There is a problem with the organization. At least one of the explanatory paragraphs in "2" of the table of contents should come before "why I find it interesting".
Definitely recommend reading a little of this first:
Although I usually rail against Wikipedia math articles being gleefully esoteric jargon describing concepts in the most aggressively arcane way possible as if it's a competitive sport, the convex function article is fine. People have clearly done work on it
(People might say, well isn't it obvious what convex means. My response is no, it's dealer's choice)
Definitely recommend reading a little of this first:
https://en.m.wikipedia.org/wiki/Jensen%27s_inequality
(Could just provide a link to it near the beginning of the article for reference.)