That's totally the standard way that all mathematicians think about n-dimensional spaces.
I've never heard a mathematician claim math is the universal solution to all problems... sounds like you had a bad high school experience. Do you need a math-hug? :)
>sounds like you had a bad high school experience.
Not exactly high school. I'm a university student in Germany.
But yes, it's pretty much a bad experience. I've seen quite a lot of other students which are otherwise bright persons struggle with math simply because they aren't good at learning to interpret arcane sequences of symbols which pretty much represent nothing relevant to reality. Math the way it is taught here is essentially useless for 95% of all CS students.
I think you are obsessing about minutiae. Perhaps mathematical instruction is very different in Germany than in the United States, or perhaps our brains are simply incompatible, but I've never found symbology to significantly affect my understanding.
Symbols are just convenient and useful abbreviations. In my experience, they facilitate both speed and precision in mathematical work, far and above what is possible in a natural language like English. There is no particular reason why certain concepts are associated with certain symbols apart from convention. Any decent mathematician should be able to operate with any set of symbols, although not necessarily with equal proficiency.
I won't deny that many mathematicians have a hard time expressing themselves in natural-language speech and writing. Perhaps for them the symbols have become a crutch. But I still think you have erected a mental block around an ultimately inconsequential aspect of mathematics, which is needlessly impeding your understanding.
That having been said, I think there are definitely bad ways to approach the use of symbols in instruction. Concepts and their related symbols should be introduced incrementally, and you should always have ample opportunity to practice with the ones you have just learned before having to learn new ones. I think that a well rounded mathematics curriculum should include a course with a significant focus on understanding and manipulating common mathematical and logical techniques, with mathematical language being a significant if not necessary part thereof.
>I won't deny that many mathematicians have a hard time expressing themselves in natural-language speech and writing.
Yes, that's exactly what I've been getting at. As I said in other comments, I respect math as a field. What I'm pointing out is that there's a heavy communication problem between math and other fields, and this is something that needs to be solved.
I studied math and CS in Germany. The mathematicians were usually adept at CS, but the computer scientist didn't--with some exceptions of course--even get what math was about at all.
They should probably stop trying to dumb down the math for computer scientist. Math is hard, and pretending otherwise, won't save one from reality.
I've never heard a mathematician claim math is the universal solution to all problems... sounds like you had a bad high school experience. Do you need a math-hug? :)