My idea on why math is hard...

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Slonimsky
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My idea on why math is hard...

Postby Slonimsky » Sun Oct 31, 2010 5:52 pm UTC

For every mathematical definition/idea/proof/theorem I have to study, there had to be this really, really, REALLY smart guy, and he struggled for hours/days/months/years on formalizing this idea he had.

He worked so long and so hard, and then finally he came to this almost ridiculously short proof for his obvious theory.

And now, I have to study the result of all these decades of hard work (if you'd combine the hours of work of Leibniz, Euler, Newton, Bolzano, Weierstrass, ...) in one semester.


:shock:

This idea keeps me from killing myself every evening. I just think:" Years ago, some guy suffered a lot more on it and he was a lot smarter than me. So hey, I'm not doing that bad at all..."

Struggling with the epsilon delta-proofs... It's seeping in a little, but slowly...

I looked for some threads where this could fit but I didn't really find one, and I think the random thread would just absorb my post like a*0=0 ∀ a ∈ R

(Last thing is also an indication that I'm slowly going crazy because of math. I once was in a night club and I thought about dancing with this girl and said to myself "It's not that hard, you just have to separate the x's", and I thought about integrals when preparing my cheese sandwiches because I kept using smaller and smaller bars of cheese to approach the curve of the bread, oh and I use set theory to illustrate who can go to which party if you take certain combinations (like the XKCD comic) what's happening with me you guys? )

Some of you might remember (probably not, meh) my thread about me doubting about doing physics because I didn't have that much math on high school and I considered myself a little dumb with math, well, 1 month passed and: it's difficult each day, but now when I pick up a book that I didn't understand a month ago, it looks very easy. So I'm improving a lot, but the difficulty level of the courses is always a little higher than my level of understanding. I can follow 50% of the time, and I consider that quite much if you know that I sit with other people who had thousands of hours of extra math in their high school carreer. As stated above I sometimes incorporate certain mathematical concepts in every day life, so it's not that that things that I learn don't 'settle' in my brain.

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Re: My idea on why math is hard...

Postby mister k » Sun Oct 31, 2010 6:30 pm UTC

I shouldn't worry too much. 50% sounds pretty good to me. Degree levels maths IS hard, and is taught by people who don't necessarily remember that it is hard. I am currently studying a phd, but found, and still find certain concepts incredibly difficult. Education at a higher level is about understanding your ignorance,while slowly absorbing basic concepts. Epsilon-delta stuff will look pretty easy to you given another two years, but of course there'll be other challenges to hurdle. Basically: its never going to be easy, but you are never alone in finding that to be the case.
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Re: My idea on why math is hard...

Postby Syrin » Sun Oct 31, 2010 7:10 pm UTC

The best case scenario isn't when you're good at thinking math when you're doing math problems for school or when you're learning at school - it's when you're thinking math always. Looks like you are, so it would seem that you're doing fine.

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Re: My idea on why math is hard...

Postby Qaanol » Sun Oct 31, 2010 7:12 pm UTC

I do remember your previous thread, and it sounds like you’re doing quite well. If you’re looking for advice to make things easier, I’d say find a group of classmates who you can study with.
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Re: My idea on why math is hard...

Postby Yesila » Mon Nov 01, 2010 4:19 am UTC

There's a nice quote (which I'll misquote here and not attribute since I can't remember his name) by a Mathematician that talked about Math being impossibly hard while you try to learn it, and then after you 'see the light' and figure out that problem/idea/proof it becomes so trivially easy that you can't possibly fathom what was so hard about it before.

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Slonimsky
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Re: My idea on why math is hard...

Postby Slonimsky » Mon Nov 01, 2010 10:08 am UTC

Quote in my math course:

"A mathematician is a device for turning coffee into theorems."

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Re: My idea on why math is hard...

Postby philoctetes » Mon Nov 01, 2010 10:22 am UTC

There's the famous von Neumann quote (I really love it):

"Young man, in mathematics you don't understand things, you just get used to them."

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Re: My idea on why math is hard...

Postby EstLladon » Mon Nov 01, 2010 10:59 am UTC

I think it is not math that is hard. Math, after all by definition is the simplest thing there is - we take most basic things and make them interact in the most basic ways. The hard part is to properly describe it with words. You see, words are good for what they were made for - i.e. communication between people. They are not really good for describing stuff as it is. Even the simplest stuff. Some times especially the simplest stuff.

Math is easy. Words are hard.
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Re: My idea on why math is hard...

Postby agelessdrifter » Mon Nov 01, 2010 12:45 pm UTC

Since around Calc II (I'm in Diff Eq now) I fairly frequently have dreams involving math ridiculous situations requiring me to work out some complicated integral. The other morning I laid half-awake in bed for several hours absolutely convinced that once I got up I was going to need to help my dog work out an arc-length parameter. Turns out she actually needed to pee =/

I take it as a good sign, though.

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Re: My idea on why math is hard...

Postby SlyReaper » Mon Nov 01, 2010 12:54 pm UTC

Slonimsky wrote:Quote in my math course:

"A mathematician is a device for turning coffee into theorems."


