While I can not claim to have made any imporant progress on the sorts of toy problems I like to work on (e.g. counting/bounding the number of strings two regula

While I can not claim to have made any imporant progress on the sorts of toy problems I like to work on (e.g. counting/bounding the number of strings two regular expressions both accept, counting the number of ways to represent integers using polynomials), I find the mere process of working on them, inventing new notation to succinctly express ideas and read relevant (and completely irrelevant) mathematical textbooks and articles a way to keep an "active brain" but relax: probably because nobody expects me to produce anything and my career doesn't depend on it.