Is Statistics Mathematics? I am from the mathematics community on StackExchange. I should say that I know absolutely nothing in statistics. I have never taken a statistics course or read any book on it. I am familiar with basic probability theory though, because it is a mathematics subject. After all probability is an application of real analysis to finite measure spaces, and the subject of probability has a rigorous mathematical foundation to it. But what about statistics? 
I view statistics as a way to derive quantitative results from observable data. (Please correct me if this is an inaccurate description of statistics.) This is why statistics is very valuable to scientists whose work entirely consists of observable data. But mathematics is entirely non-empirical. None of the major mathematicians of the last century, or the current one, (at least that I know of), know any statistics. This is why I am asking if you, statisticians, agree with the statement that, "statistics is a numerical branch of science, rather than mathematics". 
Now I understand that statisticians use mathematics, sometimes even advanced results. But does not necessarily make them mathematics. Physicists use a lot of mathematics too, but they are not mathematicians. For them mathematics is a means to solve some other problem, it is not the math that inherently interests them.   
 A: If you go deeper in any discipline, especially when you get near the boundaries, you will find that those boundaries between disciplines are fairly arbitrary. For example, as a sociologist I would say that economics is just a branch of sociology, they typically don't agree... In practice, the boundaries between disciplines have a lot to do with group identity and university politics. They are an interesting subject for study by sociologist, social psychologist and political scientists, but not much more than that. 
So unless you are interested in the sociology of university organization, I would just say that mathematics is whatever mathematicians do, and a mathematician is whoever calls him or herself a mathematician.
A: I think it's pretty clear that the theory behind statistics is mostly pure mathematics, while the application is not. For example, showing that the sample mean is the optimal unbiased estimator for the mean of a normal distribution is clearly a rigorous mathematical theorem based on the laws of probability. 
In the same way, there are many theorems for statistical algorithms (bootstraping, MCMC) showing that they converge under certain assumptions.
When applying statistics to real world problems there are other more practical elements to discuss. But the theory behind statistics is very profound mathematics.
