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This is pretty fascinating. For easier reading, the Signal blog post [0] they link to is great.
Both Signal and Apple went with CRYSTALS-Kyber [1] as their post-quantum algorithm. If you're interested in the math, and maybe learned at some point about how classic public key cryptography is built on the idea that it's easy to multiply two primes, but hard to factor them, and how this (or other math problems) can be used as a one-way function to make encryption hard to break, the hard math problem that backs Kyber is the "learning-with-errors" [2] problem.
[0] https://signal.org/blog/pqxdh/
[1] https://pq-crystals.org/kyber/
[2] https://en.wikipedia.org/wiki/Learning_with_errors