
Mathematicians Are Overselling the Idea That “Math Is Everywhere” - jimsojim
http://blogs.scientificamerican.com/guest-blog/mathematicians-are-overselling-the-idea-that-math-is-everywhere/?WT.mc_id=SA_FB_MATH_BLOG
======
tokenadult
I looked up the author's profile as a graduate student of history at
Princeton.

[https://history.princeton.edu/people/michael-j-
barany](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."

~~~
adrianN
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.

~~~
vidarh
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.

~~~
digitalarborist
> 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](http://onegoodmove.org/fallacy/falsean.htm)

------
ivan_ah
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?

------
jasode
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:

    
    
      + number theory
      + theory finite elements
      + topology
      + Navier-Stokes equation
    

It's possible that the photo was a random clipart but it does seem to be the
type of "math" he's talking about. Therefore, _" math isn't everywhere"_
should be translated as _" advanced university math isn't everywhere"_. So
yes, it seems reasonable that we don't have to convince every part of society
that they must learn to derive public key cryptography from first principles
of number theory. But the question is, who was pushing that agenda?

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.

~~~
kaitai
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.

------
sevensor
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.

~~~
jib
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".

------
Kenji
> 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.

~~~
davidy123
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?

~~~
Kenji
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'.

~~~
davidy123
Of course there are, many stories I'm sure. There are a lot of people on the
planet. The point is not that people can't, they can and will if the
conditions and imperatives exist.

------
openasocket
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.

------
yaps8
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.

~~~
gus_massa
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.

------
kaitai
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.

------
mathattack
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.

------
aarghh
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?

------
n00b101
Would he also argue that physics is "not everywhere" since we are not all
elite physicists?

------
greydius
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.

~~~
lcnmrn
It’s a figure of speech. Math is everywhere, but not everyone have access to
it. So math isn’t actually everywhere.

~~~
samastur
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.

------
nprecup
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.

------
Smaug123
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/](https://kill-or-cure.herokuapp.com/) )

------
haliax
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.

~~~
saskurambo
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

------
Vexs
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/](https://xkcd.com/spiral/)

------
ashark
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.

------
saskurambo
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

------
jessaustin
Ugh. I didn't need to be reminded of "Harrison Bergeron" before breakfast.
Very poor satire, if that were the intention.

------
amelius
I think they should quantify that statement :)

