What makes something a pure math theorem or an applied math theorem.

[Man of Knowledge]

Let X = {x1,x2,x3,...,xn}

let fX|Theta be a pdf of X|Theta

for all Theta-hat such that E(Theta-hat) = Theta

http://upload.wikimedia.org/math/4/8/6/4863a647daf34f1e0b8a05c316c03a05.png

This a theorem in Statistics and Applied Math, but why can't it be considered a theorem in pure math.

[Imaginary Mark]

If you had a purely theoretical theorem and then later found an application for it, I suppose it would become an applied theorem.

But really, Applied Mathematics (http://en.wikipedia.org/wiki/Applied_mathematics) is just another branch of mathematics. So there could be an Applied Math theorem that was purely theoretical.

[JohannGoodflag]

The branch of mathematics usually called "applied mathematics" seems to do mostly with the study and evaluation of real-valued functions of the integers, and evaluating the derivatives of piece-wise differentiable real-valued functions. The reason for this nomenclature probably has to with the importance of this study for physics, chemistry, and engineering.

[Draconis]

I remember a book entitled "Calculus made Simple" (!) which took applied maths equations and "unapplied" them back into pure maths, kind of such-and-such equation is this, but forget about that, just solve the equation.

[uncool]

The difference is the way in which it is used.
If it is used to prove other theorems, mainly, such as the basic geometry theorems, it is pure math. If it is used usually for outside reasons, such as physics, economics, etc., then it is applied math.

In this case, it is used for some statistical purposes (no idea what), that are very important in the real world, more so than in the mathematical world.
=Uncool-

[Man of Knowledge]

The difference is the way in which it is used.
If it is used to prove other theorems, mainly, such as the basic geometry theorems, it is pure math. If it is used usually for outside reasons, such as physics, economics, etc., then it is applied math.

In this case, it is used for some statistical purposes (no idea what), that are very important in the real world, more so than in the mathematical world.
=Uncool-

It is used to determine if an unbias estimator has the smallest possible variance of all unbiased estimators.

[uncool]

Right! sorry, been a year since I took theoretical stat,. It's the MVUE thing, right?

Usually, I think you'd see that used outside of the pure math realms - you'd see it in medical studies, chemical studies, even physics studies (quantum), not usally in pure math.
=Uncool-

[premjan]

I suppose pure maths theorems have to be derivable without any consideration to semantics (i.e. they are pure algebra / logic starting from premises and leading to conclusions). Though maybe that is just all maths, rather than just pure maths.