Thank you for all these interesting references. I enjoyed reading all of them, and rereading in Thurston’s case.

Do people pathologize Grothendieck as having gone crazy? I mostly think people think of him as being a little bit strange. The story I heard was that because of philosophical disagreements with military funding and personal conflicts with other mathematicians he left the community and was more or less refusing to speak to anyone about mathematics, and people were sad about this and wished he would come back.

Just a quick note on your main example—in math, and I’m guessing in theoretic areas of CS as well, we often find that searching for fundamental obstructions to a solution is the very thing that allows us to find the solution. This is true for a number of reasons. First, if we find no obstructions, we are more confident that there is some way to find a solution, which always helps. Second, if we find a partial obstruction to solutions of a certain sort, we learn something crucial about how a solution must look. Third, and perhaps most importantly, when we seek to find obstructions and fail, we may find out way blocked by some kind of obstruction to an obstruction, which is a shadow of the very solution we seek to find, and by feeling it out we can find our way to the solution.