Fascinating. Still reading through and processing this paper. "Mathematicians are those humans who advance human understanding of mathematics." I would submi

Fascinating. Still reading through and processing this paper. "Mathematicians are those humans who advance human understanding of mathematics." I would submit that there are mathematicians (great ones indeed) who did not seek to advance human understanding of the subject, but may have regardless done so as a side effect of the thread they tugged upon, the tapestry unraveled. Of course, a utilitarian perspective (at least in retrospect) would consider their ultimately accepted works to have advanced human understanding. Yet I have observed some mathematicians regard their pursuit to be entirely personal, something to the effect of daring to perceive the true contours of logic and patterns in the universe, in their purest form. They revel in the beauty of universal abstractions, the way another might admire and gaze upon a blue lilac in one's own garden. With this in mind, I would consider these mathematicians having only first undertaken the more lofty goal of advancing human understanding, at the moment they communicate their perceptions with the rest of the world (by publication or other discourse). At that time, they have decidedly entered into the more heavily social nature inherent in any modern intellectual discipline.