Another matter worth mentioning, which relates only partially to cryptology itself, is that you might hear claims that new lossless compression methods have been discovered that have fundamentally new properties. In extreme cases, a compression algorithm is sometimes purported to compress any data sequence by some amount. There is a one-line reductio ad absurdum for this case: Iterate compression of each "compressed" result; if everything is compressible, you wind up with a one-bit (or zero-bit) representation for every original data sequence. But weaker claims are often similarly absurd.

A basic understanding of compression is important to cryptology because both largely come down to the same concept of entropy and information content. Not all data is compressible for the same reason that PRGs cannot generate OTPs -- the redundancy, entropy, and information content of data are fundamental properties of that data, and these factors fundamentally constrain what transformations can be made to data.