What are the math heavy CS areas with high demand?

I don't agree with this at all. What is and isn't 'real' math is subjective and very hard to quantify. The 'feel' of mathematics depends on the field but people are often overwhelmed with the level of rigour required to communicate mathematically as an undergraduate. Saying Mathematics isn't precise seems really ill-conceived, Mathematics is very similar to Computer Science in terms of language: one can take a level of abstraction of a concept which simplifies it so that it is understandable.

Saying that Maths classes are irrelevant in a workplace also seems ill-conceived and basically to be personal conjecture.

The courses he's taken so far should give him a good understanding of what applied maths is (which is the type that the OP is thinking of majoring in). The scarier, more baffling variety of maths is pure maths. In the US system, half-majoring in applied maths, you shouldn't have to do hardly any pure maths if you wanted to avoid it.

Although pure maths can be extremely hard and initially seem quite arcane, I think you paint a picture of it which is subjective and in some cases factually wrong.

I agree that maths is infinitely deep and complex, but that is exactly why maths has developed to be as elegant as possible. Good mathematics is about developing structures and analogies that allow people to drastically simplify and improve their thinking about complex situations.

You are objectively wrong when you say that maths "isn't that precise of a language". Modern maths is extremely precise and the level of rigour is leagues ahead of CS. In the early 20th century, mathematicians were worried about how precise mathematics and its proofs were. To combat this crisis, mathematicians boiled down the inherent assumptions in maths to a handful of axioms, from which the entirety of maths is logically proven. Maths is not esoteric hand waving.

I studied maths at university and in my experience, there are lots of opportunities to apply my degree to the real world. Even in a more standard software engineer role I've been able to use my maths knowledge to quickly develop solutions to problems my CS peers are struggling with (and visa versa). If anyone's interested in maths, do consider taking courses in it. It's a valuable, rich subject which has plenty of real world uses and plenty of jobs waiting for you at the end

This article, "The Shape of Math to Come",talks about applying topology to large data sets. https://www.simonsfoundation.org/quanta/20131004-the-mathema... Might stimulate your thinking.

I did a dual degree in Computer Science and Math. My recommendation is to take the classes in both areas that you find the most interesting, with no concern for your career. Your career will span decades and unlikely to involve a steady focus on a single area, as either the environment or you will change. Personally, I've been working for 11 years in a variety of roles (PM at Microsoft, Product Analyst at a SF startup, Quantitative Developer in finance).

You never know where the most valuable lessons will come from and how they will pay off. For example, my second Real Analysis class leveled up my ability to communicate clearly and precisely in a way that no writing class could have. Graph theory, automata theory, numerical methods, abstract algebra, and statistics have each made their way into my work, sometimes in ways that I never would have expected.

If you want to ignore this, Machine Learning.

Thanks for the great response. I'll also look into computational finance.