Apart from the one-time pad or something equivalent, I don't think anybody can fully guarantee (to the point of mathematical proof) that any particular encrypti

Apart from the one-time pad or something equivalent, I don't think anybody can fully guarantee (to the point of mathematical proof) that any particular encryption is mathematically unbreakable. The existence of true one-way functions is technically an open question in the first place. And even if you make the (probably reasonable) conjecture that one-way functions do in fact exist, there's still a lot that isn't known about the fundamental computational hardness of various problems used for encryption. Most statements about the strength of particular encryption methods are educated guesses based on current mathematical understanding. Some particular encryption may be unbreakable for millions of years assuming no breakthroughs in mathematics that would allow significant shortcuts in breaking the cipher. For some mathematical problems those breakthroughs may seem more likely than for others. Would be glad to hear if someone with current understanding of cryptography has more insight, though.