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The trouble with trying to arrive at any single definition of Mathematics is that Mathematics is different things to different people. A research level Mathema

by Arun2009 15y ago

The trouble with trying to arrive at any single definition of Mathematics is that Mathematics is different things to different people. A research level Mathematician might see it differently (finding patterns, abstraction, theory - axioms and proofs) from an Engineer who has a purely practical interest in it (cookie cutter methods and formulas). For everyday use Mathematics is a set of algorithms for doing stuff with percentages, fractions, basic arithmetic etc. Currently what's frustrating is that we subject everyone to the same level of training. Those whose interest lie elsewhere are subjected to unnecessary and meaningless torture, while those who are really interested in Mathematics as a subject are left to their own devices to find additional training (which thankfully is easier these days than when I was a kid, though it could be made substantially easier still).

slowpoke 15y ago
You beautifully sum up my experience with math at the university, as a CompSci student in Germany. The absolutely most frustrating thing for me, in the beginning, were the basic math lectures (which I, as a disclaimer, still haven't finished). At first, of course, I did what most students do in their first semester: bitch about the apparent uselessness of the subject. That's about one and a half years back, now. I realized by myself that math is actually pretty useful. The problem, as I still see it, is that nobody fucking tells you why. They throw it at you and expect you to deal with it. No further explanation - "It's math, we ain't gotta explain shit." Personal eye openers for me were my internship (and continued assistant work) at a department of the university that deals with image processing (which is basically a boatload of applied math), articles like Wolfire's excellent "Linear Algebra for Game Developers"[1], and plunging myself into a lecture about Fuzzy Set Theory and Artificial Neural Networks (which again is applied math). I actually like abstractions, generalizations and logic reasoning (I wouldn't study CS if I didn't). I still don't think that math is the only way to teach those, but it's arguably the largest field of science dealing with these things. I don't really think the problem is math itself, it's the way it is taught to most people - in the math way. Mathematicians teach math to do more math, which in turn is used to to even more math. And that's fine - for a mathematician. For literally every other field of science that needs math as a tool, it's highly frustrating to be subjected to what you aptly describe as "torture". [1]: http://blog.wolfire.com/2009/07/linear-algebra-for-game-developers-part-1/ http://blog.wolfire.com/2009/07/linear-algebra-for-game-deve...
- impendia 15y ago
  I am a math professor at a large state university in the US. A comment and a question: > Mathematicians teach math to do more math, which in turn is used to to even more math. That is true of some mathematicians, and of some subjects. But I think most mathematicians teach and learn math because they think it's cool, not because it's useful -- either to learn more math, or for the "real world". I might also add that I always appreciate it when teachers take a very long view of things. For example I have trained in the martial arts, and most teachers take the perspective that you want to master the art completely, rather than just learn one or two things. Some people don't like this, but I deeply appreciate it. > The problem, as I still see it, is that nobody fucking tells you why. They throw it at you and expect you to deal with it. No further explanation - "It's math, we ain't gotta explain shit." As a math instructor I am always looking for ways to improve, but I'm having trouble extracting useful criticism from your remarks. "They throw it at you and expect you to deal with it" seems to be true of challenging lessons in anything. I would cheerfully welcome general advice and suggestions from you or any other HN readers. (But please keep in mind that both my interests and my expertise skew heavily theoretical!)
  - worren 15y ago
    "They throw it at you..." I've the same gripe. Maybe, I can elucidate the parent's point. I can appreciate the mathematician's fancy for reducing numerical manipulation to an indivisible, atomic precision. Creating poetic abstractions is dear to many in applied sciences. Where it sticks in the craw, where it stops making sense, is where you have this beautiful construct and it's purpose is left a mystery. If it's a piece of art, fine. It's welcome to hang on the wall over there next to the others, but I'm not going to remember it in much detail without some context. If there isn't a concrete use, if there isn't a purpose, the idea won't make it out of short-term memory. "But it's the foundation for all of these other beautiful edifices of logic that we'll cover in the next chapter!" It's like being told, "This is red paint. This is green paint. This is burnt umber paint...", without ever being shown a Picasso, Renoir, or da Vinci. If you ground the presentation with messy, imprecise, real world numbers, the logical purity of the subject will not be lost or sullied, the esteem for it's power only more appreciated. Pull the pin, show us what it can do! You may not be a physicist or engineer, and that their respective topics will be covered in their respective classes. But those same physicists and engineers probably aren't mathematicians. So what business did they have teaching me math... better than a math teacher ever did?

