do you consider statistics a field of mathematics?

[muon2]

College-level Statistics is a total BS subject. I had to endure a whole semester of it and only barely passed by the slimmest margin.

The way introductory statistics is taught at the college level, all you really need to do is memorize the definitions of things like standard deviation and know how to calculate a confidence interval.

I learned more about statistics from my econometrics classes than I did in any of my undergraduate stat classes.

You could say the same thing about introductory calculus - all you really need to do is memorize some formulas like derivatives and integrals and know how to calculate an infinite series. Many students would say they learned more about calculus from their mechanics class in engineering or physics than the math class. Yet, calculus is pretty clearly math and so is statistics.

Introductory classes in the STEM fields tend to be heavy on definitions and formulas.

[muon2]

I would say "No". And it's my field of study. I think, if you include probability, then there's a good case to be made for "Yes" as well, but I'd say that statistics is more about applying math properly. If math includes its own application:

There would be no such thing as statistics if not for mathematics.

Nor would there be many, many things. Math is a wondrous "subject", if it's appropriate to even call something so fundamental a subject. By your definition, everything is math. And that's an appropriate answer. This is only a matter of semantics, anyway.

Perhaps I'm confused as to what is being called math here. Math is certainly not everything, and many fields that are not math use math. I find that math is that collection of studies that rely on a system of formal proof to understand the relationships between abstract idealized objects. If those objects are numbers we might be talking about algebra. If those objects are spatial forms we might be in geometry. Abstract idealized objects can include functions, graphs, and sets as well as many more esoteric constructs.

If the idealized objects are sets of numbers the field is called statistics. Like other branches of mathematics, statistics uses formal proofs and derivations to determine relationships between sets of numbers. Particularly, statistics studies the likelihood of one set belonging to another larger set based on the properties of both sets. Thus, I see no reason to think of statistics apart from mathematics.