Most interesting/beautiful math

For the discussion of math. Duh.

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iknoritesrsly
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Most interesting/beautiful math

Postby iknoritesrsly » Fri Jun 29, 2007 9:25 pm UTC

Hi all,

Let me preface this post briefly. I am not a math person. see? I told you I would keep it brief. :D

That said, my question for you is simple. What math do you find most interesting / most beautiful. I've decided to teach myself some math for fun and I'm interested in your opinions. (Or, more accurately, I will have one of my math genius friends tutor me).

discuss!
Last edited by iknoritesrsly on Fri Jun 29, 2007 9:41 pm UTC, edited 1 time in total.

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Postby iammercy » Fri Jun 29, 2007 9:29 pm UTC

Number Theory and or Combinatorics.

Although Discrete Dynamical Systems are pretty.. :P

Mercy

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3.14159265...
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Postby 3.14159265... » Fri Jun 29, 2007 10:19 pm UTC

What kind of math does your "genius" friend know? (What level)

What level of math have you studied upto now?

Number theory as a whole is super awsome, but many fields are also super connected.

Don't expect to learn "math" on a white board in a day though.
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iknoritesrsly
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Postby iknoritesrsly » Fri Jun 29, 2007 10:50 pm UTC

i really haven't the faintest clue. he was doing graduate level mathematics as a sophmore is just about all that i know, and for my purposes, his knowledge if almost limitless.

this isn't to say that he'll be the first to find a unified theory, just that in comparison to me, he's pretty sharp. ;)

as for me, i've had highschool math. (up through a little bit of calculus). i also do not expect to learn anything in its entirety very quickly, as it's merely something i'm doing when i'm tired of writing philosophy essays. :D but since i'm only doing it for fun, i would rather study something interesting than something ugly and boring.

i don't mind hard, but i do mind boring.

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Postby Robin S » Fri Jun 29, 2007 10:56 pm UTC

Just thought I'd point out: unified theories are physics, not maths. Maths doesn't have theories. It has theorems, but they're different.

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Postby aguacate » Fri Jun 29, 2007 11:00 pm UTC

Robin S wrote:Maths doesn't have theories. It has theorems, but they're different.


Conjectures?
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iknoritesrsly
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Postby iknoritesrsly » Fri Jun 29, 2007 11:02 pm UTC

Robin S wrote:Just thought I'd point out: unified theories are physics, not maths. Maths doesn't have theories. It has theorems, but they're different.


you sir, have just blown my mind. :roll:

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Alpha Omicron
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Postby Alpha Omicron » Sat Jun 30, 2007 2:16 am UTC

Euler's Identity. 'Nuff said.
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Postby crazyjimbo » Sat Jun 30, 2007 2:27 am UTC

Alpha Omicron wrote:Euler's Identity. 'Nuff said.


So cliched! :)

The most interesting/beautiful things I find are when you're busy doing some maths in <some area>, and you realise it's exactly the same as something in <some other area>, just in a different form. It blows my mind.

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Postby Token » Sat Jun 30, 2007 2:41 am UTC

Yeah, there's plenty of awesome stuff in maths. For example, the fact that the least positive root of sin(x) is equal to the ratio of the circumference of a circle to its diameter.

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Postby chrispy1 » Sat Jun 30, 2007 3:14 am UTC

Token wrote:Yeah, there's plenty of awesome stuff in maths. For example, the fact that the least positive root of sin(x) is equal to the ratio of the circumference of a circle to its diameter.


Scratches head. Scratches armpit. Thinks Token is a hell of a lot smarter than me. Continues with reply to a topic I'm not sure I'm qualifed. And yes, I just spelt qualified wrong. Oh dear.

I've always loved the "math of nature", a large part of which is contained in Phi (terminology off. Please refer to previous statement). If you are interested, I highly recommend The Golden Ratio by Mario Livio - I grinned like a fool through most of this book, because it all made sense.

I've also started reading up on Fractals and particularly the Mandelbrot Set (check out the article on fractals on Wikipedia, it's what got me started - I put a new image of the Mandelbrot up as my wallpaper every Monday...)

Good luck and post back what you decide on!!
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Postby Blatm » Sat Jun 30, 2007 5:05 am UTC

chrispy1 wrote:
Token wrote:Yeah, there's plenty of awesome stuff in maths. For example, the fact that the least positive root of sin(x) is equal to the ratio of the circumference of a circle to its diameter.


