The non-popular or non-widespread aspect of a "prompt" (e.g., "derive the geometric product given axioms/definitions ...") should be understood as a data point that it might lack reasoning skills. As it seemingly parrots what most of its dataset "says". For more details, check my other past comments. Calling such LLMs "AI" seems to be sensationalism at work.

This is a problem of your expectations. Things don't need to be perfect to qualify as AI.

Hmm... wouldn't you agree that a formal (relatively accurate language) such as math is easier to get right than an non-accurate human language?