- If one were to think about maths and children’s education one would need to look at the needs of other subjects too. It should be easy for people here to work out how cats ties in with physics and biology — having a maths of open systems could help a lot there. But one would also want to help maths tie in with the humanities. In France children sometime after 13 or so read Voltaire’s Candide published 1759, where Voltaire makes fun of Leibniz’ idea that we live in the best possible world, by having Candide go around the world and witness all the suffering known at the time. It would be good if the maths department then also gave some introduction to fragments of contemporary modal logic, so that the children could see that the “best possible world” idea is abandoned by contemporary modal logics.
I’ve never found much use for modal logic in mathematics proper since mathematics is all about possible existence, in the sense of what is not inconsistent with a given set of premisses. Of course, one can entertain modal logic as an endeavor to construct mathematical models of natural language intuitions about possibility, contingency, necessity, etc. but that is an application of mathematics to an empirical domain.
As far as best possibilities go we certainly do a lot of work on optimization in math and its applications to the special sciences and engineering. For instance, a lot of physics begins with skiers on snowy slopes and their contemplation of gradients. That very sort of thinking by Leibniz led to his personal discovery of differential calculus.