Would this be a valid rephrasing of your statement? “When you have done a certain number of problems and understood complex connected conceptions, your intuition becomes molded so that it becomes useful to trust them, but verify them as well.”
Pretty close, but my intuition can still be useful even in instances where it can be less reliable than “trust but verify” would suggest, because in a sufficiently difficult problem, the first possible solution that my intuition hits on is more likely than not to be wrong, but it’s still a lot better than chance. I trust that my intuitions are likely to help me find the right answer or a correct proof eventually if I work at it long enough. In these cases, I don’t assume that a possible solution suggested by my intuition is probably right, and that I just have to verify it. Instead, I assume that it is worth exploring since it has a reasonable probability of being either right or close to right.
Would this be a valid rephrasing of your statement? “When you have done a certain number of problems and understood complex connected conceptions, your intuition becomes molded so that it becomes useful to trust them, but verify them as well.”
Pretty close, but my intuition can still be useful even in instances where it can be less reliable than “trust but verify” would suggest, because in a sufficiently difficult problem, the first possible solution that my intuition hits on is more likely than not to be wrong, but it’s still a lot better than chance. I trust that my intuitions are likely to help me find the right answer or a correct proof eventually if I work at it long enough. In these cases, I don’t assume that a possible solution suggested by my intuition is probably right, and that I just have to verify it. Instead, I assume that it is worth exploring since it has a reasonable probability of being either right or close to right.