4 ms·

Many math teahcers (and likely mathematicians) could not care less about the real world applications of math. My college calculus teacher had no interest in phy

Many math teahcers (and likely mathematicians) could not care less about the real world applications of math. My college calculus teacher had no interest in physics or science. She liked math in the same way someone would like doing a crossword or Sudoku. A puzzle game with a well defined rule set and the challenge of finding answers. I cannot overstate how destructive this is, because it basically presents math as this arbitrary logic game rather than as a fundamental language of the universe.

anon291 3y ago
> I cannot overstate how destructive this is, because it basically presents math as this arbitrary logic game rather than as a fundamental language of the universe. You are making a clear philosophical assumption yet don't realize it. Is math really the 'fundamental language of the universe'? or is it an arbitrary logic game that, in its most common interpretation, describes the universe well? Given that we have no full formulation of the universe in terms of mathematics (no theory of everything), the claim that mathematics as it is today is the 'fundamental language of the universe' seems laughably wrong. On the other hand, there are thousands of formal mathematical systems that don't describe anything 'real' as far as we can tell. I mean, the entirety of the lambda calculus was developed before there were any computers that could realize any it in any physical system. Yet, its development has proven incredibly important in the entire foundations of mathematics (many theorem provers, etc are based on some variant of lambda calculus). I'm not denying that some people learn calculus, algebra, etc (i.e., standard high-school/early college maths) with physical systems in mind. However, mathematics is much more than that and limiting the field only to that which we can sense is actually detrimental to mathematical progress as a whole. It seems best to me to encourage purely mathematical thinking itself in the hope that the arbitrary systems humans create may one day be used to describe something. History is littered with 'useless' subfields of math later becoming fundamental to the economy (number theory and elliptic curves to cryptography, lambda calculus to computation, group theory to quantum physics, etc)
- ajkjk 3y ago
  Personally I don't care that it's about physical things. But I care that it's about doing things: understanding concepts intuitively, solving problems, being adept at thinking mathematically. The thing that is not useful is tedious definitions and tedious proofs. A simple example is: nobody needs a proof of how differentiation or integration work. They need to know how to do it, think with it, apply it to problems, and generalize it. The proof is a tool for not being wrong, and that is a perfectly fine thing for mathematicians to do and a waste of everybody else's time (unless they really need convincing). It is an absolute travesty how many people enjoy math until they get to their first college class which is taught by a disconnected mathematician that ruins the subject for them. At my school everyone stopped at multivariable because that's the level at which mathematicians systematically ruined math -- by teaching and testing the wrong stuff. Personally, I survived by the skin of my teeth, and then later found physics and actually learned multivariable calculus and learned to love math again. Despite the efforts of the people who were paid to teach it.
  - anon291 3y ago
    > Personally I don't care that it's about physical things. But I care that it's about doing things: understanding concepts intuitively, solving problems, being adept at thinking mathematically. The thing that is not useful is tedious definitions and tedious proofs. That's great. Not everyone does. Thinking simply via formal systems is not inherently inferior to 'doing' something with it. Both have their uses. In particular, as I said, quantum mechanics would not be where it's at today if it weren't for many pre-quantum mathematicians pushing around symbols on a page.
    - ajkjk 3y ago
      I'm very much not arguing that nobody should do pure math. I'm arguing that teaching pure math to undergrads who are trying to learn applied math is a tragedy and ruins math for a lot of people.
  - Koshkin 3y ago
    > nobody needs a proof of how differentiation or integration work This "nobody" includes a lot of industry workers, e.g. those in finance and economics, not only "pure" mathematicians.
Koshkin 3y ago
I would not call this "destructive." Solving problems is fun in its own right, and things would start making sense in their interconnection, regardless of whether they can be applied to sciences or not.
- RoyalHenOil 3y ago
  It is destructive to people who do not find abstract math problems inherently fun, which is (I would guess) the great majority of people. They come to the conclusion that they hate math or that they are bad at math, even though they would have grasped it better and enjoyed it had it been presented to them differently. If your goal is teach math to the bulk of people, including those who will not go on to be mathematicians, it makes sense to tie math to something that the bulk of people can relate to. And most people DO enjoy thinking about physical objects and physical space (because we ourselves are physical beings who evolved to interact with our physical environment), so this is a really great starting point for introductory math for the average person. If your goal is to only teach the subset of the population who prefer highly abstract puzzles, and to alienate all others, then our current methods are working fine I guess. But I don't think this is a good goal for general math education.
eszed 3y ago
I think you put your finger on a challenge fundamental to teaching itself. Speaking as a (former, at least for now) teacher, the concepts that I find most intuitive were always the most difficult to teach, whereas skills I struggled to master were the ones I was best able to instruct. For problems in the second category I could diagnose the gaps in my students' understanding or application - likely because I'd faced them, or similar, myself - and strategize an approach that would help. Conversely, the subjects that I "got" without effort, left me floundering (at least at first) to find an alternate way to present to students. (I suppose that's where the terrible canard of "those who can't, teach" comes from. There's a kernel of truth to it, of course, but the more generous and relevant point is that success through effort is better preparation for teaching than success through natural ability alone.) My guess is not that your teacher would disagree that math is "a fundamental language of the universe", just that she spoke it so fluently that she wasn't well able to relate to people who don't.

