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Ya know... looking back on the various algorithms I invented I'm not really sure how much of it is luck (trial and error) and how much of it comes from knowledge (math, algorithms, etc)... I have invented a few fairly well used algorithms that are novel and performant that were systematic trial and error in the end and don't resemble my original plans on paper at all. I have others that are a mathematical symphony that just git together well from the first go.
Then again I only create new algorithms when I'm learning new ideas or revisiting them, usually inspired by the thought process it takes for me to understand an idea and apply it in other somewhat abstract ways. So maybe invention is just an extension of learning in a way. Afterall i often find when I am learning I try to predict the next logical step, such as with math. Which is sort of like inventing the idea yourself if you haven't turned the page in the textbook yet to get the answer.
Perhaps the people who are inventors of anything are also the ones who learn through exploration rather than just repetition.
