Yeah agreed - there are actually many, smaller flashes of insight, but most of them don't lead to anything. I once joked that you could probably compress all the time I was actually going in the right direction in my PhD down to about a month or two. That's a bit glib, often seeing why an approach fails gives you a much better idea of what a proof 'has to look like' or 'has to be able to overcome'. But many months of my PhD were working on complete dead-ends, and I certainly had a few very dark days because of that. Research math takes a lot of perseverance.

> Research math takes a lot of perseverance.

Yup, I think stubbornness/perseverance is the most useful transferrable skill I got from doing research math. It's a double-edged sword though as I often just can't give up working on something when I really should in my tech job.