Should students be taught to be first and foremost: scientists or mathematicians?
This answer addresses something very different from the other answer I posted on this question, which is why it merits its own answer:

Almost every field in computer science is built on some mathematical theory (this sentence is the only overlap between answers): 


The most basic: the number of options that an $n$ long binary number is $2^n$, and that's where it all starts (until Quantum computers come along, but that's something else)
Algorithm correctness: proof by induction.
The entire field of boolean algebra. Need I say more?
The entire field of Machine Learning is nothing but computations of mathematical models (Neural networks are nothing more than the simplest of arithmetic calculations - weighted sums of weighted sums of...)


This list can go on and it strengthens the point that, regardless of learning mathematics before learning Computer Science (that is, learning math with the intent of learning basic Computer science), most applications of computer science are implementations of mathematical models. 

This means that when learning a subfield of computer science, an introduction to the relevant mathematics is almost always necessary. 

That being said, being a talented mathematician surely would not harm one's level of understanding of those subfields of Computer Science.