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
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