## Math is really hard

(8,866,128,975,287,528)^{3} + (–8,778,405,442,862,239)^{3} + (–2,736,111,468,807,040)^{3} = 33.

“So what?” you ask: And here’s why:

One reason to find the answers to these so-called “stubborn numbers” is because mathematicians don’t really like having unsolved equations laying around. Another is that finding solutions like this can play a role in some future attempts to find proofs for

k = xor proofs that use it.^{3}+ y^{3}+ z^{3}

What made 33 “stubborn”? The luck of the draw, mostly. It is now known that if you divide an integer by 9 and get a remainder of 4 of 5, that integer cannot be expressed as the sum of three cubes. Excluding those poor unfortunates, the next-to-last integer to be verified was 33, with the complicated-looking equation up top being the actual solution. It took three weeks of supercomputer cycles to find this solution, which suddenly makes bitcoin mining seem almost whimsically simple.

Anyway, 1 through 99 are almost now accounted for. The last holdout: 42, because of course it is.

## McGehee »

31 March 2019 · 9:02 am

So we really DON’T know the question yet. Those mice better keep the Vogons away this time.

## hollyh »

1 April 2019 · 8:10 am

ha ha! Nice reference to the Ultimate Question to Life, the Universe and Everything.