In this case, that happens to be preventing poor passwords. That is a concrete, real-world problem, requiring practical solutions, which these patents purport to provide (probably) novel, non-obvious variations of. For example, one of the less "decent" patents uses (what seem to be) bloom filters to track and test for poor passwords. This does not mean all uses of bloom filters are covered by it. The claims specifically cover the method of using bloom filters to test for bad passwords.
Really, it becomes clear what is covered when you simply read the claims.
Edit: An early example of a mechanical "algorithm" patent - http://www.google.com/patents/US3765263
The premise of your argument relies on the vague notion of what's a "practical" problem and what's not. I don't think that's any more tenable than any other defense of the current patent system I've ever seen. It's all vague, and exchanges like this are pushing me to a more extreme position that all patents are bogus, rather than granting that some "math" patents are connected to specific practical problems and thus patentable.