Maybe that's why I only got a desmond in my maths degree. I don't drink coffee.
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Re: My idea on why math is hard...

Postby Cleverbeans » Mon Nov 01, 2010 1:51 pm UTC

"Thinking is the hardest work there is, which is probably the reason why so few engage in it." - Henry Ford
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Re: My idea on why math is hard...

Postby Yakk » Mon Nov 01, 2010 3:10 pm UTC

Learning math is easier than doing it, because we have spent centuries figuring out how to write down mathematical conclusions in ways that are easier to "follow" and "agree" with than they where to think up. We call these things "proofs".

But because of this, what we get is a huge pile of knowledge that has been repeatedly distilled and polished and checked and verified. There are centuries of human lifetime distilled into gems of symbols and thought.

And you get to stuff them into your head in a single semester.

It isn't that this stuff is inherently hard -- it is just that it will be made as hard as the students can typically take it. If it was easy, they'd just turn up the flow until it was hard again.

If you want to see what I mean by "turn up the flow", see if you can get your hands on "introductory" textbooks for graduate students. You can teach an entire 4 month undergrad class out of the preface chapter, and maybe the first few pages of the first chapter. A dozen pages that you can spend 50 class-hours and 100+ hours of homework teaching. A quantity of text that it would take you minutes to read if it was in English. The density of mathematics can be turned up as high as you like thanks to the compression ability of modern mathematical symbols.

Once you are familiar with the use of the symbols and many of the things going on, you can get through the material much faster. But that is just the hose being turned up...
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Slonimsky
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Re: My idea on why math is hard...

Postby Slonimsky » Mon Nov 01, 2010 5:27 pm UTC

Yakk wrote:
If you want to see what I mean by "turn up the flow", see if you can get your hands on "introductory" textbooks for graduate students. You can teach an entire 4 month undergrad class out of the preface chapter, and maybe the first few pages of the first chapter. A dozen pages that you can spend 50 class-hours and 100+ hours of homework teaching. A quantity of text that it would take you minutes to read if it was in English. The density of mathematics can be turned up as high as you like thanks to the compression ability of modern mathematical symbols.

Once you are familiar with the use of the symbols and many of the things going on, you can get through the material much faster. But that is just the hose being turned up...



Epsilon-Delta proofs take about 0,0004% of the total page surface of my Calc Course (that's 40 cm² out of a total 82 000 cm²).

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Re: My idea on why math is hard...

Postby SlyReaper » Mon Nov 01, 2010 5:48 pm UTC

That would be because epsilon-delta proofs tend to be more a staple of analysis courses rather than calculus.
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Re: My idea on why math is hard...

Postby voidPtr » Mon Nov 01, 2010 8:55 pm UTC

I have my own theories on this.

- Math is extremely information intensive. A lot of information is condensed in very little space. Is there a more information intensive pursuit? Imagine if we wrote math papers like we wrote novels, there wouldn't be any trees left.

- Without ever having taken a philosophy course in your life you can sit in an upper year philosophy course and get something out of it just by attending that one class, you may even be able to participate. However in math, you can't dabble. It's all the way or nothing. If you are shaky in one area, you're more likely than not going to be shaky in any areas that depended on that.

- Math at least seems to have more disagreeable professors than other subjects. There's nothing more frustrating than not understanding a professors notation, and trying to get help but finding out nobody else understands it either.

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Re: My idea on why math is hard...

Postby agelessdrifter » Tue Nov 02, 2010 12:35 am UTC

voidPtr wrote:- Math at least seems to have more disagreeable professors than other subjects. There's nothing more frustrating than not understanding a professors notation, and trying to get help but finding out nobody else understands it either.


I suppose I've been lucky, or it might be because I'm still at a fairly low level of math, but notation in math has been pretty consistent and understandable for me thus-far (and I have certainly been lucky in having more-than-agreeable professors thus-far). I'm just taking my first college-level physics course, though, and *that* notation is thoroughly aggravating. It is not yet difficult to follow, but I can easily imagine it becoming so in the future. Whose idea was it to make two so-nearly related concepts as pressure and density be signified by P and rho respectively? It's all well-and-good in a text book, but on a blackboard? And when I see [imath]F_x[/imath] I'm thinking [imath]\partial F/\partial x[/imath], not "the component of Force in the x-direction. :?

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Re: My idea on why math is hard...

Postby MostlyHarmless » Tue Nov 02, 2010 4:09 am UTC

voidPtr wrote:- Math at least seems to have more disagreeable professors than other subjects. There's nothing more frustrating than not understanding a professors notation, and trying to get help but finding out nobody else understands it either.


I actually disagree with this point. Math professors have spent most of their lives trying to figure out unfamiliar notation or concepts. I have never explained what I thought to a math professor and had them not be able to figure out what I'm saying. This makes it really easy to find out why I didn't understand a concept. On the other hand, I've had several English/Literature professors who could not comprehend the logic behind my point. Whether that's because of a flaw in my logic or theirs, there was still a breakdown in communication that I haven't experienced in math classes.

