Maybe its because I'm a plebe and haven't taken any advanced mathematical courses, but I don't see why statistics isn't mathematics. The arguments here and on a duplicate question seem to argue two primary points as to why statistics isn't mathematics*.
- It isn't exact/certain, and as such relies on assumptions.
- It applies math to problems and anytime you apply math it is no longer math.
Isn't exact and uses assumptions
Assumptions/approximations are useful for lots of math.
The properties of a triangle that I learned about in grade school I believe are considered true math, even though they don't hold true in non-Elucidean geometry. So clearly an admission of the limits, or stated another way "assuming XYZ the following is valid", to a branch of math doesn't disqualify the branch from being "true" math.
Calculus I'm certain would be considered a pure form of math, but limits are the core tool we built it on. We can keep calculating up to the limit, just as we can keep making a sample size larger, but neither give increased insight past a certain threshold.
Once you apply math it isn't math
The obvious contradiction here is we use math to prove mathematical theorems, and no one argues that proving mathematical theorems isn't math.
The next statement might be that
thing x isn't math if you use math to get a result. That doesn't make any sense either.
The statement I would agree with is that when you use the results of a calculation to make a decision then the decision isn't math. That doesn't mean that the analysis leading up to the decision isn't math.
I think when we use statistical analysis all the math performed is real math. It is only once we hand the results to someone for interpretation does statistics exit mathematics. As such statistics and statisticians are doing real mathematics and are real mathematicians. It is the interpretation done by the business and/or the translation of the results to the business by the statistician that isn't math.
From the comments:
If you were to replace "statistics" by "chemistry," "economics,"
"engineering," or any other field that employs mathematics (such as
home economics), it appears none of your argument would change.
I think the key difference between "chemistry", "engineering", and "balancing my checkbook" is that those fields just use existing mathematical concepts. It is my understanding that statisticians like Guass expanded the body of mathematical concepts. I believe (this might be blatantly wrong) that in order to earn a PhD in statistics you have to contribute, in some way, to expanding the body of mathematical concepts. Chemistry/Engineering PhD candidates don't have that requirement to my knowledge.
The distinction that statistics contributes to the body of mathematical concepts is what sets it apart from the other fields that merely use mathematical concepts.
*: The notable exception is this answer that effectively states the boundaries are artificial due to various social reasons. I think that is the only true answer, but where is the fun in that? ;)