This reminds me of a story my graph theory professor told me (long before LLMs). One of their grad students discovered that a subset of graphs that are of type A and B at once has fantastic properties, such as fast searching, and a few others, useful in communication networks etc.

Excited about their potential thesis, student asked the professor to take a look. After calculating which graphs actually are types A and B at the same time, professor found that the intersection of such graph types is a null set. So the theoretically nice graphs the student “discovered” simply do not exist.