Half of all math proofs are guys walking around in nature or sitting in it. The last one I read was Ken Ono's breaththrough on partition numbers ... he was on a hike with a friend.
I might also add hard work gets you to a frustration point you might need first before it comes in its time ... IOW I'm not 100% sold on it just comes for free ... maybe better expressed as know when it's time to take a break too.
And nothing says they weren't thinking about the problem when it happened.
I've had a lot of "aha" moments not sitting by my desk, but that doesn't mean that I wasn't thinking of the problem. When people say they had an idea in the shower, I suspect it's precisely because they were undistracted enough to focus on the problem.
I might also add hard work gets you to a frustration point you might need first before it comes in its time ... IOW I'm not 100% sold on it just comes for free ... maybe better expressed as know when it's time to take a break too.