I think most people commenting in this thread are reading the headline and/or reading the article as outside the context of mathematics. This is Terry Tao's blog and not a VC's microblog. The very first block of text is a quote from "I want to be a mathematician". He is purely talking about how to approach mathematics at a level sufficiently close to the frontier. What he is saying is that when you are taught something like optimization theory, the definition of convexity is presented to you in the first lecture. A "stupid" question to ask is what makes convex functions special. After thinking a lot about this question, I've come to the conclusion that convex functions are functions that are trivial to optimize but the converse is not true. Not all function that are trivial to optimize are convex functions. There are then plenty of questions like which other classes are easy to optimize. In Terry's words, "the answers to these questions will occasionally lead to a surprising conclusion, but more often will simply tell you why the conventional wisdom is there in the first place, which is well worth knowing.". Another example I ran into was the notion of metric spaces and completeness. It is "stupid" to ask what happens if you get rid of completeness. Stupid because you were just taught completeness for a reason. Trying to understand gives you a whole new appreciation than being presented the formal definition refined over many years.