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I took 10 semesters of 'math' in college, was on a 'math' team in high school, and got a 780 on the 'math' SATs. Yet by the OP's definition, I don't know any Ma

I took 10 semesters of 'math' in college, was on a 'math' team in high school, and got a 780 on the 'math' SATs. Yet by the OP's definition, I don't know any Math because I'm not doing his definition of Math. That's like arguing that you can't swim unless you are an Olympic swimmer. I can't do the back stroke like Michael Phelps, but I sure can swim. High school math - at least for most - includes Calculus 1. Yes, that involves memorizing integrals and using them later. But if you are going to be that flippant about it, basically what you can marginalize everything. Organic chemistry? Meh, that's just a bunch of memorizing compounds, it is not more difficult than 1st grade memorization of multiplication tables. Anatomy? Ha, that's child's play, it's just like memorizing the names of colors.

sold 15y ago
I think the poster is arguing against the conflation. Organic chemistry is not memorizing compounds; mathematics is not memorizing integrals; anatomy is not like memorizing colors. There is a great difference between understanding and memorizing. I had a very bad history teacher. On most tests, he required the class to learn about 20 different dates (only) and some facts like where a peace treaty was signed. Nobody cared what those events meant, what were connections between the dates etc. Now, many years later, I don't recall anything. I learned nothing. Was I really learning history or just arbitrary numbers? You could claim that it was real history, and probably be technically correct, but I think that's silly. In my mind, the semantics of what I knew did not resemble history at all. In contrast, my chemistry teacher visibly required understanding, and till now I can discuss basic chemistry, even though I did not exercise my skills for a long time. It's the same with mathematics, learning algorithms means essentially you are programmed to do mechanical work, just I like I was acting like a lookup table during history classes. "Real" mathematics starts when the problem you are doing is not directly amenable to a mechanical approach.
- wtallis 15y ago
  Exactly. In the case of mathematics, if you aren't doing proofs yet, you don't even know what math is. Most high school math curricula are completely devoid of proofs or abstract reasoning with the exception of at most a few months during geometry. How many college students have wrongly expected "Modern Algebra" to be a rehash of what they learned in high school? The distinction between mathematics and what gets taught in high school is very similar to the distinction between computer science and computer programming.
scott_s 15y ago
Your analogy doesn't quite work because the difference between a high school swimmer and an Olympic swimmer is a difference of degree. That its, they both do the same thing, one is just (much) better. But the difference between what people do when they take most math courses up to about their third year in college, and what mathematicians do, is a difference of kind, not degree. You can see my other comments in this thread to see what I think that difference in kind actually is.

sold 15y ago

I think the poster is arguing against the conflation. Organic chemistry is not memorizing compounds; mathematics is not memorizing integrals; anatomy is not like memorizing colors. There is a great difference between understanding and memorizing. I had a very bad history teacher. On most tests, he required the class to learn about 20 different dates (only) and some facts like where a peace treaty was signed. Nobody cared what those events meant, what were connections between the dates etc. Now, many years later, I don't recall anything. I learned nothing. Was I really learning history or just arbitrary numbers? You could claim that it was real history, and probably be technically correct, but I think that's silly. In my mind, the semantics of what I knew did not resemble history at all. In contrast, my chemistry teacher visibly required understanding, and till now I can discuss basic chemistry, even though I did not exercise my skills for a long time. It's the same with mathematics, learning algorithms means essentially you are programmed to do mechanical work, just I like I was acting like a lookup table during history classes. "Real" mathematics starts when the problem you are doing is not directly amenable to a mechanical approach.

wtallis 15y ago
Exactly. In the case of mathematics, if you aren't doing proofs yet, you don't even know what math is. Most high school math curricula are completely devoid of proofs or abstract reasoning with the exception of at most a few months during geometry. How many college students have wrongly expected "Modern Algebra" to be a rehash of what they learned in high school? The distinction between mathematics and what gets taught in high school is very similar to the distinction between computer science and computer programming.

scott_s 15y ago

Your analogy doesn't quite work because the difference between a high school swimmer and an Olympic swimmer is a difference of degree. That its, they both do the same thing, one is just (much) better. But the difference between what people do when they take most math courses up to about their third year in college, and what mathematicians do, is a difference of kind, not degree. You can see my other comments in this thread to see what I think that difference in kind actually is.