You shouldn’t take this post as a dismissal of intuition, just a reminder that intution is not magically reliable. Generally, intuition is a way of saying, “I sense similarities between this problem and other ones I have worked on. Before I work on this problem, I have some expectation about the answer.” And often your expectation will be right, so it’s not something to throw away. You just need to have the right degree of confidence in it.
Often one has worked through the argument before and remembers the conclusion but not the actual steps taken. In this case it is valid to use the memory of the result even though your thought process is a sort of black box at the time you apply it. “Intuition” is sometimes used to describe the inferences we draw from these sorts of memories; for example, people will say, “These problems will really build up your intuition for how mathematical structure X behaves.” Even if you cannot immediately verbalize the reason you think something, it doesn’t mean you are stupid to place confidence in your intuitions. How much confidence depends on how frequently you tend to be right after actually trying to prove your claim in whatever area you are concerned with.
You shouldn’t take this post as a dismissal of intuition, just a reminder that intution is not magically reliable. Generally, intuition is a way of saying, “I sense similarities between this problem and other ones I have worked on. Before I work on this problem, I have some expectation about the answer.” And often your expectation will be right, so it’s not something to throw away. You just need to have the right degree of confidence in it.
Often one has worked through the argument before and remembers the conclusion but not the actual steps taken. In this case it is valid to use the memory of the result even though your thought process is a sort of black box at the time you apply it. “Intuition” is sometimes used to describe the inferences we draw from these sorts of memories; for example, people will say, “These problems will really build up your intuition for how mathematical structure X behaves.” Even if you cannot immediately verbalize the reason you think something, it doesn’t mean you are stupid to place confidence in your intuitions. How much confidence depends on how frequently you tend to be right after actually trying to prove your claim in whatever area you are concerned with.