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Capla comments on The "best" mathematically-informed topics? - Less Wrong Discussion
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Can you elaborate? What is the difference between "mathematical facts" and "statistical intuitions"? Can you give an example of each?
If you take the average introductory statistics textbook it tells you thinks that are true for normally distributed data.
If you are faced with a real world problem that doesn't follow the normal distribution and try to apply statistical techniques proven to work for normal distributed data you are getting mistakes.
Being good at statistical modelling means that you have an idea of what assumptions you can make about a certain data set and the kind of errors you will get when your assumptions don't match reality.
Example of a mathematical fact: a formula for calculating correlation coefficient. Example of a statistical intuition: knowing when to conclude that close-to-zero correlation implies independence. (To see the problem, see this picture for some datasets in which variables are uncorrelated, but not independent.)
Not sure why are you calling this "intuition". Understanding that Pearson correlation attempts to measure a linear relationship and many relationships are not linear is just statistical knowledge, only a bit higher level than knowing the formula.