[klibertp]

> If you can't just see those things in your head, and write them down, then you won't have a reserve of mental bandwidth to think about the higher level structure of the problem that you're working on, and you'll reach a level of complexity and abstraction where the cumulative effect of small mistakes prevents you from ever getting to B.

The big difference between math and music is that the latter is a real-time applied form of the former, with "real-time" being the key. You can waste as much time as you want thinking over things and research solutions to the given math problem; the solution you arrive at after a week is as valid as someone else's solution written down in minutes.

[analog31]

I think that's true to a certain extent. However, being able to write down a solution in minutes might be beneficial if it's a small part of a larger effort, because it doesn't interrupt your "flow," to borrow a popular term. That kind of facility is also beneficial if you're working with other people. "Hold on, give me a week to come up with an explanation for my idea" has much less impact than "here is how it works."