I enjoyed this account very much, but I can offer one small bit of constructive criticism. You wrote: “Mathematicians worry about spending time on problems of insufficient difficulty, what they dismissively call “toy problems”; Claude Shannon worked with actual toys in public!“ You seem to have the wrong idea about how mathematicians use the term “toy problem.” To a mathematician the term “toy problem” refers to what is left of a problem after removing all of the “bells and whistles” (to borrow your terminology), and, in fact, is a term that mathematicians use with great affection. A “toy problem” is a problem where all technical garbage has been stripped away, leaving the problem-solver with nothing but the most essential part of what matters in the original problem.
Best,
Ivan Blank
Associate Professor of Mathematics
Kansas State University