My understanding is that AI can be understood as a very generalized and abstract statistics software package handling input data in a general way to find the "best fit" to some form of problem. Is that correct? I know it isn't. But is it vaguely correct?
No. It's not correct, in my opinion, not even vaguely (maybe partially yes) and in many ways.
- AI is not (necessarily) abstract (although there are examples of theoretical frameworks of AI, such as AIXI, which may be of interest to you, given that you are about to become a theoretical physicist)
- AI does not necessarily generalize statistics or statistical concepts
- AI is not just machine learning or, more precisely, supervised learning. You're very likely referring to supervised learning when you say "best fit", but there are other forms of learning (such as reinforcement learning) and there are other aspects of AI apart from learning, such as perception, control, etc. Some people sometimes claim that machine learning is glorified statistics, but, although the two are similar and related, I don't think that's exactly correct.
To know what AI is, you should read the book Artificial Intelligence: A Modern Approach. If you want to know what machine learning is, then there are many books that you can read, such as Machine Learning (1997) by Tom M. Mitchell. If you are interested in the relationship between machine learning and statistics, you may be interested in this post. You should also read this answer, which describes what AI is or may refer to. This answer gives a nice brief description of the difference between AI and ML.