Scratches head. Scratches armpit. Thinks Token is a hell of a lot smarter than me. Continues with reply to a topic I'm not sure I'm qualifed. And yes, I just spelt qualified wrong. Oh dear


He said "sin(pi) = 0"

I can't give a valid opinion to the topic at hand, as I'm still trapped in highschool.

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Postby EradicateIV » Sat Jun 30, 2007 5:11 am UTC

Start with logic, if you can understand the essence of logic, then you can understand proofs a lot better.
Keep in mind a statement can either be true XOR false (not both).
So if you want to prove something, either get the statement to show true from which you started or, like a lot of clever proofs, assume it's false (negate it) and see if you can get a contradiction (two truth values colliding with each other, something being true and false).

Proofs are beautiful for one reason, TRUTH.
We assume simple things then build an entire world out of them.
1010011010

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Postby arbivark » Sat Jun 30, 2007 5:35 am UTC

Agree that symbolic logic might be a good project.
Powerful, elegant, easy to learn as a hobby.
Probably good online tutorials.

Next idea: game theory.

The most interesting/beautiful things I find are when you're busy doing some maths in <some area>, and you realise it's exactly the same as something in <some other area>, just in a different form. It blows my mind.

Agree. I found it mindblowing to realize that ecology and market economics are talking about the same thing, using different jargon. Later i learned that there was a historical basis for this; Darwin based his work on Adam Smith.
GEB
< yup
Last edited by arbivark on Sat Jun 30, 2007 11:50 pm UTC, edited 2 times in total.

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Postby zenten » Sat Jun 30, 2007 7:07 am UTC

My favourite is all the N dimensional linear algebra stuff. It just gets to me on a primal level.

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Postby dp » Sat Jun 30, 2007 7:41 am UTC

zenten wrote:My favourite is all the N dimensional linear algebra stuff. It just gets to me on a primal level.

Word. Now just let N -> infinity.

Fuck this discrete shit - life is a continuum.

Oh, and do some probablility. People who say it's boring don't know what they're talking about.

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Postby zenten » Sat Jun 30, 2007 7:59 am UTC

My problem with probability was that the professors couldn't get their terms straight. They would write out functions like variables, and not define what's what. But that's more a problem with how it is presented than the field itself.

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Postby dp » Sat Jun 30, 2007 8:25 am UTC

zenten wrote:My problem with probability was that the professors couldn't get their terms straight. They would write out functions like variables, and not define what's what. But that's more a problem with how it is presented than the field itself.


Spoiler alert: It turns out that they're the same thing.

Edit: in the same way that summation and integration are the same and, more abstractly, n+1 dimensional vectos are the same as n dimsensional polynomials

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Postby Zohar » Sat Jun 30, 2007 12:48 pm UTC

A wonderful subject to start with, and a pretty easy one, is discreet mathematics. It's very helpful for later subjects and it has some very beautiful things (try to read up on "Hilbert's Hotel" if it interests you).
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Postby dp » Sat Jun 30, 2007 2:00 pm UTC

Zohar wrote:A wonderful subject to start with, and a pretty easy one, is discreet mathematics. It's very helpful for later subjects and it has some very beautiful things (try to read up on "Hilbert's Hotel" if it interests you).

This is probably the one are of maths that I've never been interested in. As for beautiful areas, I'm a big fan of Gaussian Processes.

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Postby LE4dGOLEM » Sat Jun 30, 2007 2:47 pm UTC

I like factorials...
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Postby ptveite » Sat Jun 30, 2007 3:22 pm UTC

My favorite field of math that I've studied is set theory, it ranges from easy to get ahold of to mind-bogglingly counter-intuitive, which is fun!

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Postby HenryS » Sat Jun 30, 2007 6:19 pm UTC

Read Gödel, Escher, Bach.

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Postby adlaiff6 » Sun Jul 01, 2007 12:41 am UTC

dp wrote:Fuck this discrete shit - life is a continuum.

rly

I think the universe is mostly discrete.

To original poster: You may want to reserve some of your enthusiasm until you really start doing it. Definitely start with logic, because you'll need to understand how proofs work, but even so, if you say you're "not a math person," that probably means that some of the beauty of math has already passed by you, and you thought it was boring or useless. I know math is awesome, and I think it's great that you want to try to learn more, but be aware that some people just don't enjoy it as much as others.

