Most employers don't really care what degree you do as long as you have done well in it. Doing a pure maths degree can lead to great career prospects as it proves you can think quantitatively. Mathematicians can work in such a wide variety of fields.
Also pure maths has plenty of applications to the real world and statisticians don't just enter numbers into a database.
This.
Mathematicians in my opinion have much more diverse employability areas than most other disciplines because mathematics is used in such a wide variety of areas. Anything that requires modelling will require a mathematician. This includes banking, environmental research, gaming software, meteorology, mining, consulting, trading, defence,....etc.
Employers are often impressed with people who have done mathematics majors (especially pure) because they have superior quantitative skills and problem solving skills. It's not so much the theory you learn they are concerned with, but more of the skills you have acquired in learning it. A lot of pure mathematics majors I know have gone into areas like trading because unlike most 'typical' commerce students, they have the capacity to handle complex financial instruments like exotic derivative securities.
A pure mathematician I know of who works at trading at an investment bank who visited uni last year for a careers session actually made a very interesting point about modelling which I think is worth sharing. He said that people who are real mathematicians understand exactly where a model comes from (i.e. its derivation) and therefore know when it works and when it fails. They are able to develop new models to suit the circumstances where the original model fails. People who lack this mathematical grounding (i.e. the 'typical' commerce student...no offence btw) usually just plug the numbers into this model without really knowing what it does and the moment the model does fail, they struggle to understand why it did fail and are unable to develop a new model.
Also, statisticians do not just enter numbers in a database (that's something that TAFE level accountants often do). They also do modelling, examine the quality of data, determine the methods of sampling and make inferences. There is a lot of variety in what they do. If you search up the methodologies used by the ABS, you'll find there is a lot of sophistication in the data analysis depending on the context of the data itself.