slowpoke 15y ago

You beautifully sum up my experience with math at the university, as a CompSci student in Germany. The absolutely most frustrating thing for me, in the beginning, were the basic math lectures (which I, as a disclaimer, still haven't finished). At first, of course, I did what most students do in their first semester: bitch about the apparent uselessness of the subject. That's about one and a half years back, now. I realized by myself that math is actually pretty useful. The problem, as I still see it, is that nobody fucking tells you why. They throw it at you and expect you to deal with it. No further explanation - "It's math, we ain't gotta explain shit." Personal eye openers for me were my internship (and continued assistant work) at a department of the university that deals with image processing (which is basically a boatload of applied math), articles like Wolfire's excellent "Linear Algebra for Game Developers"[1], and plunging myself into a lecture about Fuzzy Set Theory and Artificial Neural Networks (which again is applied math). I actually like abstractions, generalizations and logic reasoning (I wouldn't study CS if I didn't). I still don't think that math is the only way to teach those, but it's arguably the largest field of science dealing with these things. I don't really think the problem is math itself, it's the way it is taught to most people - in the math way. Mathematicians teach math to do more math, which in turn is used to to even more math. And that's fine - for a mathematician. For literally every other field of science that needs math as a tool, it's highly frustrating to be subjected to what you aptly describe as "torture". [1]: http://blog.wolfire.com/2009/07/linear-algebra-for-game-developers-part-1/ http://blog.wolfire.com/2009/07/linear-algebra-for-game-deve...

impendia 15y ago
I am a math professor at a large state university in the US. A comment and a question: > Mathematicians teach math to do more math, which in turn is used to to even more math. That is true of some mathematicians, and of some subjects. But I think most mathematicians teach and learn math because they think it's cool, not because it's useful -- either to learn more math, or for the "real world". I might also add that I always appreciate it when teachers take a very long view of things. For example I have trained in the martial arts, and most teachers take the perspective that you want to master the art completely, rather than just learn one or two things. Some people don't like this, but I deeply appreciate it. > The problem, as I still see it, is that nobody fucking tells you why. They throw it at you and expect you to deal with it. No further explanation - "It's math, we ain't gotta explain shit." As a math instructor I am always looking for ways to improve, but I'm having trouble extracting useful criticism from your remarks. "They throw it at you and expect you to deal with it" seems to be true of challenging lessons in anything. I would cheerfully welcome general advice and suggestions from you or any other HN readers. (But please keep in mind that both my interests and my expertise skew heavily theoretical!)
- worren 15y ago
  "They throw it at you..." I've the same gripe. Maybe, I can elucidate the parent's point. I can appreciate the mathematician's fancy for reducing numerical manipulation to an indivisible, atomic precision. Creating poetic abstractions is dear to many in applied sciences. Where it sticks in the craw, where it stops making sense, is where you have this beautiful construct and it's purpose is left a mystery. If it's a piece of art, fine. It's welcome to hang on the wall over there next to the others, but I'm not going to remember it in much detail without some context. If there isn't a concrete use, if there isn't a purpose, the idea won't make it out of short-term memory. "But it's the foundation for all of these other beautiful edifices of logic that we'll cover in the next chapter!" It's like being told, "This is red paint. This is green paint. This is burnt umber paint...", without ever being shown a Picasso, Renoir, or da Vinci. If you ground the presentation with messy, imprecise, real world numbers, the logical purity of the subject will not be lost or sullied, the esteem for it's power only more appreciated. Pull the pin, show us what it can do! You may not be a physicist or engineer, and that their respective topics will be covered in their respective classes. But those same physicists and engineers probably aren't mathematicians. So what business did they have teaching me math... better than a math teacher ever did?