I'm an applied mathematician. I don't do much theorem proving in my day to day work, though I have worked closely with people who do. In my experience, the "guessing" is just half of what makes really good mathematicians really good. The other part is verification: taking intuition and turning it into proof. Most of the time the proof works out exactly as one would expect, occasionally one discovers something -- maybe a technical wrinkle that can be overcome with a bit more effort but requires a new idea, maybe a major conceptual gap overlooked before. I'm not a professional programmer or an electrical engineer, but I've been around people who were very good at those things, and being able to think simultaneously at a conceptual level and dig down to the nitty gritty details are both important.
In short, good mathematicians make correct guesses because they've been down the wrong path many times, and know where their intuition may lead them astray.
The thing about math (and most other subjects) is that at the undergrad level, we teach mostly the nitty gritty stuff. In PhD courses we gradually start to teach how to think at a more conceptual level. But the part that I find both hardest and most rewarding -- taking vaguely understood ideas and giving them precise mathematical formulation -- isn't done much in math departments.
Edit: I know I'm not addressing your point directly, which I think is a good one. More clarifying some of the points raised in the article from my perspective.
In short, good mathematicians make correct guesses because they've been down the wrong path many times, and know where their intuition may lead them astray.
The thing about math (and most other subjects) is that at the undergrad level, we teach mostly the nitty gritty stuff. In PhD courses we gradually start to teach how to think at a more conceptual level. But the part that I find both hardest and most rewarding -- taking vaguely understood ideas and giving them precise mathematical formulation -- isn't done much in math departments.
Edit: I know I'm not addressing your point directly, which I think is a good one. More clarifying some of the points raised in the article from my perspective.