Scott Kim wrote--
I think it's an occupational hazard of being an expert in any field, not just math, that it can be hard to explain what you do to an outsider. Nonetheless I think it's important to do, and not just for outsiders, but also for people inside the field. At least it's important to me — the dearth of mathematicians talking about what mathematics is I find intolerable, and makes me distrustful of mathematics as a field. Ted Nelson's _Computer Lib_ (1974) for me was a taste of what the good thing can be:
An enthusiastic insider in a field who is also a skeptical outsider without missing a beat. There's the public-facing importance of that (especially with something commercial like computers), but also I like the way I oriented myself after reading that book. Stewart Brand, Martin Gardner, Aubrey de Grey, Vi Hart. https://youtu.be/v-pyuaThp-c "Doodling in Math Class: Connecting Dots" (talk about not missing beats) --Steve