Is this still going on, that geometry isn't mathematics?
It's defined by topic, literally, as one of the earlier areas of mathematics.
The semantics about what's math and what isn't is interesting. In college, I took calculus three and was sort of struggling until figuring out that I'm no good at learning from a lecture. Figuring out the material on my own from the text, though - far better. After that, everything was pretty much a breeze. What I said to the instructor was "I know I have a bunch of math courses dropped my first several semesters, but I want to change my major to math. here's why". The math department advisor said "you can do whatever you want. I'll approve it. Calculus 1-3 aren't math courses, anyway".
After wondering why she allowed me to declare a math major so easily with a relatively "unstellar" course history, she said she never was able to learn from lectures either.
Most of the proofs of geometry require mathematics and at least in routine geometry, none really violate anything mathematical, either.
You can mix fluids and measure the results and use them. That doesn't mean that differential mixing equations aren't mathematics.
If you're not following why a (by then retired) math professor working as an advisor would call calculus courses "not mathematics", she didn't mean calculus isn't math. She meant practical application of mathematics in those courses (which are mostly learning application and memorizing) can be done without actually understanding things at a granular level.
You can use geometry without being able to do a mathematical proof. That doesn't mean it isn't mathematics.
It's defined by topic, literally, as one of the earlier areas of mathematics.
The semantics about what's math and what isn't is interesting. In college, I took calculus three and was sort of struggling until figuring out that I'm no good at learning from a lecture. Figuring out the material on my own from the text, though - far better. After that, everything was pretty much a breeze. What I said to the instructor was "I know I have a bunch of math courses dropped my first several semesters, but I want to change my major to math. here's why". The math department advisor said "you can do whatever you want. I'll approve it. Calculus 1-3 aren't math courses, anyway".
After wondering why she allowed me to declare a math major so easily with a relatively "unstellar" course history, she said she never was able to learn from lectures either.
Most of the proofs of geometry require mathematics and at least in routine geometry, none really violate anything mathematical, either.
You can mix fluids and measure the results and use them. That doesn't mean that differential mixing equations aren't mathematics.
If you're not following why a (by then retired) math professor working as an advisor would call calculus courses "not mathematics", she didn't mean calculus isn't math. She meant practical application of mathematics in those courses (which are mostly learning application and memorizing) can be done without actually understanding things at a granular level.
You can use geometry without being able to do a mathematical proof. That doesn't mean it isn't mathematics.
