PhD in maths here, no longer a mathematician, partly because I wanted to do stuff more connected with real life.

I actually want to see interesting theories and mathematical ideas come out of proofs more than I want solutions/proofs. After all most maths doesn't have direct practical applications. So although unsolved problems are a good barometer of 'there's still stuff left to understand here', the interesting part about solving them is less knowing what is true and more 'how does this help us understand this field better than we did before?'.

I would still like to know if the Riemann Hypothesis is true though!