Should students be taught to be first and foremost: scientists or mathematicians? It's undeniable that Computer Science is a mixture of disciplines including science (the scientific method, some physics needed to truly understand how computers work at all levels, testing methodologies etc etc.) and maths (theoretical computer science, programming is essentially logic puzzles that equate to mathematical proofs - at least complex ones, algorithm analysis etc. etc.) and to some extent it's created it's own discipline in programmatic thinking and the learning and analysis of programming languages. - What are the disciplines of computer science/how important is maths in computer science/is it really a science? - are not the questions to be answered here.

Assuming Mathematical and Scientific knowledge are both important in computer science (which they are) - which do we train students to become principally? Is it most important for computer science students to be first and foremost scientists or mathematicians? e.g. in the first year of a CS course is it more appropriate to teach The Scientific Method. Structure of a scientific investigation. Hypotheses. Occam's razor. Controls. Correlation vs causation. Falsification. Examples such as intention to treat etc etc. Or is it more appropriate to teach Mathematical topics - matrix operations, algorithm analysis, complexity, logical expressions, etc etc.

Or maybe a mixture of both? Maths is inherently important to science - but to what degree should budding computer scientists be taught mathematics.

Which skills and talents in the field of mathematics are beneficial to Computer Scientists?
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.