Personally, I think some things in linear algebra and number theory are absolutely brilliant, so I would steer you in that direction.
3.14159265... wrote:What about quantization? we DO live in a integer world?

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Postby sillybear25 » Sun Jul 01, 2007 2:01 am UTC

fractals can be pretty. http://en.wikipedia.org/wiki/Fractal
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Postby shill » Sun Jul 01, 2007 2:09 am UTC

HenryS wrote:Read Gödel, Escher, Bach.

Gödel?

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Postby dp » Sun Jul 01, 2007 2:58 am UTC

adlaiff6 wrote:[rly

I think the universe is mostly discrete.


:shock:

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Postby Blatm » Sun Jul 01, 2007 3:43 am UTC

I agree, GEB is awesome.

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Postby Alpha Omicron » Sun Jul 01, 2007 4:46 am UTC

HenryS wrote:Read Gödel, Escher, Bach.


FAIL.
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Postby HenryS » Sun Jul 01, 2007 5:53 am UTC

Yeah, dunno where that came from...

book is by Douglas Hofstadter, and alternates between wonderful dialogs (often between Achilles and the Tortoise) and the actual chapters, the content of which is reflected in the dialog before. It's really well done.

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Postby iknoritesrsly » Sun Jul 01, 2007 3:36 pm UTC

EradicateIV wrote:Start with logic, if you can understand the essence of logic, then you can understand proofs a lot better.


i'm taking upper level symbolic logic next spring, so that one's out *for fun* unfortunately. :)

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Postby iknoritesrsly » Sun Jul 01, 2007 3:40 pm UTC

adlaiff6 wrote:To original poster: You may want to reserve some of your enthusiasm until you really start doing it. Definitely start with logic, because you'll need to understand how proofs work, but even so, if you say you're "not a math person," that probably means that some of the beauty of math has already passed by you, and you thought it was boring or useless. I know math is awesome, and I think it's great that you want to try to learn more, but be aware that some people just don't enjoy it as much as others.


well, I've already endeavored to learn a bit of math on my own, and I've found it quite enjoyable. :) I enjoy math if it is presented well. id est, I have never enjoyed learning math in a classroom, but I love talking about it and learning it in a more one on one, or independent environment.

Personally, I think some things in linear algebra and number theory are absolutely brilliant, so I would steer you in that direction.


thanks.

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Postby devdavad » Mon Jul 02, 2007 3:09 am UTC

Definitely number theory. Above that, Mental math. It's used everyday

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Postby Dobblesworth » Mon Jul 02, 2007 5:24 pm UTC

Polar co-ordinates I like personally.

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Postby Alpha Omicron » Mon Jul 02, 2007 5:27 pm UTC

devdavad wrote:Definitely number theory. Above that, Mental math. It's used everyday


To the inroductions thread with you. OR PERISH!
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Postby techfish » Mon Jul 02, 2007 5:34 pm UTC

Complex tetration anybody?

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Postby MFHodge » Mon Jul 02, 2007 6:15 pm UTC

I find the natural occurances of Golden Ratios amazing. We spent a whole math class measure each other looking for Golden Ratios. Pretty mind-blowing.
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Postby Blatm » Mon Jul 02, 2007 7:37 pm UTC

I can't stand that golden ratio stuff. It's been so over hyped through certain books that people think it's an incredible coincidence and the proof of God's existence and whatnot when it makes perfect sense for it to show up often. And sometimes people will come up with new places to find it, as if it weren't common enough. A good example of this is total hight/top of head to belly button = phi. It gives me ~1.65, and on a friend of mine it gives ~1.72. People have an overactive imagination.

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Postby Token » Mon Jul 02, 2007 7:51 pm UTC

VTHodge wrote:I find the natural occurances of Golden Ratios amazing. We spent a whole math class measure each other looking for Golden Ratios. Pretty mind-blowing.

What a waste of a good maths lesson. You could have been doing interesting things instead.

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Postby roundedge » Mon Jul 02, 2007 8:47 pm UTC

I really enjoyed linear algebra, it makes you think about the world differently, in terms of transformations. I always find myself thinking about puzzles and games in terms of linear transformations, and inverse transformations.


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