1. What is the value of skepticism? I thought math was a clear example: math is counterintuitive and so skepticism is good. But this is not always true: intuition in math is one of the most useful things! I think I am confusing two things, let’s see. Skepticism: not taking things for granted; looking for the proof; reducing to bare essentials. Intuition in math: what you expect to be true is true; things that are not equal can be assumed to be equal and to have similar properties. The difference: you can use your intuition and be a skeptic. How? Perform the step without believing it. A skeptic, non-intuitive person will say “I don’t know whether this is True, so I cannot move forward”. A skeptic, intuitive person will say “I don’t know whether this is True, let’s see what happens if we assume it.” This works in technical subjects, but it is more complicated in your personal life. Exploring things that you don’t understand might lead to addictions. (This is more of a problem if you are an “optimist under uncertainty.”) The right way of being a skeptic requires exploration (so requires intuition.) But how much do you explore? It is a question of reversibility.

1′. I have a very insightful math collaborator that doesn’t know how to pronounce several math words (and he is a native English speaker.) In the same way that he mixes the letters, he can mix concepts that are not clearly related, and this might be the source of his insight. He doesn’t require a proof of two concepts being the same to operate under that assumption (he might not even notice they are different.)