Earlier quoted context omitted.
> We will be able to crack today’s encryption algorithms in the future because we’ll find flaws in them. Big if. We already knew how to design good and strong symmetric ciphers way back in the 1970s. One of the standard blocking blocks of modern symmetric cipher is called the Feistel network , which was used to create DES. Despite that it's the first widely used encryption standard, even today there's essentially no…
Placing no time constraints, my gut tells me it’s almost inevitable those breakthroughs will eventually come. Either in mathematics or quantum computing. Or both. Namely I’d ask when not if. My opinion is that short of the one time pad, we won’t come up with provably unbreakable schemes.
The big assumption of cryptography is that, there exists some problems that are not provably unsolvable but difficult enough for almost any practical purposes. To engineers, no assumption can be more reasonable than that. Given unlimited time, it's a provable fact that any (brand new) processor with asynchronous input signal will malfunction due to metastability in digital circuits, it's also a provable fact that metastability is a fundamental flaw in all digital electronics - but computers still work because the MTBF can be made as large as necessary, longer than the lifetime of the Solar system if you really want to.
So the only problem here is, how long is the MTBF of today's building blocks of symmetric ciphers? If it's on the scale of 100 years or so, sure, everything is breakable if you're patient. If it's on the scale of 1000 years, well, breaking it is "only" a matter of time. But if it's on the scale of 10000 years, I don't believe it's relevant to the human civilization (as we know it) anymore - your standard may vary.
The problem is that computerized cryptography is a young subject, the best data we have so far is symmetric ciphers tend to be more secure than asymmetric ones. We know that Feistel networks have an excellent safety record and remain unbroken after 50 years. We also know that we can break almost all widely used asymmetric ciphers today with large quantum computers if we can build one, but we can't do the same to symmetric ones - even the ancient DES is unbreakable if it's redesigned to use 256-bit keys. So while nobody knows for sure, but most rational agents will certainly assign higher and higher confidence every year - until a breakthrough occurs.
> My opinion is that short of the one time pad, we won’t come up with provably unbreakable schemes.
Many mathematicians and some physicists may prefer a higher standard of security than "lowly" practical engineers. This is the main motivation behind quantum cryptography - rather than placing security on empirical observations, its slogan is that the security is placed on the laws of physics. Many have pointed that the this slogan is misleading: any practical form of quantum cryptography must exist in the engineering sense, and there will certainly be some forms of security flaws such as sensor imperfection or at least side channels... That being said, I certainly understand why it looks so attractive to many people if you're the kind of person who really worry about provability.