Mathematicians Are Overselling the Idea That “Math Is Everywhere”(blogs.scientificamerican.com)
blogs.scientificamerican.com
Mathematicians Are Overselling the Idea That “Math Is Everywhere”
http://blogs.scientificamerican.com/guest-blog/mathematicians-are-overselling-the-idea-that-math-is-everywhere/?WT.mc_id=SA_FB_MATH_BLOG
59 comments
Wow, that conclusion is crap. Mathematics is one of the most open fields of science. There are excellent free resources for learning math, even cutting edge research is usually easily found for free, the scientists are very open to sharing ideas. Anyone who has the necessary talent can learn any part of Mathematics they fancy.
Large portions of the worlds children grow up with barely primary school level education and an economic reality that requires them to go into work as soon as possible.
When would they have the time and money to set aside to get deep into a subject that most of them do not have the academic background to see the value of?
Yes, everyone could learn mathematics. Just like everyone could get rich and go into space. It's just that for a huge proportion of people the pre-requisites are not there.
When would they have the time and money to set aside to get deep into a subject that most of them do not have the academic background to see the value of?
Yes, everyone could learn mathematics. Just like everyone could get rich and go into space. It's just that for a huge proportion of people the pre-requisites are not there.
> Yes, everyone could learn mathematics. Just like everyone could get rich and go into space.
Ah the false analogy[1], we meet again. You don't really believe this do you? I mean you could make the same argument about gardening. Literally anyone can learn at least basic math, most people just don't have the inclination.
1) http://onegoodmove.org/fallacy/falsean.htm
Ah the false analogy[1], we meet again. You don't really believe this do you? I mean you could make the same argument about gardening. Literally anyone can learn at least basic math, most people just don't have the inclination.
1) http://onegoodmove.org/fallacy/falsean.htm
While not denying that access to academic math is a privilege, we should also notice and be clear that math is used by many people without formal training. People manage their money, for instance, and often learn sophisticated methods for accounting and calculation via apprenticeship. People build physical objects using measurements and geometry and, again, understandings of mechanics gained through apprenticeship. The formal language of math as written down in books is available to only a fraction of the world's population, but many people do use economic and maker math in their everyday lives.
Right and many proofs math textbooks are so old that anyone can print them, so they're actually much more available than say a chemistry textbook.
Indeed. I've learned more mathematics from free online resources (IRC, Math.SE, nLab, papers available online) than anywhere else. In most other fields, when you pester experts to share their knowledge, the very first thing they first ask you is how much you're going to pay them. In mathematics, the only real bottleneck for the transmission of knowledge is my own ability to assimilate it.
I feel particularly deceived about this state of affairs because my parents paid a lot of money for my formal education (school, university), and I got significantly less value from it than from people simply willing to share their knowledge for free.
I feel particularly deceived about this state of affairs because my parents paid a lot of money for my formal education (school, university), and I got significantly less value from it than from people simply willing to share their knowledge for free.
I've thought extensively about this and one of the conclusions I've reached is for example:
Imagine me or someone else that was never part of the math research establishment came up with the exact same proof Perelman came up with. Ipsis verbis.
You can rest assured that at least the slack that they cut him on sketchy details would not be extended to an outsider. (In a way the Yau debacle was a manifestation of this)
There are a few examples of this already in somewhat obscure fields.
That's assuming anyone would even give the proof the time of day.
Imagine me or someone else that was never part of the math research establishment came up with the exact same proof Perelman came up with. Ipsis verbis.
You can rest assured that at least the slack that they cut him on sketchy details would not be extended to an outsider. (In a way the Yau debacle was a manifestation of this)
There are a few examples of this already in somewhat obscure fields.
That's assuming anyone would even give the proof the time of day.
the evidence given in the article doesn't directly support this, but the author may have tried to get at the "[those that have] the necessary talent can learn any part of maths" statement you made. Without exposure to and engagement with a comprehensive education in mathematics (even just basic numeracy and arithmetic), it's incredibly difficult to teach oneself any given mathematical concept. Access to maths educational resources is ostensibly unrestricted, as (at least in the US) library cards are free of charge and the internet is readily accessible there; however, one can easily point at the many banes of lower-income households as immediate barriers to receiving any sort of education, either autodidactic in nature (i.e. sitting in a library with an geometry textbook) or through public schools.
It might be worth thinking in this "math for and from the elites" mindset when describing public aversion to the subject. Seeing it as beyond oneself or not relevant to one's life lends little towards anyone's desire to learn anything about it.
