The Mathematical Grue

A discussion over at God Plays Dice had me nodding in agreement: proving a theorem is like playing an adventure game. As Isabel puts it

You are in a maze of twisty little equations, all alike

alluding to a particularly fiendish puzzle in the text adventure Colossal Cave.

Having recently grappled with some tricky proofs I was wondering how they might play out as a piece of interactive fiction…

You are sitting before a particularly thorny conjecture. Possible proofs lead away from here in several directions. > inventory You are carrying the following items: A ream of blank paper A pencil The Cauchy-Schwarz inequality Some half-remembered undergraduate mathematics > look conjecture You stare blankly at the conjecture. You think it might have something to do with convexity. > w You surf over to Wikipedia and read up on sub-tangents. The notation makes you confused. There is a lemma here. > take lemma Taken. > e You wander off to go get a bite to eat and some coffee. You see a colleague here. > talk colleague After explaining your conjecture your colleague mutters that it was probably proven in the 50s by a Russian. > s You sit back down at your desk and spend half an hour reading pages linked to from reddit. You see an unproved conjecture here. > use lemma [on the conjecture] With a bit of manipulation you turn the equation into one involving the expectation of a product. > use Cauchy-Schwarz [on the conjecture] Hooray! You now have a tight bound on a key quantity, proving your conjecture. > generalise assumptions Your theorem was eaten by a Grue.