
Why I love math - dpatru
http://www.reddit.com/r/math/comments/eo4e1/respectful_question_you_guys_actually_like_this/c19lh2k
======
btilly
For any layperson who wants to understand what mathematicians think about
math, I cannot recommend _The Mathematical Experience_ highly enough.

It is accessible to a high school student. Yet has insights for a PhD in
mathematics. And more than any other book I know, it captures the _experience_
of mathematics. Both good and bad.

I like to say that I went into mathematics for reasons given in that book. And
I left it for reasons given in that book.

~~~
nickpinkston
Look like the full text here:
[http://books.google.com/books?id=lMdz84dWNnAC&lpg=PP1...](http://books.google.com/books?id=lMdz84dWNnAC&lpg=PP1&dq=The%20Mathematical%20Experience&pg=PP1#v=onepage&q&f=false)

~~~
tianyicui
Not full text, the book preview is limited.

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samatman
The comparison of early maths (algebra in particular) to spelling is spot on.
It also reminds me of a somewhat wry observation from one of my mathematics
professors: that if we taught spelling and grammar exclusively through
crossword puzzles and competitive Scrabble, many fewer people would learn to
spell and write grammatically.

The analogy is to teaching algebra through endless, dry repetition of problem
solving. Some of you won't get what the big deal is; you're the ones who are
good at 'crossword puzzles'.

~~~
Benjo
Just curious: what is the better way to teach math? Or is that not obvious?

~~~
redthrowaway
I had a fantastic calculus teacher in high school (Freddie Irani, many thanks
if this somehow finds you). He's probably the only math teacher or professor I
ever had who made math both fun and intuitive. We had no homework, and regular
quizzes.

He taught math by talking about the history of the problems we were trying to
solve, and how people went about solving them. It was the concepts that
mattered; the equations were secondary. He would put a problem on the board,
and ask the class to solve it. He would then give us pieces of the puzzle,
until we had enough that we could figure it out ourselves. I found the class
participation to be key. With most math classes in college, the instructor
works through 3 or 4 problems for a given topic on the board, and the students
spend the entire class furiously copying down what he writes. It's pointless.
I get that it's driven by the need to cover a lot of material, but I'd rather
the class work through two examples then the instructor work through 4. Also,
regular quizzes were a key part of Irani's class that made retention much,
much easier. Instead of the typical weekly homework, two midterms and a final,
I would much prefer weekly quizzes, 3 (or 4) midterms, and a final worth a
much smaller chunk of the grade.

Last semester, I took linear algebra. We had weekly assignments that I did
with a tutor (bad decision), two midterms, and a final worth 45%. I went into
the final with ~40% in the class, crammed for it, and ended up with a mid-60
in the course. It was pointless, and I don't feel like I learned much. I would
much prefer the system Irani set up, but he's not a university professor, and
he doesn't have a PhD. He taught himself calculus with an inch-thick pocket
book he picked up from a second hand store.

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iwwr
Any specialized field becomes obscure to the uninitiated. While it may be
possible to use metaphors to give them a glimpse into the field, it's
ultimately a false picture. And so, analogies should be used to whet
appetites, not attempt to explain expert knowledge.

Feynman on magnetism: "I can't explain that attraction in any of the terms
that's familiar to you. For example, if we said that magnets attract as if
they were connected by rubber bands, I would be cheating you[...] and if you
were curious enough, you would ask me why rubber bands tend to pull back
together again and I would end up having to explain that in terms of
electrical forces."

<http://www.youtube.com/watch?v=wMFPe-DwULM>

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kenjackson
Conrad Wolfram gave a great talk at Ted about how to reform math. He is spot
on. I think this is one way Mathematica could really jump to the next level...
develop a full on home-school curriculum from age 3 through 12th grade.

Math education today is broken.

UPDATE: Link to talk with some other resources:
<http://computerbasedmath.org/>

~~~
codejoust
I've used Teaching Textbooks (<http://teachingtextbooks.com/>) for math up to
Precalculus. It's a self-paced, rather engaging math program with good word
problems. For elementary school, their curriculum has a more interactive
program with word problems, quizzes, etc. and in middle school and high school
it becomes self-paced lectures with problem set / workbooks. Another good,
similar program for high school is k12 which I've heard good things about too.
There are some good / new curriculums out there for homeschoolers.

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kiba
Not being forced to rush through everything make it a lot easier for me to
learn math.

Thanks to Khan Academy, I now understand trigonometry in a much cooler and
intuitive way.

However, I don't know if that mean I am beginning to transcend the
mechanics/grammar of mathematics.

~~~
CallMeV
That, like mastery of music, language and art, takes persistence, time,
practice, learning, error and experience - make the most of your time to
devote yourself to furthering what you know. The expertise you seek will come
to you.

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fooandbarify
Wow. This post is a revelation for me. I have frequently explained to people
that have bothered to ask (and probably a few who didn't) that the reason I
love programming has a lot to do with my love of language - the elegant
syntax, the rules and their exceptions. Despite rigorous math training (I'm an
electrical engineering student), until now I had never been able to see it as
more than a means to an end. I hated math classes so much, but they allowed me
to do interesting things with electricity so I put up with them. On occasion,
I have maybe been struck by a part of what this person is referring to, but
this puts it together in a way that I had never really understood before.