anon291 3y ago

> I cannot overstate how destructive this is, because it basically presents math as this arbitrary logic game rather than as a fundamental language of the universe. You are making a clear philosophical assumption yet don't realize it. Is math really the 'fundamental language of the universe'? or is it an arbitrary logic game that, in its most common interpretation, describes the universe well? Given that we have no full formulation of the universe in terms of mathematics (no theory of everything), the claim that mathematics as it is today is the 'fundamental language of the universe' seems laughably wrong. On the other hand, there are thousands of formal mathematical systems that don't describe anything 'real' as far as we can tell. I mean, the entirety of the lambda calculus was developed before there were any computers that could realize any it in any physical system. Yet, its development has proven incredibly important in the entire foundations of mathematics (many theorem provers, etc are based on some variant of lambda calculus). I'm not denying that some people learn calculus, algebra, etc (i.e., standard high-school/early college maths) with physical systems in mind. However, mathematics is much more than that and limiting the field only to that which we can sense is actually detrimental to mathematical progress as a whole. It seems best to me to encourage purely mathematical thinking itself in the hope that the arbitrary systems humans create may one day be used to describe something. History is littered with 'useless' subfields of math later becoming fundamental to the economy (number theory and elliptic curves to cryptography, lambda calculus to computation, group theory to quantum physics, etc)

ajkjk 3y ago
Personally I don't care that it's about physical things. But I care that it's about doing things: understanding concepts intuitively, solving problems, being adept at thinking mathematically. The thing that is not useful is tedious definitions and tedious proofs. A simple example is: nobody needs a proof of how differentiation or integration work. They need to know how to do it, think with it, apply it to problems, and generalize it. The proof is a tool for not being wrong, and that is a perfectly fine thing for mathematicians to do and a waste of everybody else's time (unless they really need convincing). It is an absolute travesty how many people enjoy math until they get to their first college class which is taught by a disconnected mathematician that ruins the subject for them. At my school everyone stopped at multivariable because that's the level at which mathematicians systematically ruined math -- by teaching and testing the wrong stuff. Personally, I survived by the skin of my teeth, and then later found physics and actually learned multivariable calculus and learned to love math again. Despite the efforts of the people who were paid to teach it.
- anon291 3y ago
  > Personally I don't care that it's about physical things. But I care that it's about doing things: understanding concepts intuitively, solving problems, being adept at thinking mathematically. The thing that is not useful is tedious definitions and tedious proofs. That's great. Not everyone does. Thinking simply via formal systems is not inherently inferior to 'doing' something with it. Both have their uses. In particular, as I said, quantum mechanics would not be where it's at today if it weren't for many pre-quantum mathematicians pushing around symbols on a page.
  - ajkjk 3y ago
    I'm very much not arguing that nobody should do pure math. I'm arguing that teaching pure math to undergrads who are trying to learn applied math is a tragedy and ruins math for a lot of people.
- Koshkin 3y ago
  > nobody needs a proof of how differentiation or integration work This "nobody" includes a lot of industry workers, e.g. those in finance and economics, not only "pure" mathematicians.

Koshkin 3y ago

I would not call this "destructive." Solving problems is fun in its own right, and things would start making sense in their interconnection, regardless of whether they can be applied to sciences or not.

RoyalHenOil 3y ago
It is destructive to people who do not find abstract math problems inherently fun, which is (I would guess) the great majority of people. They come to the conclusion that they hate math or that they are bad at math, even though they would have grasped it better and enjoyed it had it been presented to them differently. If your goal is teach math to the bulk of people, including those who will not go on to be mathematicians, it makes sense to tie math to something that the bulk of people can relate to. And most people DO enjoy thinking about physical objects and physical space (because we ourselves are physical beings who evolved to interact with our physical environment), so this is a really great starting point for introductory math for the average person. If your goal is to only teach the subset of the population who prefer highly abstract puzzles, and to alienate all others, then our current methods are working fine I guess. But I don't think this is a good goal for general math education.

eszed 3y ago

I think you put your finger on a challenge fundamental to teaching itself. Speaking as a (former, at least for now) teacher, the concepts that I find most intuitive were always the most difficult to teach, whereas skills I struggled to master were the ones I was best able to instruct. For problems in the second category I could diagnose the gaps in my students' understanding or application - likely because I'd faced them, or similar, myself - and strategize an approach that would help. Conversely, the subjects that I "got" without effort, left me floundering (at least at first) to find an alternate way to present to students. (I suppose that's where the terrible canard of "those who can't, teach" comes from. There's a kernel of truth to it, of course, but the more generous and relevant point is that success through effort is better preparation for teaching than success through natural ability alone.) My guess is not that your teacher would disagree that math is "a fundamental language of the universe", just that she spoke it so fluently that she wasn't well able to relate to people who don't.