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DanielLC comments on Strong intutions. Weak arguments. What to do? - Less Wrong Discussion
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Many of the results are counter-intuitive, but most are not, especially for someone trained in that area. In fact, intuition is required to make progress on math.
But that intuition is in many cases essentially many years of experience with similar contexts all put together operating in the back of one's head. In this case the set of experience to inform/create intuition is pretty small. So it isn't at all clear when there are strongly contradicting intuitions which one makes more sense to pay attention to.