> problems in his mind constantly, like a monk, is easy said but difficult to do.
You're misunderstanding what's being described - there's nothing monk like about it.
Using myself as an example, you have a couple techniques you're good at (linear programming) and a couple of problems you've tried to solve before but failed (fixed parameter tractable problems). Every time someone tells you about a problem (or you run into one) you try apply the thing you're good at ("will an LP work here"). Every time someone tells you about an approach they took with their problem you try it out on your thing.
It all happens completely automatically/naturally/fluently if you're good at the technique and have actually tried to solve said pet problem. Like I don't need to write code or calculate anything because I know by now exactly where/what my blockers. Conversely I know very quickly when an LP is appropriate because I know the assumptions/requirements very well.
On a lay level, people think I'm a genius because I can finish their unfinished crossword puzzles. But they never see me when I fail to do a crossword puzzle from scratch myself.
I used to be amazed that my dad could finish crosswords when I was a kid until one time as an adult I was sitting across from him at the table and realized that I knew several of the answers that he hadn't figured out yet. I suspect a lot of it is generational too, where the questions get updated for more current events and that makes them more approachable for working aged adults vs the children or the retired class.
You're misunderstanding what's being described - there's nothing monk like about it.
Using myself as an example, you have a couple techniques you're good at (linear programming) and a couple of problems you've tried to solve before but failed (fixed parameter tractable problems). Every time someone tells you about a problem (or you run into one) you try apply the thing you're good at ("will an LP work here"). Every time someone tells you about an approach they took with their problem you try it out on your thing.
It all happens completely automatically/naturally/fluently if you're good at the technique and have actually tried to solve said pet problem. Like I don't need to write code or calculate anything because I know by now exactly where/what my blockers. Conversely I know very quickly when an LP is appropriate because I know the assumptions/requirements very well.