Math Therapy

If mathematics is supposed to be the underlying structure and grain of the universe, but so many people have trouble resonating with it, then why not math therapy — to restore one’s personal harmony with math?  Sometimes I think that, at its best, the part of my job that’s actually teaching math should approach this ideal.  When you peel away the techniques of classroom management, when you peel away the signposts to important facts and theorems — what, ultimately, I mean, are you trying to pass on?

Even more so recently than ever before, I’ve come to feel that the search for interesting and rewarding mathematical topics leads in a plethora of unexpected directions.  I imagine that for many of these, even calculus might be mostly or entirely unnecessary.  Why shouldn’t it be one of the multitude of natural states available to a person to make, and then try to answer, interesting mathematical inquiries?  Why shouldn’t it be an integrated part, if one chooses, of personal, of social life?

Maybe I’ll write a story about a math therapist.

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de Gua’s Theorem

Last week I was first made aware of de Gua’s Theorem about triangle areas in 3-dimensional space.  It’s (I find) a supremely pretty theorem, easy to state, and not horrendous to prove either: I even attempted to demonstrate a proof I had come up with to some precalculus students this past week.  (Anyone who’s interested in a proof should let me know!) So why had I never heard of it before?  This is the kind of theorem for which I expect several gorgeous demonstrations….