As someone with only passing exposure to serious math, this section was by far the most interesting to me:

> The author assessed the problem as follows.

> [number of mathematicians familiar, number trying, how long an expert would take, how notable, etc]

How reliably can we know these things a-priori? Are these mostly guesses? I don't mean to diminish the value of guesses; I'm curious how reliable these kinds of guesses are.

For number of mathematicians familiar with and actively working on the problem, modern mathematics research is incredibly specialized, so it's easy to keep track of who's working on similar problems. You read each other's papers, go to the same conferences etc.

For "how long an expert would take" to solve a problem, for truly open problems I don't think you can usually answer this question with much confidence until the problem has been solved. But once it has been solved, people with experience have a good sense of how long it would have taken them (though most people underestimate how much time they need, since you always run into unanticipated challenges).

Read about Paul Erdös... not all math is the Riemann Hypothesis, there is yeoman's work connecting things and whatever...

Certainly knowing how many/which people are working on a problem you are looking at, and how long it will take you to solve it, are critical skills in being a working researcher. What kind of answer are you looking for? It's hard to quantify. Most suck at this type of assessment as a PhD student and then you get better as time goes on.