Nope. Logical axioms are required logically, but not associated with time. Comprehension is associated with time, so I can understand how you might arrive where you did.
Sorry but I don't understand how you're using the word 'comprehension' here. I agree that logical axioms aren't associated with time (this is what I mean when I say that math doesn't require an idea of time).
How condescending can you be? I guess that's solved!?
There are multiple 'types' of homeless, that I have encountered across multiple states. There is some overlap. Most of the homeless DO NOT WANT to have the responsibility (cognitive or financial) of a home, bills, etc. They believe that they are happy making do and tend to congregate in the same municipal areas. What do you think happens to the least intelligent of a society? Honestly, this population will only grow. On the other side, people who want help get it, as every camp and clearout includes copious social workers. You need 0 resources to get a medical and dental insurance in Washington State. Social services are offered everywhere the homeless gather, but unsurprisingly they don't usually take it.
One of the most common 'types' is the homesteader. The kind of people who live out in the desert in trailers have moved to more populous, relatively comfortable areas to live as they like due to the purchase/development of the areas they would normally squat on. This type of nomad living isn't strictly a mental illness, but it's also not an issue of housing.
The second 'type' is the addict. Now this isn't always drugs, although it almost always devolves into that. Some people are hoarders (an addiction) or pet hoarders, or whatever and slowly but surely are stripped of everything they have. Then it tends to turn to a replacement like drugs. These are also the most common criminal element. Stealing bikes, hoses, whatever to feed their various addictions and to give them purpose. Being homeless is boring.
The third type is the more sympathetic hard case. These are the people that are turned away from shelters, but won't let go of the dog they keep, which is all that's left from their previous life. They tend to accept help, but there's a shortage for even this sliver.
For now, making homelessness illegal in incorporated counties, without enrollment and participation in rehabilitation programs, this will continue.