For anyone who wonders about the applicability of advanced math to everyday life:

There’s a good chance your data integrity relies on it.

When you think about RAID-5 at a superficial level, it kinda makes sense – ‘sure, you can take a 1/n capacity hit to ensure that you still have all your data if one drive dies, why not?’

Then you think about it a bit harder and think waiiiiiiiit, how does that work EXACTLY?

Then you go look up how RAID-6 works and bless the mathematics departments…

(note to mathematicians: this may well not be ‘advanced’ to you. It sure is to the rest of us, though.)

RAID 5 is trivial math. RAID 6 is indeed more interesting, you need more number theory (i.e. abstract algebra applied to integers) there (and the Wikipedia summary is very confusing, parts of the paragraph try (and fail) to be intuitive to everyone, and then other parts assume knowledge of algebraic notation such as quotient rings, but parts of the algebra were “simplified” away; the PDF it links as a source is a much better reference).