I would caution you that you haven't seen `real math` as an undergraduate who still has time to decide on your major - you will find that real math is not elegant. Math is baroque, infinitely deep and you success will entirely depend on the community and the perspective you get from your mentors. For example, conversations I had with math professors were able to frame problems so that I could look past the equations and understand the big picture. Then I had to describe it in the precise language of mathematics. I quickly realized that math wasn't that precise of a language - just esoteric hand waving. I then realized that Mathematics is a language that is unintelligible without context.
When I did my CS algorithm classes, I skipped all the lectures and spent 8 hours doing homework from a textbook - my school is rated 3rd in the US.
If you only take Math classes you will not find a job or find yourself in a situation where you have not learned the creative skill necessary to extend upon existing solutions.
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
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.
I would caution you that you haven't seen `real math` as an undergraduate who still has time to decide on your major - you will find that real math is not elegant. Math is baroque, infinitely deep and you success will entirely depend on the community and the perspective you get from your mentors. For example, conversations I had with math professors were able to frame problems so that I could look past the equations and understand the big picture. Then I had to describe it in the precise language of mathematics. I quickly realized that math wasn't that precise of a language - just esoteric hand waving. I then realized that Mathematics is a language that is unintelligible without context.
When I did my CS algorithm classes, I skipped all the lectures and spent 8 hours doing homework from a textbook - my school is rated 3rd in the US.
If you only take Math classes you will not find a job or find yourself in a situation where you have not learned the creative skill necessary to extend upon existing solutions.