Keep in mind that it is easy to make mistakes.

The most striking thing I learned from doing mathematics is that even in an environment entirely devoid of ambiguities and *characterized* by precise axiomatic constraints to the point that it became synonymous with it, even when I am doing my absolute best to be completely careful and precise, even when I double check each of my words, then show it to two careful colleagues, then let it simmer for a while, then go through it again with a critical eye, then show it to an authority in the field, then re-read it again; even after this excruciating process of constant self-examination, even after the strength of my arguments has confounded (perhaps in the two sense of the word) my utmost critical self as well as the objections of several knowledgeable observers, I know that dozens of mistakes, inaccuracies and outright errors still remain.

Doing math is certainly not the only way to come to this bitter conclusion-simply interacting with people is usually enough, as Philipp Roth once famously remarked-yet I can't help to shudder when I sometimes contemplate how many things I *must* be getting completely and obviously wrong whenever I am outside my tiny bubble of professional rigour, where a prompt and witty remark is more than often enough to obtain general assent.