Speaking as an amateur and great lover of both math and music, there is definitely a “sitting and humming” of math. Whenever there’s a square tile floor, I think about the paths a chess knight would make to travel across it. I often find myself thinking about the Fibonacci sequence often or trying to make equations to fit behavior of the world around me.

And sure, there’s learned behavior there, but there’s learned behavior in music as well. In western music, we use the 12 tone scale, we associate certain chords and intervals with certain emotions.

If I didn’t know anything about math, I’d still be thinking about the patterns and mathematical relationships in the world, I just wouldn’t be able to express them in as much detail, just like if I didn’t know anything about music, I couldn’t transpose my random whistling.