The former, because it's anthropomorphizing a model.

Anthropic is especially guilty of this. They have been using such language for a while, like when they analyze model weights for mechanistic interpretability and call it the model's "biology".

It's just distasteful.

But the words don't really matter, do they? The model thought "user said believe in yourself, it means they want me to continue"..

AI did a fixed amount of guesses, didn't yield anything. It probably documented the tries, outcome, and some numbers hinting at why they failed. So the user could have prompted "continue", or "try again with previous outcome in mind, generate new ideas and test them" and it would probably yield the same result.

For me, personally, it's that the Bun guy - specifically him, not a mathematician - indirectly progressed the Riemann hypothesis by repeatedly telling a model to ganbatte!

It's a ridiculous position we find ourselves in.