Thanks.

~~~
kenjackson
I'm the opposite, I love programming, but dislike languages. I can recall in
junior high wondering why these certain rules existed. "This is simply more
verbose and doesn't disambiguate anything as far as I can tell." The problem I
encountered with natural languages is I rarely could get an answer as to why
we have a form for this word. Whereas with programming, I can usually get an
answer for almost any question I have about a language.

~~~
nollidge
Natural language is evolved (and therefore haphazard and merely "good
enough"), whereas programming languages are designed. Natural languages are to
programming what biology is to robotics.

~~~
kenjackson
Agreed. In fact its funny you make that analogy... in that whenever I think
about doing some biology I want to use nanotechnology. My brain just has more
trouble settling into emergent systems.

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ez77
_When studying mathematics, the math major sees pure truth._

Then you take foundation of mathematics, metamathematics and more of that ilk
and you are labeled a Platonist. Well, guilty as charged.

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jakevoytko
As I read this, I noticed the similarity between mathematics and programing.
In fact, if you substitute the word "mathematics" with "programming," the post
sounds like my experience with my computer science degree. Algorithms and
programming languages were unnatural at first. I spent most of my formative
years fighting with programming languages instead of using them. But after a
few years, I moved past the point of fighting algorithms and languages and
started using them to actually solve problems.

Writing software doesn't help you discover the laws that govern everything,
but it affects people on a much more pragmatic level - software satisfies our
curiosity, tells us how to go where we need to go, and affects every aspect of
my day-to-day life. And that's not half bad.

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mathfornerds
In the film Matrix you discover an alternative reality and choose to take the
red pill. When you are able to think mathematically you discover a new
universe and you can choose to take the red pill to evolve, but that universe
is only accessible to those that can understand maths.

~~~
marknutter
"..can understand mathematics." FTFY

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edge17
Great explanation. The only shortcoming, or maybe not, is that he could have
pointed out that the parallel he drew is true for anyone that specializes and
transcends towards ideas rather than frets mechanics of a field. I'm much this
way about computer science, engineering, economics, finance, etc. The things
they teach you in an undergraduate education are just tools in your toolbox,
the bread and butter so to speak. It's the ideas are what's important.

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js2
Obligatory <http://xkcd.com/435/>

~~~
dnautics
I actually posted this in the lab an drew a red line bell curve over it that
was labelled "usefulness".

~~~
ek
Honestly, it seems like people on HN so often assess things based on their raw
usefulness. It makes sense, given that HN is read by many people who think
like engineers, but in another recent thread on /r/math, people are talking
about how the reason mathematicians study mathematics is not because it is
useful, but because it possesses an inherent beauty/logic/whatever that makes
the people who study it want to keep studying it. I'm doubling in math and CS
and I have to say that the reason I am studying math is not because of any
potential applicability to work I might do in software later in life, but
because it has an allure for me that is unmatched by almost anything else.

~~~
dnautics
hehe I unoffically doubled in math/chemistry, and I gave up on math because
precisely due to its inapplicability, I was competing with people who were
learning calculus at age nine. Chemistry was a better choice, because most
sane parent do not allow their sixteen year old children to tinker around with
carcinogens and explosives.

In retrospect, I should have been a coder. Although all my coding adventures
post high-school have basically been autodidactic, I jumped in the deep end
and took a high-level undergrad/grad CS class and coded my own web server... I
was the only person whose server didn't allow the user to drill through the
directory structure and hack the server because at the time I didn't know the
posix file functions and actually wrote my own string parser/handler.

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CallMeV
I wonder if anyone here has studied the Trachtenberg Method of Speed
Mathematics, or Vedic Mathematics. If anyone here has, I'd like to find out
what they thought of the way those methods are taught.

~~~
jules
I have taught a series of lectures on the Trachtenberg method in high school.
It has some cute tricks, but really this is not mathematics, it's arithmetic.
Don't waste your time with it. If you're interested in maths, study maths not
mental arithmetic. I promise it is much more interesting.

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bennyk
I always had trouble in regular math classes until physics. I think it was the
type of problem solving I understood and related to

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toast76
Can someone explain why Americans call it "math". If the word is a shortening
of Mathematics, shouldn't it be called "maths"?

~~~
greenlblue
"Mathematics" is a singular noun so shortening it to "maths" just doesn't make
sense.

~~~
toast76
For years I've heard the argument that Mathematics should be Maths (being
Australian). That's the first time any one has made a sensible argument (to
me) for the alternative.

I've never heard anyone call Gymnastics "Gyms". :P

~~~
ez77
Interestingly, in Spanish and French the unambiguously plural terms 'las
matemáticas' and 'les mathématiques' are commonly used, so the 's' in
'mathematics' may be of a different kind than that in 'gymnastics' or
'economics'.

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CallMeV
A magnificent explanation.

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yters
The most important truths of reality cannot be captured by math. Plus, we
create truth, and math can only represent what already exists.

~~~
nickpinkston
Tell that to Mr. Boole and his logic + algebra...

~~~
yters
For instance, logic, math and probability can describe what free will is, but
cannot predict the choices made by a free will.

On a grander scheme, how can math describe things like love, goodness and
beauty?

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cogspa
Mathematica is a great tool as well. If only they could raise their user base
beyond 3%.