It's easy to say "why don't they just do it," with some diffuse definition of "they" in mind, but even the most basic things can be hard to get for the poor. A proper maths education is one of them, I think.
It might be worth thinking in this "math for and from the elites" mindset when describing public aversion to the subject. Seeing it as beyond oneself or not relevant to one's life lends little towards anyone's desire to learn anything about it.
It's easy to say "why don't they just do it," with some diffuse definition of "they" in mind, but even the most basic things can be hard to get for the poor. A proper maths education is one of them, I think.
He's not comparing math to other academic fields, he's comparing it to the most realistic alternative for most people, which is working a garbage McJob in which math isn't relevant to their lives at all. There's a lot of privilege involved in burying your head in books, no matter what the field, barring a few obsessive prodigies who live in public libraries and have extremely supportive parents.
Then why point out Math? Everything is inaccessible to people who work all day to get by. Art, Sports, DIY, whatever, not just STEM.
The author seems to conflate general math (arithmetic, variables, functions, basic modelling) with specialized math, used for advanced research topics like topology, number theory, etc.
Apart from this conflation, the article is very confused, mixes lots of unrelated topics, and is hard to follow. Maybe a rewrite is in order? Or perhaps writing logical arguments, with clear ideas that make sense is also an elitist thing we should avoid?
Apart from this conflation, the article is very confused, mixes lots of unrelated topics, and is hard to follow. Maybe a rewrite is in order? Or perhaps writing logical arguments, with clear ideas that make sense is also an elitist thing we should avoid?
That was a strange article to read. As I parsed his words, it seemed like Michael J. Barany is responding to someone else's essay or policy opinion but we don't know who or what it is. If we had that, it would fill in the blanks of what he's arguing against.
For example, he mentions "math" repeatedly but doesn't put boundaries around it. Is he talking about Algebra not being everywhere? Or Calculus is not necessary for everyone? Well, if you magnify the photo at the top of the article, you'll see books such as:
Because of my tech background, my first pass at his essay made me think it was a variation of arguing against the "coding is for everyone -- everyone should learn programming". However, I don't think Barany's opinion about math is an equivalent analogy.
For example, he mentions "math" repeatedly but doesn't put boundaries around it. Is he talking about Algebra not being everywhere? Or Calculus is not necessary for everyone? Well, if you magnify the photo at the top of the article, you'll see books such as:
+ number theory
+ theory finite elements
+ topology
+ Navier-Stokes equation
Because of my tech background, my first pass at his essay made me think it was a variation of arguing against the "coding is for everyone -- everyone should learn programming". However, I don't think Barany's opinion about math is an equivalent analogy.
That's what I don't get about the article, and some other comments address this as well. Fluid flow is everywhere, whether we have flush toilets or throw a bucket into a gutter somewhere! The statements "differential equations exist that describe fluid flow in certain contexts" and "all people can write down Navier-Stokes on command" are two versions of "math is everywhere". Mathematicians mean the first and this author basically discusses the second, which no mathematician ever would say. Straw man indeed.
I too would like to know what/who Barany might be arguing against; maybe it would clarify the article.
I too would like to know what/who Barany might be arguing against; maybe it would clarify the article.
If anything, math should be for everyone at least as much as programming is. If only to reduce the amount of crap code evidently written without regard for the basics of computing science (which is effectively applied math).
I think the author is deliberately conflating two interpretations of "Math is Everywhere." It's hard to argue that it isn't, when we talk about different fields of endeavor. Deep in any remunerative profession, from selling groceries to manufacturing semiconductors, there are quantitative models, and it helps to know at least trigonometry and calculus, if not differential equations, to understand them. But the author isn't actually talking about quantitative models -- this is the bait-and-switch -- he's actually talking about dramatically uneven mathematical education and widespread innumeracy.
Yeah it is a straw man from what I can see.
"Math can be used to model just about everything, and so can make a meaningful contribution to almost every endeavour" is a completely different statement from "Everyone has access to learning math to do anything math-related they want".
The second argument is not one I have heard people making, and if they make it I doubt they would express it as "Math is Everywhere". I have heard people make the first argument as "Math is Everywhere".
"Math can be used to model just about everything, and so can make a meaningful contribution to almost every endeavour" is a completely different statement from "Everyone has access to learning math to do anything math-related they want".
The second argument is not one I have heard people making, and if they make it I doubt they would express it as "Math is Everywhere". I have heard people make the first argument as "Math is Everywhere".
There is this, but the bait and switch actually has a justification in his mind : by publicly acknowledging that math is everywhere in the first and promoting this fact, we reinforce the extent to which innumeracy impacts those who suffer from it.
