I agree that the answer is complicated, but I don't agree that we must appeal to mathematics to solve the problem. We need to have a discussion about what is a good compromise and how much security and privacy we have to sacrifice in order to ultimately strengthen them. We sacrifice some of our privacy and security by allowing government to break into our homes, yet we feel safer and more private because law enforcement and our justice system is on our side and works to thwart criminals. It isn't perfect, but I personally would feel less comfortable if our homes were impenetrable - think of the ramsomware cases with encryption. The fact that there's no way to unlock those encrypted machines without the key is a tragedy. You might say the answer is to stop the ramsomware nuts instead of undermining encryption, but that's like saying we should stop the pedophile from raping our kid in his impenetrable basement instead of making it so we can break in.

How do we solve this? It's hard to say, but there are solutions. foolshdropout's first Guardian link presents a good example with the TSA luggage lock standardization. That is essentially a backdoor and has led to many thefts. The flaw in that example, however, is that with enough force, a lock can be broken, and any luggage can be penetrated, making the need for master keys and standardized locks unnecessary. So, it's not a good analogy with encryption, which cannot realistically be broken into.

Giving the government master keys to standardized encryption methods is not a good way to do it. However, the FBI's method of getting Apple to disable the guess limit is a "lesser" backdoor, if you must call it that. That provides some compromise because it requires the government going to Apple for each warrant and having them on a case-by-case basis disable the limit. This adds a few hurdles to slow down the process, which is basically what encryption does in the first place, while allowing authorities to lawfully search and seize.

I'm not sure what the answer is, but I know that if we stick to absolutes (total encryption, no encryption), we are only hurting ourselves.