I mean 40 bits is better than a correct-horse-battery-staple format password by a little bit. The space of all interesting equations is presumably tiny, but I do think I could memorize a random twenty-expression password almost as well as I could remember 6 or 7 words (since many random arrangements will be somewhat meaningful). I'll stick with my 5 random words because they're easy to type, but so long as you draw at random it really doesn't matter what you're sampling from.
That's right. My million-x-million estimate was rhetorically generous. (xkcd's specific example was about 44 bits.)
OP -- not to put too fine a point on it, but it's a terrible idea. So much money has been lost to brain wallets in the digital-currency space by people who picked obscure song lyrics, wrote it backward in pig latin, capitalized every third letter etc. etc. etc. and then wondered why their balances were zeroed out. You want the competition to be about the limits of physics, not about the limits of your creativity vs. an army of computers.
Read Moonwalking with Einstein by Joshua Foer to see how easy it is to memorize things using the memory-palace technique (https://en.wikipedia.org/wiki/Method_of_loci). Anyone can remember a 10-word phrase, especially if you build it up by adding a word or two every few weeks. The key is to start with something unguessable, as ravi-delia says, like https://iancoleman.io/bip39/. If you start with something guessable like a transliterated math expression, then you brought a knife to a gun fight.
