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Society thinks of math as technical and functional, rather than beautiful. The math used in jobs are also to “get things done” rather than for the sake of thei

by j7ake 3y ago

Society thinks of math as technical and functional, rather than beautiful. The math used in jobs are also to “get things done” rather than for the sake of their beauty. A very tiny fraction of population will ever be pure mathematicians. Most just need to know enough to “get things done”. Considering how much society throws money at STEM, rather than art and music, it makes sense society wants a return in their investment in terms of training practical people.

TeMPOraL 3y ago
I disagree somewhat with both you and GP here: > Society thinks of math as technical and functional, rather than beautiful. The math people suck at is the technical and functional part, just as much as the beautiful parts. I'd frame the issue like this: there's the journey of arriving at the result, there's wielding the result, and then there's applying it to a very particular problem. Schools are teaching mostly the last part - applying a^2+b^2=c^2 to a set of contrived problems that are meant to exercise your ability in arithmetic, variable substitution, and simple symbolic transformation. They do not teach people how to wield the formula - as in, how can you realize on your own that any particular real-life challenge calls for application of that tool (or of mathematics in general). That's the middle part that's directly valuable, in the immediate term. That's the difference between a carpenter, and a person who figured out how to use a hammer to drive a nail into a wall. The beauty and journey part? That's study of history and art of inventing new types of hammers and other impactors, and perhaps inventing your own. Even further upstream of the "knowing how to use it to build something" part, but neither is taught in schools.
ndriscoll 3y ago
I tend to not like A Mathematician’s Lament for being so lofty, but there's a more straightforward reason to care about "pure" math: students complain that math "doesn't make sense" or is a bunch of random difficult to remember rules, which is absurd. More than any other field, math has logical reasons for everything. You can figure out pretty much anything you'll encounter in school by just thinking about it; you don't need to have any external knowledge from having done some experiment or being told some fact. On the flip side, if you do use physical intuition, you'll usually go down the right path (for anything pre-university, or even most undergraduate level material). Regardless of how beautiful music is, teaching how to read sheet music without actually listening to music is stupid because you're not teaching what the symbols even mean. Of course no one will understand what you're talking about.
edanm 3y ago
> A very tiny fraction of population will ever be pure mathematicians. Most just need to know enough to “get things done”. I agree with this, but I want to point out that the few "pure mathematicians" are not the only ones who can enjoy the beauty of math, similar to how the few classical musicians (or classical music experts) aren't the only ones who can enjoy classical music. In fact, looking at the success of various YouTube math channels, or Science channels, etc, there are clearly orders of magnitude more people interested in material on Science and Math than there are people who actively engage in these fields professionally. (This is true of probably every field, btw.)

by j7ake 3y ago

TeMPOraL 3y ago

I disagree somewhat with both you and GP here: > Society thinks of math as technical and functional, rather than beautiful. The math people suck at is the technical and functional part, just as much as the beautiful parts. I'd frame the issue like this: there's the journey of arriving at the result, there's wielding the result, and then there's applying it to a very particular problem. Schools are teaching mostly the last part - applying a^2+b^2=c^2 to a set of contrived problems that are meant to exercise your ability in arithmetic, variable substitution, and simple symbolic transformation. They do not teach people how to wield the formula - as in, how can you realize on your own that any particular real-life challenge calls for application of that tool (or of mathematics in general). That's the middle part that's directly valuable, in the immediate term. That's the difference between a carpenter, and a person who figured out how to use a hammer to drive a nail into a wall. The beauty and journey part? That's study of history and art of inventing new types of hammers and other impactors, and perhaps inventing your own. Even further upstream of the "knowing how to use it to build something" part, but neither is taught in schools.

ndriscoll 3y ago

I tend to not like A Mathematician’s Lament for being so lofty, but there's a more straightforward reason to care about "pure" math: students complain that math "doesn't make sense" or is a bunch of random difficult to remember rules, which is absurd. More than any other field, math has logical reasons for everything. You can figure out pretty much anything you'll encounter in school by just thinking about it; you don't need to have any external knowledge from having done some experiment or being told some fact. On the flip side, if you do use physical intuition, you'll usually go down the right path (for anything pre-university, or even most undergraduate level material). Regardless of how beautiful music is, teaching how to read sheet music without actually listening to music is stupid because you're not teaching what the symbols even mean. Of course no one will understand what you're talking about.

edanm 3y ago

> A very tiny fraction of population will ever be pure mathematicians. Most just need to know enough to “get things done”. I agree with this, but I want to point out that the few "pure mathematicians" are not the only ones who can enjoy the beauty of math, similar to how the few classical musicians (or classical music experts) aren't the only ones who can enjoy classical music. In fact, looking at the success of various YouTube math channels, or Science channels, etc, there are clearly orders of magnitude more people interested in material on Science and Math than there are people who actively engage in these fields professionally. (This is true of probably every field, btw.)