Yesterday I had one of those moments that’s probably the worst nightmare of any PhD student who’s writing their thesis dissertation, and doubly so in mathematics.
Reading through a proof I’d first written some three years ago, I found an error.
What at first seemed to be a small issue, when investigated, turned out to be major.
Mathematical proofs are like towers, each proof sits on top of others, which rest on others and so on, all the way down to axioms that define the basis of everything else.
Well, my entire thesis is sitting on top of a couple of theorems, and it was in the proof of one of those that I found the error.
To put this in perspective, if this theorem turned out not to be true, over 40 pages of mathematical proofs and my entire thesis would be worthless, sitting on a base that wasn’t even there.
Of course, I never really expected that to be the case, but writing a proof can be a tricky thing, and it’s often hard to tell how long it will take to finish one.
Anyway, a day and a half later and while I don’t have it all written out, I’ve got the structure of a new proof sorted out and am confident that I’ve covered everything this time.
As an added bonus, it looks like I can prove something that’s a bit stronger than the original theorem and if that’s the case, it will make the last chapter I have to write a bit more straight forward.
It’s the silver lining that’s important after all.
Note: The xkcd comic is a tenuous link at best, but how could I resist sticking a proof based comic here?