A word on difficulty

An aphorism, no doubt unoriginal, but my own work anyway:

In studying mathematics the perceived difficulty of learning anything tends to be a constant; but as the absolute difficulty of the things you learn tends to increase, you’re getting better, aren’t you?

Not that you notice unless you have a reason to look back; doing TA work or something similar. Then the realization really brings a smile (leer?) to your face.

The same thought in Finnish, though formulated a bit differently:

Matematiikassa asiat tuntuvat aina yhtä vaikeilta; mutta kun ne kuitenkin ovat aina absoluuttisesti vaikeampia, se kai tarkoittaa että olet oppinut jotain. Tai sitten päässä viiraa jo niin pahasti ettei huomaa ettei enää ymmärrä pahimpia vaikeuksia.

(In mathematics things always feel just as thorny as they used to; but as they’re always more difficult than they used to be, that probably means you’ve learned something. Or then your brain’s going and you don’t even notice the really hard parts.)

Or: a harrowing exam problem today; a trivial aside consideration in a harrowing exam problem tomorrow.

(This probably stops applying when you get your doctorate and become a Dark God of ineffable perspective and unspeakable omniscience; but those beyond that singularity seldom reflect on things like this: when you ask, their eyes simply start to glow, they levitate a few feet off the ground, and say: “Learn? Yes, I suppose I did that in my previous life, mortal. Now fetch me a sacrificial coffee offering, no milk, three sugar!”)

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