Logic and Creativity

This is a text I wrote a few years ago about the false dichotomy between logic and creativity. But with the advent of LLMs I thought about again.

I think current LLMs are capable of both logic and creativity, but still to a limited extent. While LLMs can solve competition math problems, they often fail at simple variations of logical puzzles and cannot yet contribute proofs of novel mathematical theorems. In the creative department, they can make simple combinations of ideas, but I have yet to hear of some really breathtaking creative output. It very easily falls into cliche, or disintegrates into non-sense.

My completely unsupported theory is that these two shortcomings are related, and that with greater logical and mathematical ability comes greater creativity. Much like how LLMs got a lot better in all parts when we trained them on code. Perhaps once they are trained on formalised logical reasoning, they will create truly astounding new ideas?