alt Hacker NewsTerrence Tao seems to think it has it's use in finding solutions for maths problemms:
https://mathstodon.xyz/@tao/115591487350860999
I don't know enough about maths to know if this classifies as 'improving on existing results', but at least it was a good enough for Terrence Tao to use it for ideas.
That is, unfortunately, a tiny niche where there even exists a way of formally verifying that the AI's output makes sense.