This is a political opinion, of course, and not an assessment on the extent to which maths help people.
This is a political opinion, of course, and not an assessment on the extent to which maths help people.
> An article, written on a keyboard with keys measured to fit in their place.
> Transmitted to the computer using error detecting codes (in USB)
> Being run through a CPU that essentially performs arithmetic, comparisons and branches.
> Being processed by a word processor that has been compiled in one of many of the highly mathematical languages that run on our computers.
> Written onto a disk with error detecting codes.
> Sent over the internet with error detecting codes.
> Written into a database that probably bases on relational algebra.
> I open the article and everything happens in reverse on my computer so I can view it.
And it claims maths is not everywhere. I just have to laugh.
We have to recognize that elite mathematics today, while much more inclusive than it was one or five or fifty centuries ago, remains a discipline that vests special authority in those who, by virtue of gender, race, and class, are often already among our society’s most powerful.
No, we do not. This is a factually false statement. We have to recognize that maths is open to everyone who is determined enough and has access to the internet or a library and that tribalism like this brings us nowhere. Anyone can participate in elite mathematics. If you come up with a proof for the Riemann hypothesis, go ahead and publish it! Nobody cares about your background if your work is good. Mathematics is blind to gender, race and class.
> Transmitted to the computer using error detecting codes (in USB)
> Being run through a CPU that essentially performs arithmetic, comparisons and branches.
> Being processed by a word processor that has been compiled in one of many of the highly mathematical languages that run on our computers.
> Written onto a disk with error detecting codes.
> Sent over the internet with error detecting codes.
> Written into a database that probably bases on relational algebra.
> I open the article and everything happens in reverse on my computer so I can view it.
And it claims maths is not everywhere. I just have to laugh.
We have to recognize that elite mathematics today, while much more inclusive than it was one or five or fifty centuries ago, remains a discipline that vests special authority in those who, by virtue of gender, race, and class, are often already among our society’s most powerful.
No, we do not. This is a factually false statement. We have to recognize that maths is open to everyone who is determined enough and has access to the internet or a library and that tribalism like this brings us nowhere. Anyone can participate in elite mathematics. If you come up with a proof for the Riemann hypothesis, go ahead and publish it! Nobody cares about your background if your work is good. Mathematics is blind to gender, race and class.
> And it claims maths is not everywhere. I just have to laugh.
Math is everywhere in the same sense that I need an understanding of physics to throw a ball. That is, yes, you can find it if you look, and sometimes you may even have a trained understanding of the application of some principle, but you do not need to be able to explain it or consciously apply it step by step.
Sometimes it would help to know how to apply it, or know other ways of solving a problem, but most people need far less conscious use of maths than people with a maths background tend to think.
> No, we do not. This is a factually false statement. We have to recognize that maths is open to everyone who is determined enough and has access to the internet or a library and that tribalism like this brings us nowhere. Anyone can participate in elite mathematics. If you come up with a proof for the Riemann hypothesis, go ahead and publish it! Nobody cares about your background if your work is good. Mathematics is blind to gender, race and class.
This both manages to not address the quote you were "answering" and be a demonstration of relative privilege at the same time.
It doesn't address it because the quote is not saying that elite mathematics isn't open to everyone in theory, but that it de facto is something that is mostly accessed by a certain group.
You brush against this yourself when you write that it is open to everyone "who is determined enough". And this is where privilege comes in.
People are shaped by their surroundings. If you grow up in a working class family, it is not always that you couldn't get into a top university and aim for a top job, but that even if you can you are vastly less likely to be aware of the opportunities, and to have the support network, and to have the contacts, or to have the same expectations of being able to do something, because you constantly see people around you who has achieved it, as someone growing up more privileged.
It is not just about money. I did not grow up in a rich household. But I did grow up in a household where getting a university degree and aiming for a job requiring one was considered so self evident it was never something we discussed. It wasn't "are you planning on going to university or trade school or start working after graduation?" it was "which universities are you applying to?" Most of my close relatives are academics, with three professors amongst my aunts and uncles.
As a result it never once crossed my mind growing up to go for a career in a manual trade for example.
Subtle differences, some backed by money, some just byproducts of growing up in families with money or connections or, as in my case, an innate expectation that your future should involve studying for a degree, makes a huge difference.
I've also noted in the past on HN that one of the things that growing up in Norway did for me was that I never had a sense of worrying about unemployment.
When I did my first startup, it was never a consideration that I might be without a job. Why would it? I'd be financially secure no matter what.
