I was "good at math" in school and all through uni. Discrete mathematics crushed me.

These are questions that, again, are tread pretty well in the copyright space. ChatGPT in this case acts more like a platform than a tool, because it hosts and can reproduce material that it is given. Again, US only perspective, and perspective of a non-lawyer, the DMCA outlines requirements for platforms to be protected from being sued for hosting and reproducing copyrighted works. But part of the problem is that the owners of the platforms are the parties that are uploading, via training the MLL, copyrighted works. That automatically disqualifies a platform from any sort of safe harbor protections, and so the owners of the ChatGPT platform would be in violation.

The current (at least in the US) laws do cover work that isn't created by a human. It's well-tread legal ground. The highest profile case of it was a monkey taking a photograph: https://en.m.wikipedia.org/wiki/Monkey_selfie_copyright_dispute

Non-human third parties cannot hold copyright. They are not afforded protections by copyright. They cannot claim fair use of copyrighted material.

But derivative and transformative are legal terms with legal meanings. Arguing how you feel the word derivative applies to our brain chemistry is entirely irrelevant.

You've memorized poems, and (assuming the poem is not in the public domain) if you reproduce that poem housed in a collection of poems without any license from the copyright owner you've infringed on that copyright. It is not any different when ChatGPT reproduces a poem in it's output.

By nature of a human creating something "connected" to another work, then the work is transformative. Copyright law places some value on human creativity modifying a work in a way that transforms it into something new.

Depending on your point of view, it's possible to argue that machine learning lacks the capacity for transformative work. It is all derivative of its source material, and therefore is infringing on that source material's copyright. This is especially true when learning models like ChatGPT reproduce their training material whole-cloth like is mentioned elsewhere in the thread.