Either somewhere on the far left, and we'll see some actual breakthrough with major impact in the future which actually gets hyped, or on the far right and it already happened, it was just too niche for anyone other than a specific small group to notice.
I think the big breakthrough was in cryptography, and yeah, most people don't care. All of your passwords will be useless against brute force attacks in 10-15 years from it tho!
That's a pretty big assumption though, and even then you can just switch to a new password format that allows for passwords that aren't solvable using mathematical means. e.g. my password is to fill in a picture on 10x10 grid using 10 different colours. There's no mathematical basis to guess my picture and there are more posibilites than there are particles in the observable universe.
That's perfectly solveable with math. Each grid square can take 10 colors, so there are 10^100 possibilities. That's about 330 bits of entropy, or equivalent to a 51 character password. That's gross overkill if the underlying cryptosystem isn't broken, but insufficient if it is (depending on the details).
Cryptography routinely deals with much, much larger numbers than what you're suggesting (e.g. any RSA key), and even those get broken occasionally.
It's no more an assumption than "Our current quantum-proof passwords are secure against a type of computer that is entirely conceptual at current time."