4 ms·

Mathematics without history is soulless

19 points by endswapper 10y ago

ColinWright 10y ago
This was submitted by the author a few days ago, but it gained no upvotes, and only one comment. The comment was mine, and I repeat it here. The "you" in this comment is the author: On this I beg to differ. Or at least, you are making a sweeping generalisation. Not everyone thinks and feels as you do. For me, being given "historical context" and having to understand where these things came from, or why they were interesting, or how they were developed, or who did them, was tedious agony, and I hated it with a passion that's hard to describe. I understand that for some people it brings mathematics to life, for others, like me, it kills it. Please don't think everyone is like you.
- endswapper 10y ago
  The author's statements are reasonable. I am surprised by your comment as well as the need to repost it. He's taking the time to remind us of the richness beyond the technical understanding of mathematics. I think this is a good reminder, in particular, for a technically proficient audience that may spend the majority of their time on technical matters. Nowhere did he say that we should be historians or encyclopedias of/for mathematics. At worst, his point stimulates an additional portion of our brains and may make mathematics more accessible to some. The title might be hyperbolic, but it's effective.
  - ColinWright 10y ago
    I am surprised at your surprise. All I'm saying is that for me, what the author proposes would have been strongly counter-productive. I'm sure I'm not alone in this. I'm sure some students would benefit, I'm sure others, equally, would not. I just wanted to be sure that the complementary point of view was expressed, especially since it affects me personally. The title might be hyperbolic, but it's effective. Actually, I disagree with the title. Mathematics has a life and soul of its own separately and independently of its history. The real problem is that in school one doesn't actually study mathematics anyway, one mostly does arithmetic and manipulation. Perhaps for many students the problem lies not in understanding the history, but in not doing mathematics to start with.
nine_k 10y ago
I think it's often useful to provide the mathematics first, then add history when / if it's interesting. Same applies to physics, imho. There's a lot of interesting historical development behind most topics, but physics is complicated enough as it is, and understanding the current state first is important if you ever hope to understand how it developed historically.
nikofeyn 10y ago
"mathematics without context is soulless" is my preferred sentiment.
- dTal 10y ago
  Exactly. It's a false dichotomy between "mathematics, unadorned" and "the history of math". Philosophy is an example of a subject at the other end of the spectrum, taught almost entirely through history, yielding a strangely disjointed and unstructured experience: "Plato thought we all live in a cave. Descartes thought he might be a brain in a vat. Sarte claimed God was dead. etc..." Meanwhile the student is wondering what on earth all these looney toons have to do with each other and why she should care, because the larger framework is neglected and discredited ideas aren't pruned. I think the correct approach is to teach structure first, justification/usefulness second, and history a distant third - best reserved for explaining awkward but hard-to-change inconsistencies (such as the use of pi instead of tau as the circle constant). I would also submit that if the justification for some aspect of a subject is only historical, it should probably be dropped...

19 points by endswapper 10y ago

This was submitted by the author a few days ago, but it gained no upvotes, and only one comment. The comment was mine, and I repeat it here. The "you" in this comment is the author: On this I beg to differ. Or at least, you are making a sweeping generalisation. Not everyone thinks and feels as you do. For me, being given "historical context" and having to understand where these things came from, or why they were interesting, or how they were developed, or who did them, was tedious agony, and I hated it with a passion that's hard to describe. I understand that for some people it brings mathematics to life, for others, like me, it kills it. Please don't think everyone is like you.

endswapper 10y ago
The author's statements are reasonable. I am surprised by your comment as well as the need to repost it. He's taking the time to remind us of the richness beyond the technical understanding of mathematics. I think this is a good reminder, in particular, for a technically proficient audience that may spend the majority of their time on technical matters. Nowhere did he say that we should be historians or encyclopedias of/for mathematics. At worst, his point stimulates an additional portion of our brains and may make mathematics more accessible to some. The title might be hyperbolic, but it's effective.
- ColinWright 10y ago
  I am surprised at your surprise. All I'm saying is that for me, what the author proposes would have been strongly counter-productive. I'm sure I'm not alone in this. I'm sure some students would benefit, I'm sure others, equally, would not. I just wanted to be sure that the complementary point of view was expressed, especially since it affects me personally. The title might be hyperbolic, but it's effective. Actually, I disagree with the title. Mathematics has a life and soul of its own separately and independently of its history. The real problem is that in school one doesn't actually study mathematics anyway, one mostly does arithmetic and manipulation. Perhaps for many students the problem lies not in understanding the history, but in not doing mathematics to start with.

nine_k 10y ago

I think it's often useful to provide the mathematics first, then add history when / if it's interesting. Same applies to physics, imho. There's a lot of interesting historical development behind most topics, but physics is complicated enough as it is, and understanding the current state first is important if you ever hope to understand how it developed historically.

nikofeyn 10y ago

"mathematics without context is soulless" is my preferred sentiment.

dTal 10y ago
Exactly. It's a false dichotomy between "mathematics, unadorned" and "the history of math". Philosophy is an example of a subject at the other end of the spectrum, taught almost entirely through history, yielding a strangely disjointed and unstructured experience: "Plato thought we all live in a cave. Descartes thought he might be a brain in a vat. Sarte claimed God was dead. etc..." Meanwhile the student is wondering what on earth all these looney toons have to do with each other and why she should care, because the larger framework is neglected and discredited ideas aren't pruned. I think the correct approach is to teach structure first, justification/usefulness second, and history a distant third - best reserved for explaining awkward but hard-to-change inconsistencies (such as the use of pi instead of tau as the circle constant). I would also submit that if the justification for some aspect of a subject is only historical, it should probably be dropped...