
The Art of Mathematics - mathgenius
https://krieger.jhu.edu/magazine/fall-2018-v16n1/the-art-of-mathematics/
======
j7ake
Reminds me of Lockhart's Lament
([https://www.maa.org/external_archive/devlin/LockhartsLament....](https://www.maa.org/external_archive/devlin/LockhartsLament.pdf)).

Lockhart has a description of an analogous world where music education from
K-12 is pushed as important and all kids must learn it to do well in the
world.

The kids are educated by music teachers who have never wrote or have any deep
connection with music. Kids are rewarded for filling in note correctly on a
scoresheet and doing difficult things such as transposing music to one key to
another, but they never learn to write or play music.

~~~
wyldfire
> “Oh we don’t actually apply paint until high school,” I was told by the
> students. ... “So your students don’t actually do any painting?” I asked.
> “Well, next year they take Pre Paint-by-Numbers. That prepares them for the
> main Paint-by-Numbers sequence in high school.

This was worth a chuckle. I recall taking pre-calculus/calculus in high school
from a particularly passionate teacher. He really enjoyed his job and I felt
like I got a greater appreciation for mathematics from his teaching. He did
live graphing of equations with a then-novel overhead-transparency peripheral
display for his computer. He included lots of practical engineering
applications. After reflecting on this article I wonder if he were
unconstrained in the curriculum whether he would've been yet more inspiring
still.

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xtiansimon
"...you can find Kitchloo at a cafe. He admits he’ll spend hours there,
nursing a coffee or tea, and staring off into space, deep in thought...trying
to get a feeling for the object he’s studying."

That's how people who 'hate' math feel. They stare at the page, run their
minds in circles and feel like they're lost in space.

I came back to mathematics as I was learning programming as an adult.

One thing I cannot stand is the general lack of definitions. My mind is
oriented to programming where anything outside of the language must be defined
in scope. Or maps, which have a legend and define abstract symbols.

But that's just not the case in mathematics. You read the book. Start on page
one. Eventually you get to a formula. You can scrape the text all you want,
but there are characters without a definition.

What's more, if you try to use other texts to find the definition, some
special characters have different values. Or the forumla is defined
differently.

OK. I get it. Just as with a programming language, once you pass a certain
threashold, it's possible to reason past these inconsistencies and over the
gaps.

My question to math-heads, is abstraction more perverse in Mathematics? Does
it serve a purpose?

~~~
mathgenius
For me I need to see examples. The abstraction almost always just confuses me.
Unfortunately most (advanced) mathematics texts are very thin on examples. It
wasn't always like this. Mathematics used to (hundreds of years ago) be done
with _all_ examples and _no_ theory! That would suit me just fine. It seems
that some people are better at one way or the other. The present trend is
towards the abstract side.

~~~
ashrk
I've found I have to turn mathematics algorithmic to understand it, thinking
through what each symbol _does_ to the things passing "through" it. Attempting
to understand equations _per se_ does nothing for me. They're important for
proofs, I get it, but aid me not at all figuring out what it all actually
means. Yet equations are the primary tool and presentation method used in most
math books.

I'm pretty sure this is why I've never had trouble with programming, despite
feeling the way I imagine a dyslexic must when I try to read very "mathy"
material _even about things that I already understand_. Programming's
algorithm-first. Except the few languages that aren't, and I bounce off those,
too.

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roenxi
One way to divide people on mathematics is to separate those who see it as a
technology (have problem -> apply mathematics -> problem is solved) from those
who see it as a way of interpreting the world (eg, the stock market /is/ a set
of correlated random variables, adding things to a heap /is/ addition,
geometry /is/ how the world fits together).

Usually there isn't a huge amount of difference between these competing
philosophies, but it really rears its head in probability and statistics where
a huge amount of damage is done, eg, p-value-hacking by people who think
statistics is a technology rather than a perspective.

~~~
throwaway487548
> the stock market /is/ a set of correlated random variables

No. this is neo-platonic bullshit. In this context _is_ here must be a type-
error. What could be imagined in not what really is - reality is one,
interpretations are infinite. Stock Market is the result of human (and
computer) actions - the result of actions of all institutional participants.
This is what it _is_.

A model could be created to be superimposed on these partially-observable
stochastic processes (and, boy, there is no shortage of these, and no one is
right, of course) but it will be only a model, usefulness and applicability of
which depends upon who is using it and for what means (usually, bullshitting).

Geometry is closer to "what is" because it abstracts out "concrete" patterns
this universe is able to produce (and lots of imaginary bullshit, of course).

Let me stress is a gain - maths are generalized and abstracted out patterns of
what is, plus abstract sectarian bullshit. Reality comes first, (it is a
closure) interpretations and abstractions are bound by it.

~~~
throwawaymath
I'm having difficulty following what you're saying here. I think you're saying
mathematical models are only an (imperfect) interpretetion of reality, which
sounds fine.

But then you're talking about "sectarian bullshit" and "neo-platonic
bullshit". And at the same time, you called the stock market a "partially
observable stochastic process" \- why do you have an issue with calling
something in reality a set of random variables, but you don't have an issue
with calling it a stochastic process? Those are the same thing.

Honestly it feels like you launched into a tirade over a perfectly innocent
and fine choice of words. I don't think the commenter you responded to meant
to push some kind of weird philosophical agenda.

------
eftychis
"Even mathematicians will tell you that mathematics has a bit of an image
problem, particularly in the U.S."

That is something that strikes me constantly and I try to understand. I was
amazed the first time I heard the phrase "just do the math" to imply do the
menial calculations et cetera. This embodies the negative perception and
misunderstanding that a lot of people have in general, but perhaps at a
different level entirely in the U.S. What is more surprising is this is
despite a math degree opening a lot of opportunities in the U.S. In
comparison, in a lot of countries one can easily be stuck between teaching or
research (if they are lucky and have the passion), or abandoning their degree.

Consider yourselves lucky to have been exposed early on to math, is not a good
approach or feeling to have. I think the demeanor of "you are good at it, or
you are just not" is too damaging to the field in general. People that are
passionate, innately or via some environmental factor acting as nurtury and
"pylon", are perhaps going to persevere, like in other fields.

Nobody told a kid that they should stop drawing, writing, or playing the
guitar or piano, because they are bad at it. Math though apparently...

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knightswhosayni
Nice to know that more people are aware of the "pipeline issue" as noted in
the article.

So many people have experienced implicit bias as mathematicians, especially
people who "shouldn't be good at math".

------
HiroshiSan
Ha, I'd say 4 in 10 is quite a lot of people that hate math...so in that sense
it is a majority. It's more people than I'd like, that hate math.

~~~
nkoren
But that isn't what "majority" means...!

~~~
unhkbfukgfjb
It is, if half of the rest doesn't care either way.

~~~
mkl
No, then it would be a plurality.