In my case it was because of a strong social security net first and foremost, but access to help from family etc. does the same. Even just living in a society where making enough to save to set aside a rainy day fun is something a majority can do makes a huge difference.
Growing up in a position of relative privilege alters things in many ways:
You may be expected to study instead of being expected to start earning as early as possible. You likely grew up with enough food to avoid being damaged by malnourishment. You're less likely to have urgent, stressful financial concerns make it infeasible to set aside time to ponder more intellectual issues. You're more likely to have a job that earns you enough to allow you to spend time on other things. You're more likely to have people around you that achieve something intellectual to inspire you. And so on.
So yes, "anyone" can participate in elite mathematics. And sometimes people from unexpected backgrounds does. But in practice, more privileged people are more likely to.
This isn't specific to mathematics - it applies to pretty much any field where "payoff" is uncertain or requires lengthy investment in education first, which causes less privileged people to self-select away to a greater extent than people with more privilege.
Math is everywhere in the same sense that I need an understanding of physics to throw a ball. That is, yes, you can find it if you look, and sometimes you may even have a trained understanding of the application of some principle, but you do not need to be able to explain it or consciously apply it step by step.
Sometimes it would help to know how to apply it, or know other ways of solving a problem, but most people need far less conscious use of maths than people with a maths background tend to think.
> No, we do not. This is a factually false statement. We have to recognize that maths is open to everyone who is determined enough and has access to the internet or a library and that tribalism like this brings us nowhere. Anyone can participate in elite mathematics. If you come up with a proof for the Riemann hypothesis, go ahead and publish it! Nobody cares about your background if your work is good. Mathematics is blind to gender, race and class.
This both manages to not address the quote you were "answering" and be a demonstration of relative privilege at the same time.
It doesn't address it because the quote is not saying that elite mathematics isn't open to everyone in theory, but that it de facto is something that is mostly accessed by a certain group.
You brush against this yourself when you write that it is open to everyone "who is determined enough". And this is where privilege comes in.
People are shaped by their surroundings. If you grow up in a working class family, it is not always that you couldn't get into a top university and aim for a top job, but that even if you can you are vastly less likely to be aware of the opportunities, and to have the support network, and to have the contacts, or to have the same expectations of being able to do something, because you constantly see people around you who has achieved it, as someone growing up more privileged.
It is not just about money. I did not grow up in a rich household. But I did grow up in a household where getting a university degree and aiming for a job requiring one was considered so self evident it was never something we discussed. It wasn't "are you planning on going to university or trade school or start working after graduation?" it was "which universities are you applying to?" Most of my close relatives are academics, with three professors amongst my aunts and uncles.
As a result it never once crossed my mind growing up to go for a career in a manual trade for example.
Subtle differences, some backed by money, some just byproducts of growing up in families with money or connections or, as in my case, an innate expectation that your future should involve studying for a degree, makes a huge difference.
I've also noted in the past on HN that one of the things that growing up in Norway did for me was that I never had a sense of worrying about unemployment.
When I did my first startup, it was never a consideration that I might be without a job. Why would it? I'd be financially secure no matter what.
In my case it was because of a strong social security net first and foremost, but access to help from family etc. does the same. Even just living in a society where making enough to save to set aside a rainy day fun is something a majority can do makes a huge difference.
Growing up in a position of relative privilege alters things in many ways:
You may be expected to study instead of being expected to start earning as early as possible. You likely grew up with enough food to avoid being damaged by malnourishment. You're less likely to have urgent, stressful financial concerns make it infeasible to set aside time to ponder more intellectual issues. You're more likely to have a job that earns you enough to allow you to spend time on other things. You're more likely to have people around you that achieve something intellectual to inspire you. And so on.
So yes, "anyone" can participate in elite mathematics. And sometimes people from unexpected backgrounds does. But in practice, more privileged people are more likely to.
This isn't specific to mathematics - it applies to pretty much any field where "payoff" is uncertain or requires lengthy investment in education first, which causes less privileged people to self-select away to a greater extent than people with more privilege.
Oh, so it's my privilege if some parents fuck up at telling their kids how important education is and mine didn't? What a strange way to reason. Everyone complains about privilege but nobody takes responsibility for mistakes.
The only people who have my sympathy in those regards are the working poor, that is, people who have to hold multiple jobs, more than full-time, just to get by and not starve. These are the people whose potential to excel in mathematics (or anything, really) is undermined.
The only people who have my sympathy in those regards are the working poor, that is, people who have to hold multiple jobs, more than full-time, just to get by and not starve. These are the people whose potential to excel in mathematics (or anything, really) is undermined.
