The domain where I've had the the most — what you might call — formal academic training is mathematics. Having spent years tutoring students in math (which means, by implication you're spending time with students who are less adept than the average at math) I understand that there is a definite peculiarity in the way people approach problems in math. Ordinary thinking involves guessing an answer — taking a shot in the dark — then trying to justify the guess as quickly as possible so you can move on to new problems. This manifests with students prepping for multiple choice tests saying something like, "It's B, isn't it?". And if I nod yes, they're right and they get to go onto the next question. But, as happens more often, I don't nod and that guess hasn't brought them any closer to a solution to the problem.
Math involves stepping back and looking at the problem from many different angles. It seems extraordinarily counter-intuitive if your goal is simply to get the pencil mark in the bubble for B.
Professor Persi Diaconis, in addition to being a professor of statistics, is also a world renowned magician, so when his work pops up in my news feed, I perk up. This is a wonderful example of the application of mathematical thinking to a very mundane problem. I guess the typical reaction to be a transition from this guy's so weird to this guy's so freakin' smart.