Worth applying to maths PhD without maths undergrad?

[csheehan10]

My undergrad is in economics, and I'm currently doing an MSc in statistics. My favourite classes have definitely been the theory based ones (measure theory, probability theory, functional analysis), and I think I would ideally like to do research in probability theory. I'm planning on applying to stats departments where there is a decent probability research group, but I'm wondering if it would also be worth applying to mathematics departments for universities without a stats department. Or is this just too long of a shot without a maths undergrad degree?

[bayessays]

Math departments will want you to have classes like abstract algebra, so if you don't have that, it will be hard to get in.  It's hard to find good probability groups in statistics departments outside of the top few programs (Stanford, Berkeley, Chicago, etc.).  UNC has a lot of applied probability people, and Michigan State has a large group of probability people too.  Outside of that, most programs will not have huge probability groups.

[Nothalfgood]

I'm sure there are plenty of examples of people getting into some top math programs without having a math degree, and statistics is certainly one of the most natural alternatives if you've already pretty much mastered real analysis and linear algebra, so my opinion is that it's worth a try to apply. I think there are some applied math programs that blur a lot of the lines between pure math and statistics like at UMaryland and Johns Hopkins which you may be interested in too.

In some sense, you may be unable to totally "escape" applications at this point, but I think you could find stats or applied math programs where you could spend virtually all of your time working without any real data and instead on almost exclusively analysis and topology flavored problems. That is my impression from some current graduate students in statistics at schools like UMichigan and UWisconsin.