Do you think it's a reasonable strategy for an average person with daily struggles to put all their effort into coming up with a proof for the Riemann hypothesis?
I take your point, but then I have no idea what the author is arguing for. He blurs the line between things like university math departments and academic culture, math as a scholastic pursuit, and math as a specific body of knowledge. In the specific case of Riemann hypothesis, contributions from outside of the system are most certainly welcome, and there are countless examples of this in history of mathematics. But no, the average person will not be able to contribute in the same way that the average person is barred from playing in professional sports leagues. Is that what he means when he argues that Math doesn't belong to everyone?
Math can be considered at least aspect of everything (though this is often reductionist). There is an unrealistic expectation that everyone can or should turn their attention to it, and a reality that those who have math training often have an advantage, especially in key societal positions. The author is stating that there is an advantage for some people to have the conditions to learn. The final paragraph seems to indicate that conditions need to be created for more people to have this opportunity. It would be magical thinking to expect the vast majority of people could juggle their everyday lives to become very good at math in ways that are more meaningful than being good at crossword puzzles or baking or taking care of their families at key times, not to mention having more than one focused interest. Since there is a "society" it shouldn't be critical for everyone to have the same developed skills, which the conclusion seems a bit disconnected from.
>There is an unrealistic expectation that everyone can or should turn their attention to it, and a reality that those who have math training often have an advantage, especially in key societal positions.
Ok. That makes sense. Specialized knowledge is required for specialized work. What's your point?
>The author is stating that there is an advantage for some people to have the conditions to learn.
I guess this is the meat of the argument the author is making, with some ideologically-driven, and here unstated, reasons that explain this 'advantage'.
>Since there is a "society" it shouldn't be critical for everyone to have the same developed skills, which the conclusion seems a bit disconnected from.
But it isn't critical. There is a requirement to have a base level understanding of mathematics in order function in society (roughly high-school level), just as there is a requirement for literacy - but there's certainly no requirement to have in-depth knowledge of it. Nor is a deep understanding of math a prerequisite for success, financial or otherwise.
Ok. That makes sense. Specialized knowledge is required for specialized work. What's your point?
>The author is stating that there is an advantage for some people to have the conditions to learn.
I guess this is the meat of the argument the author is making, with some ideologically-driven, and here unstated, reasons that explain this 'advantage'.
>Since there is a "society" it shouldn't be critical for everyone to have the same developed skills, which the conclusion seems a bit disconnected from.
But it isn't critical. There is a requirement to have a base level understanding of mathematics in order function in society (roughly high-school level), just as there is a requirement for literacy - but there's certainly no requirement to have in-depth knowledge of it. Nor is a deep understanding of math a prerequisite for success, financial or otherwise.
There are true stories of housewives with no formal advanced mathematical training at all who grew the body of mathematical knowledge by finding out new things, thus participating in 'elite mathematics'.
A reasonable strategy for what? If they're obsessed with the Riemann hypothesis and it brings them pleasure to think about it, sounds great. If they'd prefer to have the largest collection of salt and pepper shakers in the world, visiting flea markets would be a better effort.
If you're asking whether an average person has a good chance of proving the Riemann hypothesis or has access to the latest ideas in the field, the answer is no. But I make my own clothes without having access to Paris or Milan or Hong Kong. We can all do rewarding non-elite things.
If you're asking whether an average person has a good chance of proving the Riemann hypothesis or has access to the latest ideas in the field, the answer is no. But I make my own clothes without having access to Paris or Milan or Hong Kong. We can all do rewarding non-elite things.
Yes, some people by virtue of their completely average mediocrity can't excel. But isn't this the case for every field? Why is that mathematics' problem?
It's not mathematics' "problem." But it is a problem for people who may or may not be "average mediocrity" and can't drop everything to focus on this topic.
But you can say that about anything! Meaningfully contributing to any area (from academia, to sports, to Sunday bake sales) requires time commitments not everyone has. In most cases there may also be a requirement for some minimum level of knowledge, experience or skill. Welcome to life.
You're right in that it can be said about almost anything, but it's not about time. If you're born into poverty, you can have all the time in the world, but you'll find it extremely hard to get proper education before you even get a chance to put some time into it. In other words, to even get a chance to commit time to something like mathematics at the level we're talking about, there are hard practical social and economic preconditions which have nothing to do with one's abilities, or even the field of endeavor as such.
The article just conflates the field itself with these wider socio-economic conditions, constructs a weird argument out of the confusion, and comes out really bad.
The article just conflates the field itself with these wider socio-economic conditions, constructs a weird argument out of the confusion, and comes out really bad.