In case you feel like taking some unsolicited advice: if you don't understand a professor's notation, make up your own and explain it to them. They'll either show you where it's incorrect or show you how it matches their own. If you don't understand a concept, try to explain it to them. They'll tell you when you get to a problem.

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Re: My idea on why math is hard...

Postby Sagekilla » Wed Nov 03, 2010 3:32 am UTC

MostlyHarmless wrote:In case you feel like taking some unsolicited advice: if you don't understand a professor's notation, make up your own and explain it to them. They'll either show you where it's incorrect or show you how it matches their own. If you don't understand a concept, try to explain it to them. They'll tell you when you get to a problem.


To reiterate this point, I personally try to remember the all the various notations my professors use for a particular concept.
I usually just mentally pick the one I like or that seems to be the most common. Then I just mentally translate between the set
of different notations used for a particular concept and the notation I use.

For the same reasons explained above, it helps me too when I try to figure out what someone else is doing through different notation.
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Re: My idea on why math is hard...

Postby praybz » Wed Nov 03, 2010 10:06 pm UTC

Slonimsky wrote:Quote in my math course:

"A mathematician is a device for turning coffee into theorems."


Your quote is from Paul Erdos, and actually "coffee" in that case was a euphemism for amphetamines, to which he was addicted.

Not as cute now, I imagine.

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Re: My idea on why math is hard...

Postby agelessdrifter » Thu Nov 04, 2010 2:47 am UTC

praybz wrote:
Slonimsky wrote:Quote in my math course:

"A mathematician is a device for turning coffee into theorems."


Your quote is from Paul Erdos, and actually "coffee" in that case was a euphemism for amphetamines, to which he was addicted.

Not as cute now, I imagine.


No wonder he was so prolific.

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Re: My idea on why math is hard...

Postby DavCrav » Thu Nov 04, 2010 10:51 am UTC

praybz wrote:
Slonimsky wrote:Quote in my math course:

"A mathematician is a device for turning coffee into theorems."


Your quote is from Paul Erdos, and actually "coffee" in that case was a euphemism for amphetamines, to which he was addicted.

Not as cute now, I imagine.


Erm, citation needed. I thought it was Alfréd Rényi who said that, and Erdos, although taking amphetamines, also had a coffee addiction.

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Re: My idea on why math is hard...

Postby mdyrud » Thu Nov 04, 2010 4:22 pm UTC

In addition, Erdos wasn't really addicted to amphetamines. A friend bet him that he couldn't quit for a month, and he did, no problem. As soon as the month was done, he started right back up again. So not really an addiction, just something he really enjoyed.

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Re: My idea on why math is hard...

Postby Yakk » Thu Nov 04, 2010 4:33 pm UTC

mdyrud wrote:In addition, Erdos wasn't really addicted to amphetamines. A friend bet him that he couldn't quit for a month, and he did, no problem. As soon as the month was done, he started right back up again. So not really an addiction, just something he really enjoyed.

I doubt they watched him closely enough to verify this. If he was addicted, there is a high chance he'd lie about it... so the test is less than reliable.
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Re: My idea on why math is hard...

Postby MHD » Thu Nov 04, 2010 9:23 pm UTC

Well, don't worry about that weird brain behaviour. Back when I was really into hobby programming CS, I had dreams about monads.
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Re: My idea on why math is hard...

Postby letterX » Thu Nov 04, 2010 10:23 pm UTC

MHD wrote:Well, don't worry about that weird brain behaviour. Back when I was really into hobby programming CS, I had dreams about monads.


Oh, don't worry. Everyone has that dream.

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Re: My idea on why math is hard...

Postby Zamfir » Fri Nov 05, 2010 10:18 am UTC

mdyrud wrote:In addition, Erdos wasn't really addicted to amphetamines. A friend bet him that he couldn't quit for a month, and he did, no problem. As soon as the month was done, he started right back up again. So not really an addiction, just something he really enjoyed.


Not sure this really proves a lot. It's much easier to change some habit for a short period of time, with a clear reward, and with people looking over your shoulder to check. Think how many people quit smoking, or start exercising, or whatever at the start of the year. The hard part is getting to the point where you are not fighting the old habit, but have genuinely lost it.

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Re: My idea on why math is hard...

Postby agelessdrifter » Fri Nov 05, 2010 8:10 pm UTC

Then how does one who engages in habitual behavior prove that they don't have an addiction, short of permanently ceasing to engage in that behavior?

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Re: My idea on why math is hard...

Postby SlyReaper » Fri Nov 05, 2010 8:14 pm UTC

They don't. In fact, usually the desire to prove the absence of an addiction is usually taken as evidence of the addiction. The only way to win is to stop giving a shit about what other people think and live your life how you want to live it.
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Re: My idea on why math is hard...

Postby agelessdrifter » Sat Nov 06, 2010 5:04 pm UTC

Well, isn't the whole question of addiction really a question of whether or not one is actually living how they want to live (as opposed to being ruled by dependency) to begin with?


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