
There are no rules in math - hardmath123
http://hardmath123.github.io/no-rules-in-math.html
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lordnacho
My high school math teacher used to give us extra classes that weren't
directly connected to the curriculum. They were always about structure,
elegance, and beauty. Quite a lot of time was also spent on history: who was
studying what, when, and why. (Also there was a cult of Leonard Euler, which
maybe is not so surprising if you did high school math.)

I found it to be the most important glue in my math education. In fact, all
the natural science ought to be taught in this way. Kinda like Bill Bryson's
Brief History of Everything, plus actual calculations.

We won a math contest in my last year. I was expecting it to stay interesting.

Unfortunately when I got to university math (and the rest of engineering) was
taught in a very utilitarian way. There was very little context, just a lot of
similar looking derivations.

I blame the exam culture. In a way it's good because it motivates you to learn
something, but it's bad because you end up learning it in a way that isn't
useful. At the end of your college days, you are unlikely to remember just how
Stoke's theorem works or the coefficients in Runge-Kutta. That's just because
the size of the curriculum is huge. But if you had a context, a set of stories
about when and why something was studied, you'd have a much better chance of
being able to recall that it even exists.

~~~
jschwartzi
I had a college geometry professor who taught all of his classes this way. He
taught me things about math, structure, elegance, and beauty that unfolded
into a much better understanding of why math is so powerful in science.
Studying history of math and Euclid did more to enhance my understanding of
Physics and Math than any of the actual required courses, because they taught
me the context in which the thinking is grown, which is far more powerful than
the thinking itself.

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stanleydrew
Having earned an undergraduate degree in math I've often had similar thoughts
about US elementary math education's emphasis on rules and mechanical
calculation and memorization rather than more abstract concepts like pattern
matching.

Turns out there was a thing called "New Math"
([https://en.wikipedia.org/wiki/New_Math](https://en.wikipedia.org/wiki/New_Math))
in the 1960s where public elementary schools tried to teach concepts from set
theory and abstract algebra. Basically everyone hated it.

Perhaps there was just a curriculum failure, or perhaps teachers weren't well-
equipped enough to teach the material. But we can't ignore the attempt and
need to come up with an answer for why New Math failed before we can try it
again.

~~~
jeffsco
I was taught the "New Math" as a child and did not hate it. It was wonderful.
When I look at math blogs today, they use notation and terminology I learned
back then. This is a tremendous advantage (or so it seems to me).

~~~
mlvljr
And everyone else just curses when they open a Wikipedia article for smth that
is supposedly (and actually) not that complex, but is explained in those
terms, still :)

~~~
stuxnet79
This is a big problem in my opinion. I read a blog post recently that kind of
discussed it: [http://rajlaboratory.blogspot.ca/2013/12/the-over-
mathificat...](http://rajlaboratory.blogspot.ca/2013/12/the-over-
mathification-of-wikipedia.html)

Wikipedia should be a resource for the average layman, not mathematically
mature individuals who comprise the minority.

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powera
That problem is actually very easy to solve. If you number the cells in
binary, patterns fall out enough that it's easy to convert back and forth from
the original numbering to the final numbering.

If he wants to just work it out by hand, well, maybe he doesn't understand
math as well as he thinks. If you want to use math to "build hammers", it help
to know what a nail is first.

~~~
coldtea
That's not what the article is about.

~~~
powera
What is it about? (other than the statement "there are no rules in math" which
I think is so outrageously wrong I can't even argue against it here)

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vinay_ys
Totally agree with the author. In high-school, I was interested in physics
more than math and whenever I took interest in math it was because it would
help me understand some specific aspect of the physics better. As I got into
engineering, my interest in math again were only in areas where it was
directly useful to me (like signal/image processing, operations research etc.)
As a CS engineer, I've used very little math I was forced to learn by rote to
write exams. Only use that came of it I think is training my brain muscles to
do pattern recognition and fast memory recall.

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stuxnet79
First off cool blog.

But is there a reason why the maintainer of this blog hasn't shared his or her
identity? I am very interested in your background. It looks like some of your
earlier entries were made when you were in high school. In any case I am very
impressed. Sent a few of your articles to my younger siblings to read.

~~~
hardmath123
Thanks! I'm actually still in high school. Shoot me an email or find me on IRC
if you'd like to talk—I'd be happy to say hi.

I'm hesitant to tie my writing to a "real-life" identity because you get a lot
of freedom when you dissociate yourself from what you publish. If I knew my
friends/parents/potential-employers could find my blog, I would be much more
hesitant to publish, which would have been very unhealthy in the long run.

~~~
stuxnet79
Ok, I understand. I have multiple blogs and the ones that are not tied to my
real life identity are a lot more active than the ones that aren't.

But all your posts are brilliant and I personally think you are doing yourself
a disservice not putting your name out there. Like I said, I am very very
impressed with the entries.

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nuxi7
Smokey, this is not math. This is bowling. There are rules.

