not they really exist is the famous P vs NP problem, and actually proving it will win you a million dollars. This kind of question falls under the rubric of “computational complexity theory,” which formalizes how hard it is to computationally attack a well-posed problem. Scott Aaronson is one of the world’s leading thinkers in computational complexity, especially the wrinkles that enter once we consider quantum computers as well as classical ones. We talk about how we quantify complexity, and how that relates to ideas as disparate as creativity, knowledge vs. proof, and what all this has to do with black holes and quantum gravity.