>If you're born into poverty, you can have all the time in the world, but you'll find it extremely hard to get proper education before you even get a chance to put some time into it.
Your hypothetical setup is strange. If you have all the time in the world - you can do anything.
>In other words, to even get a chance to commit time to something like mathematics at the level we're talking about, there are hard practical social and economic preconditions which have nothing to do with one's abilities, or even the field of endeavor as such.
Like what preconditions exactly?
Your hypothetical setup is strange. If you have all the time in the world - you can do anything.
>In other words, to even get a chance to commit time to something like mathematics at the level we're talking about, there are hard practical social and economic preconditions which have nothing to do with one's abilities, or even the field of endeavor as such.
Like what preconditions exactly?
The one you quote first.
I feel like you s/Math/<any scientific discipline>/g and this article would still hold. Yes, the sciences and engineering, and pretty much every academic pursuit has been historically restricted to white men in the western world, but that doesn't have much bearing on the modern world.
If anything, I feel mathematics is more open than many other STEM fields. I got my degree in mathematics, and I noticed the gender gap in classes was nonexistent. In the calculus and statistics and other classes which were required for engineers, the classroom distribution would definitely skew male. But in the pure math classes, like topology, abstract algebra, real analysis, etc that would only be taken by math majors, the gender distribution was 50-50. In several of my classes the women outnumbered the men. And this was also true of the faculty: 3/6 professors I took classes with were women.
If anything, I feel mathematics is more open than many other STEM fields. I got my degree in mathematics, and I noticed the gender gap in classes was nonexistent. In the calculus and statistics and other classes which were required for engineers, the classroom distribution would definitely skew male. But in the pure math classes, like topology, abstract algebra, real analysis, etc that would only be taken by math majors, the gender distribution was 50-50. In several of my classes the women outnumbered the men. And this was also true of the faculty: 3/6 professors I took classes with were women.
I would agree with the general statement that mathematics has not been the most inclusive field (though it's getting better) and has been reserved to "elites", but I don't understand how it can be linked to statements like "math is everywhere".
His conclusions states:
"If math were really everywhere, it would already belong to everyone equally. But when it comes to accessing and supporting math, there is much work to be done. Math isn’t everywhere."
I guess the same might be told for art or history ; they are everywhere but artists and historians are not and becoming one of them is difficult.
His conclusions states:
"If math were really everywhere, it would already belong to everyone equally. But when it comes to accessing and supporting math, there is much work to be done. Math isn’t everywhere."
I guess the same might be told for art or history ; they are everywhere but artists and historians are not and becoming one of them is difficult.
By this standard, surgeons are elitist too. Try buying a green scrub and showing up in the operating room to cut someone ... Medicine is not everywhere.
I can take 15 3rd-graders out on a walk and give them an interactive math lecture about symmetry, fractals, dimension, non-Euclidean geometries, and other mathematical topics on any day. To do this I’d walk them past a brick wall and some buildings, we’d look at some ants and the directions they can go and we’d jump up and down to be different than the ants, we’d use the sidewalk and talk about the globe, we’d find some leaves and look at the veins in the leaves. Math is certainly everywhere, and that’s what we mean when we say it.
When it comes to math that influences public policy, we're often talking about actuarial mathematics. It’s not “elite”: it's an area of complicated applications that will determine whether our economy will sink under health-care costs or not. Math for national security? Crypto, and since good implementation of the math ideas is at least as important as the ideas, I don’t think it’s as elite as he makes out.
Gromov-Witten theory is built for the few. Elliptic cohomology is build for the few. Whittaker functions are built for the few, the elite, the more-likely-than-not Russian. This is what the NSF funds, among other math. But that doesn’t jibe with the intermittent discussion of policy and … economics?… attempted in the article.
I don’t think this author has a point. The author doesn’t distinguish between math used in and for public policy and math funded by the taxpayer. The author is trying to argue that since people aren’t good at math it maybe doesn’t exist (?) (“If math were really everywhere, it would already belong to everyone equally.” What does this mean?) The author tries to address racial/social/class inequities in math education access but only sort of randomly, at the end, without discussing causes, effects, or mechanisms, and while ignoring the international face of mathematics and the mathematicians who exist today.
When it comes to math that influences public policy, we're often talking about actuarial mathematics. It’s not “elite”: it's an area of complicated applications that will determine whether our economy will sink under health-care costs or not. Math for national security? Crypto, and since good implementation of the math ideas is at least as important as the ideas, I don’t think it’s as elite as he makes out.
