Advances in AI and nanobiotech can radically increase intelligence to the point where unsolved mathematical problems get solved.
What happens to Bitcoin (and other cryptocurrencies) if ⨕ 1-way functions cease to exist?
without modifications the current bitcoin system would simply be compromised.
it seems very likely all private-public key cryptography would be compromised as well, and society as we know it would change.
however, given unknown advances to begin with, there is always the chance that something entirely different could replace the current system of secrecy when it comes to trust.
there is also the possibity that no matter how many advances we get, 1-way functions might be impossible to completely break, or that we find new maths that guarantees breakage if any 1-way function but with a cost that is prohibitive.
Luckily, reverting the one-way-ness of cryptographic hash functions is not a mathematical problem. Rather, cryptographic hash functions destroy part of the information by projecting from an infinite space to a finite space. Reversing this is only possible by brute-forcing, and the finite space is sufficiently large that this is considered to be infeasible. It's not clear to me how either nanobiotech or advances in AI should improve the speed of brute-forcing.
However, quantum computing is brought up frequently in that context since it allows to try many different possibilities in parallel. Should we succeed at creating quantum computers that can search sufficiently large number spaces in parallel this would be very efficient at brute-forcing the reversion of hash functions. Mining difficulty would grow exponentially over night and ECDSA would possibly be broken as well.