"quantum resistant forever" is too strong.
I've only taken fairly general master's level courses in quantum information and regular cryptography, but I agree with this overall sentiment. My math professors used to say that no asymmetric encryption scheme has been proved unbreakable; we only know if they haven't been broken so far. Assuming something is unbreakable is like saying Fermat's last theorem is unprovable — until one day it's proved. So to me "post quantum cryptography" is essentially a buzzword.
Yes, but... I think you're confusing some things. We're talking about AES, which is a symmetric encryption algorithm, not asymmetric.
Of course, no cryptographic construction has been "proven" secure, in the sense that mathematicians use the word "prove", not symmetric or asymmetric. Asymmetric schemes have an additional challenge, though, which is they have to have some sort of "trapdoor function" that mathematically relates a public key and a private key, and the public key has to be published to the attacker. Classical asymmetric cryptography is built by finding a hard math problem and building a scheme around it -- which means that a solution to the math problem breaks the algorithm.
Symmetric systems have it a bit easier, because the attacker doesn't get to see any part of the key or anything related to the key other than plaintext and corresponding ciphertext (though the standard bar is to assume the attacker has an oracle that allows them to get plaintext of arbitrary ciphertexts, i.e. the Adaptive Chosen Ciphertext attack, IND-CCA2). And the structure of symmetric ciphers isn't usually built around a specific math problem. Instead, they tend to just mangle the input in extremely complex ways. It's hard to model these mathematically, which makes attacking them with math hard.
In both cases, we are unable to prove that they're secure. When I started working on cryptography, the only basis for trust in algorithms was that they'd stood up to scrutiny for a long period of time. That was it. Over the last 20 years or so, we've gotten more rigorous, and "security proofs" are basically required for anyone to take your algorithm seriously today... but they aren't quite like "proofs" in the usual sense. They're more precisely called "reductions". They're mathematically-rigorous proofs that the security of the algorithm (or protocol) is reducible to a small set of assumptions -- but we have to assume those, because we can't prove them.
For most asymmetric schemes, the primary underlying assumption is that the mathematical problem at the heart of the scheme is "hard". Interestingly, there is one family of asymmetric signature schemes for which this is not true. SLH-DSA, one of the post-quantum algorithms recently standardized by NIST, provably reduces to one assumption: That the hash algorithm used is secure, meaning that it has both second pre-image resistance plus a more advanced form of second pre-image resistance. Collision resistance isn't even required! This is striking because we actually have quite a lot of confidence in our secure hash algorithms. Secure hash algorithms are among the easiest to create because all you need is a one-way function with some additional properties. And we've been studying hash functions very hard, for quite a long time, and understand them pretty well.
This means that one of our "new" post-quantum asymmetric algorithms is probably the very strongest we have, not only less likely to be broken than our other asymmetric algorithms, but less likely to be broken than our symmetric algorithms. If it were broken, it would be because someone broke SHA-256 (which, BTW, would break enormous swaths of modern cryptography; it's extremely hard to find a cryptographic security protocol that doesn't use SHA-256 somewhere), and unless that same research result somehow broke all secure hash functions, we could trivially repair SLH-DSA simply by swapping out the broken hash function for a secure one.
This is an entirely different model from the way we looked at cryptography early in my career. SLH-DSA doesn't have decades of use and attack research behind it. Oh, the basic concept of hash-based signatures dates back to the late 70s, but the crucial innovations that make SPHINCS and its descendants workable are barely a decade old! BUT we have a rigorous and carefully peer-reviewed security proof that demonstrates with absolute mathematical rigor that SLH-DSA is secure iff the hash function used in it is secure.
So... a relative newcomer is more trustworthy than the algorithms we've used for decades, precisely because we no longer rely on "hasn't been broken so far" as our only evidence of security.
As for AES, the subject of the discussion above, there is no security proof for AES. There's nothing to reduce it to. There are proofs that it is secure against specific attack techniques (linear cryptanalysis and differential cryptanalysis) that were able to defeat other block ciphers, but those proofs only prove security against those specific attacks, not other attacks that are not yet known. So for AES we really do rely on the fact that it has withstood 20+ years of focused cryptanalysis, and that no one has managed to find an attack that significantly weakens it. That could change at any time, with or without quantum computers.
SLH-DSA, however, is one that very well may be secure forever, against both classical and quantum attacks. The security proof doesn't even care about classical vs quantum, it just proves that any successful attack, no matter how it's performed, provides a way to break the underlying hash function. Therefore, if the hash function is secure, SLH-DSA is secure. It's an incredibly powerful proof, like many proofs by contradiction.