Gromov-Witten theory is built for the few. Elliptic cohomology is build for the few. Whittaker functions are built for the few, the elite, the more-likely-than-not Russian. This is what the NSF funds, among other math. But that doesn’t jibe with the intermittent discussion of policy and … economics?… attempted in the article.
I don’t think this author has a point. The author doesn’t distinguish between math used in and for public policy and math funded by the taxpayer. The author is trying to argue that since people aren’t good at math it maybe doesn’t exist (?) (“If math were really everywhere, it would already belong to everyone equally.” What does this mean?) The author tries to address racial/social/class inequities in math education access but only sort of randomly, at the end, without discussing causes, effects, or mechanisms, and while ignoring the international face of mathematics and the mathematicians who exist today.
Strange - I don't know where to begin on this.
Access to data, the tools to manipulate it, and the knowledge to understand it have never been more accessible. There is a growing understanding that stats is as important as calculus in the high school mathematics curriculum.
Sure - getting a job as a tenured mathematics teacher is tough. Same as an NSA researcher. But it's crazy to say they have a monopoly on mathematics.
Access to data, the tools to manipulate it, and the knowledge to understand it have never been more accessible. There is a growing understanding that stats is as important as calculus in the high school mathematics curriculum.
Sure - getting a job as a tenured mathematics teacher is tough. Same as an NSA researcher. But it's crazy to say they have a monopoly on mathematics.
Hmm - a counterargument would be to substitute "literacy for "mathematics" in the argument; literacy was elitist in its core historically (and still is in certain societies, unfortunately) - does that imply that learning to read is irrelevant for most people?
Would he also argue that physics is "not everywhere" since we are not all elite physicists?
Math is one of those things that you'll see everywhere if you're looking for it. So its not that the mathematicians are lying, just that they have a biased perspective.
It’s a figure of speech. Math is everywhere, but not everyone have access to it. So math isn’t actually everywhere.
That's an odd argument to make. It would be like saying that printed word is not everywhere if you are illiterate (or just not familiar with society's alphabet).
I see math similar to many other types of knowledge. You can get by with fairly little, but the more you know, more often you will recognize opportunities to use it.
I see math similar to many other types of knowledge. You can get by with fairly little, but the more you know, more often you will recognize opportunities to use it.
That's my point. The real question is whether "having access to it" is of value to people. I tend to say yes because I love knowledge and take any opportunity I can to better understand the universe I am part of. But not everyone feels this way.
There is 'elite mathematics', just as there are in every other field. Should we come to the same conclusion for every other subject, just because there are a few gifted individuals who dominate their field? Yet, most math that is used frequently is not complicated and anyone can learn it (even calculus). The barriers to obtaining a high level education in mathematics and its related fields (there are too many to count) is less related to the education system and the complexity of the subject material, but more related to public policy and poverty. And hey, would you look at that, we can use statistics and math and our understanding of economics to help solve those too! I think the writer didn't have the interest in math in high school, had a bad experience, and chose to be a historian, as pointed out by tokenadult.
Statistics and trial design is something strongly mathematical that almost no-one understands and yet is vitally important to decision-making in the modern world. One need only look to the Daily Mail for evidence of this: every few days they scream that SOMETHING ELSE CAUSES CANCER based on a study which shows nothing of the sort. I imagine people actually change their behaviour based on this kind of fake "science", and given an intuitive understanding of stats, it ought to have much less power to sway people.
(See also: an offshoot of the Daily Mail Oncology Ontology, https://kill-or-cure.herokuapp.com/ )
(See also: an offshoot of the Daily Mail Oncology Ontology, https://kill-or-cure.herokuapp.com/ )
This article is riddled with poor reasoning.
1. The author's claim about "the politics of who gets to be a part of the mathematical elite" has almost nothing to do with the contention that "math is everywhere".
2. Math is everywhere. I make this claim by virtue of the facts that (1) you can, in any situation, ask questions like "how many?", "how much?", and "which one?" (which leads to encodings) and (2) Math is just our ordinary processes of reasoning, made rigorous and mechanized. Whether you're looking at someone's face, walking through the zoo, or cooking, there are underlying mathematical realities to be considered, if you're interested.
3. The author writes, "When we talk about math in public policy, especially the public’s investment in mathematical training and research, we are not talking about simple sums and measures." Except that, sums and measures and similar basic arithmetic are extremely relevant to making policy. When we talk about % growth targets, or inflation, or social security, back of the envelope arithmetic is just what you need to get an idea of what a policy actually does, or what it's results have been.
