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Solomonoff Induction. Although proven to be uncomputable (there are people working on formalizing efficient approximations) it is such a mind-blowing idea. It brings together Occam's razor, Epicurus' Principle of multiple explanations, Bayes' theorem, Algorithmic Information Theory and Universal Turing machines in a theory of universal induction. The mathematical proof and details are way above my head but I cannot help but feel like it is very underrated.

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Statistics is an applied science, and Solomonoff induction has had zero practical impact. So I feel it's not underrated at all, and perhaps overrated among a certain crowd.

My impression, for what it's worth or not worth, is that this area is sort of what Bayesian statistics was 50 years ago. Something that is fundamental but is difficult to implement so doesn't have much impact practically speaking at a given moment in time.

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