We attribute to the agency of some other that which seems to appear on its own in our minds. The apparent effect of The Muse’s visit is identical to that revelatory moment when a scientist or engineer or mathematician achieves a sudden insight.
Keith Sawyer and other cognitive scientists have pretty much explained this: the brain works on solving problems unconsciously, then passes the results to the conscious part of the mind once a “suitable” solution has been found. The brain solves problems even without our expressly wanting it to; that’s just what it does. But since we’re unaware of it doing so, the results seem to pop into our heads as if handed to us by some other agent.
This is an overly brief and superficial description of many years of work and so I’m sure ignores many significant aspects. But I do believe it captures the essence of the matter.
IOW: to the best of our knowledge, science has disproved The Muse.