4. Examples in this article are cherry-picked and without supporting context: "Priests used astronomical calculations to mark the seasons and interpret divine will, and their special command of mathematics gave them power and privilege in their societies" But this is only true if mathematical prowess (rather than say, winning a lottery or being supposedly divinely annointed) was the key to joining the priesthood. Once accepted as a priest, what difference would it make whether you gave mathematically correct, or entirely nonsensical predictions to a crowd?
5. As another commenter writes "Mathematics is one of the most open fields of [S]cience". This is spot on. Existing free resources are really fantastic, and while you can make a completely valid point that not all children are given the relevant fundamental education to allow them to take advantage of that, the same argument applies to any field of education -- down to and including basic literacy. It makes no sense to lay the blame for this on mathematics.
tl;dr: This article is a giant non-sequitur, chock-full of poor reasoning.
1. The author's claim about "the politics of who gets to be a part of the mathematical elite" has almost nothing to do with the contention that "math is everywhere".
2. Math is everywhere. I make this claim by virtue of the facts that (1) you can, in any situation, ask questions like "how many?", "how much?", and "which one?" (which leads to encodings) and (2) Math is just our ordinary processes of reasoning, made rigorous and mechanized. Whether you're looking at someone's face, walking through the zoo, or cooking, there are underlying mathematical realities to be considered, if you're interested.
3. The author writes, "When we talk about math in public policy, especially the public’s investment in mathematical training and research, we are not talking about simple sums and measures." Except that, sums and measures and similar basic arithmetic are extremely relevant to making policy. When we talk about % growth targets, or inflation, or social security, back of the envelope arithmetic is just what you need to get an idea of what a policy actually does, or what it's results have been.
4. Examples in this article are cherry-picked and without supporting context: "Priests used astronomical calculations to mark the seasons and interpret divine will, and their special command of mathematics gave them power and privilege in their societies" But this is only true if mathematical prowess (rather than say, winning a lottery or being supposedly divinely annointed) was the key to joining the priesthood. Once accepted as a priest, what difference would it make whether you gave mathematically correct, or entirely nonsensical predictions to a crowd?
5. As another commenter writes "Mathematics is one of the most open fields of [S]cience". This is spot on. Existing free resources are really fantastic, and while you can make a completely valid point that not all children are given the relevant fundamental education to allow them to take advantage of that, the same argument applies to any field of education -- down to and including basic literacy. It makes no sense to lay the blame for this on mathematics.
tl;dr: This article is a giant non-sequitur, chock-full of poor reasoning.
Thinking is math. If thinking is put in relations different things this is math.
With the dialetics of yin and yang we can compare and put in a relative relations everything.
Yin and yang relation is the binary math of I Ching for example.
All the rules of the Traditional Medicine Chinese for example can be demostrated with I Ching Math
I feel I should toss up XKCD's golden ratio overlays[1] but I think it's really a chicken or the egg kind of argument- did processes involuntarily use math to come to these arrangements, or did we apply math to understand them?
[1]https://xkcd.com/spiral/
[1]https://xkcd.com/spiral/
Especially true if we exclude stuff that's "not what math really is" when we lament how bad the teaching of mathematics is, like applying known formulas, gaining utility from knowing one's times tables, doing mental math with fractions or percentages, and so on.
Math and geometry are also used in symbolics sciences.
I-king with binary math, Astrology and tarots use math symbols for explain many priciples.
We find it in Pitagora, Platone, Plotino, Giordano Bruno
Ugh. I didn't need to be reminded of "Harrison Bergeron" before breakfast. Very poor satire, if that were the intention.
I think they should quantify that statement :)
https://history.princeton.edu/people/michael-j-barany
I'm troubled that a Princeton history student can write about a worldwide phenomenon with so little reference to non-Western cultures. (This is a pet issue of mine, as I am an American who lived in east Asia for years after studying Chinese and sinology.) I don't think he has looked at development economics and the history of popular attitudes toward economics enough to understand how important basic understanding of mathematics is. In other words, I disagree with the conclusion of his article, summed up in the last paragraph.
"Imagining math to be everywhere makes it all too easy to ignore the very real politics of who gets to be part of the mathematical elite that really count—for technology, security, and economics, for the last war and the next one. Instead, if we see that this kind of mathematics has historically been built by and for the very few, we are called to ask who gets to be part of that few and what are the responsibilities that come with their expertise. We have to recognize that elite mathematics today, while much more inclusive than it was one or five or fifty centuries ago, remains a discipline that vests special authority in those who, by virtue of gender, race, and class, are often already among our society’s most powerful. If math were really everywhere, it would already belong to everyone equally. But when it comes to accessing and supporting math, there is much work to be done. Math isn’t everywhere."