It‘s easy to google how Shazam works now, since they exist.

I‘m pretty sure that googling for „audio fingerprint“ or „algorithm for recognizing a song“ wouldn‘t have gotten you the answer in 2002.

You need to know the maths if you want to invent something new. If you just want to reimplement existing stuff, maybe you can get away without it.

(Inventing new stuff is actually pretty rare for programmers. I don‘t think I‘ve actually invented much, despite having worked as a software developer for more than 15 years...)