The common trait I've seen in all exceptional programmers is an ability to
keep a tremendous number of details in memory at one time
The best programmers can get into that space faster and pull a bigger chunk of a system into their heads at one time. This is why they don't necessarily write clean code because they don't have to. The less gifted of us need strong abstractions and code discipline or we just can't keep up. This is why somebody like Linus Torvalds can afford to be disdainful of a lot of common practices in software - he doesn't need the extra help those practices provide.
And all this happens well above the level of a strong mathematical formalism.
I've started meditation again; dual n-backed games are next to try and improve my working memory and concentration. Also, just regularly re-reading the core APIs I'm working with.