alt Hacker Newson older gemini models ide have to actively give them encouragement and/or easy bait problems that they can correctively solve without issue to avoid runaway spiraling into "i'm useless and i want to kms" behaviour with complex use case.
I have not seen this in other models.
I assumed it was more because the LLM might echo an understandable human claim of "if it's been unsolved for 370 years, it's unlikely to be solved now/likely to need expert knowledge", which is probably a mindset that appears in its training data.
The LLM likely needs to be reminded of its abilities.