> Whilst current models can't 'intuit' and come up with conjectures

I disagree. I routinely let LLMs speculate or generate hypotheses along the way of helping with technical research. Sometimes they can prove the correctness of a concrete math idea but other times even an unproven conjecture helps with the numerical algorithm implementation and the result is then simply supported by additional data. I guess that any autoresearch-adjacent application has LLMs intuiting and coming up with hypotheses/conjectures—as do the steps/lemmas along a complex proof. In my opinion the modern LLMs are powerful intuitive thinkers that generate lots of conjectures of varying quality or importance.