I've always found recursion to be my favourite subject, and this has yet to change. Recursive functions always seem to end up more efficient than the vanilla / iterative alternative, and most of all just seem incredibly elegant to me. Proving recursive functions seems to have a natural flow to it similar to the functions themselves.
Whoever originally came up with the idea of automatically reducing a problem down to near-nothingness to solve the most complicated of things must have been a real genius.
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