Most interesting/beautiful math

For the discussion of math. Duh.

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Ended
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Postby Ended » Mon Jul 02, 2007 10:25 pm UTC

Contrary to what I had expected, I've found analysis (real and complex) to be very beautiful. Also, in applied maths, fluid mechanics is nice. I find it amazing that something as ostensibly complicated as fluid flow can be modelled with just a few equations. (Also, fluid mech gets cool applications and good pictures.)
Generally I try to make myself do things I instinctively avoid, in case they are awesome.
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iknoritesrsly
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Postby iknoritesrsly » Tue Jul 03, 2007 3:18 am UTC

Neat video. :D

And thanks for the suggestions so far guys, keep 'em coming! :)

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Marbas
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Postby Marbas » Tue Jul 03, 2007 7:10 am UTC

Point-Set and Algebraic Topology are both really nifty! There are lots of different types! I have only worked with point-set and algebraic though.
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Mittins
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Postby Mittins » Wed Jul 04, 2007 3:16 pm UTC

I'd have to say that of all the maths I've studied, I ENJOYED number theory the most. I admire it for its logic and elegance. That being said, I'm not sure if it's beautiful.

I guess Linear Algebra is quite beautiful since it seems to be able to model cool things very simply. Matrices look neat on paper, too.

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FiddleMath
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Postby FiddleMath » Thu Jul 05, 2007 12:18 am UTC

Goedel, Escher, Bach has only been mentioned about ten times in this thread. It should be in every post. Seriously; it's that good.

My favorites, really, are combinatorics and graph theory, and then number theory. But then again, I find discrete math far more intuitive than continuous math. It's really a matter of personal preference; I've known people who have exactly the opposite taste in mathematics, and were probably quite a lot better at it than I.

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Postby Endomorphic » Thu Jul 05, 2007 12:35 am UTC

I'd recommend John Conway as an accessable start to entertaining maths.

http://www.msri.org/communications/book ... conway.pdf

Unlike a lot of math problems, the above *really is* easy to state, and difficult to analyse. It's also the only maths paper I've read containing the line:
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Postby Buttons » Thu Jul 05, 2007 1:12 am UTC

John Conway wrote:Theorem 3.1. The Devil can catch a Fool.
The best theorems are the ones that could go in fortune cookies. Like, maybe,
Brian Beavers wrote:Theorem 3.5. All caterpillars are graceful.

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Postby rmb » Sat Jul 14, 2007 6:59 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.

Uh, that's only because we work in radians, instead of degrees or grads.

Personally, I love number theory, algebra, algebraic number theory, algebraic geometry, and topology (topology is far behind the others). Can't stand analysis.

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Postby Briareos » Sat Jul 14, 2007 10:19 am UTC

Topology! Absolutely -- I mean, it's my research interest, and you get to draw fun things.

I've done point-set, algebraic, and some differentiable manifolds. Manifolds was actually really fun, but I would definitely go with algebraic topology. If you already have some algebra, that is. But that's where the fun stuff is.

Like homology! (When I was introduced to homology I started calculating homology groups in my other classes just for the hell of it.)
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Why learn math?

Postby supemoy » Sun Jul 15, 2007 8:39 pm UTC

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Last edited by supemoy on Sat May 12, 2018 12:48 pm UTC, edited 1 time in total.
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TRM
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Postby TRM » Sun Jul 15, 2007 9:05 pm UTC

Although I'm not an advanced mathematician, I look at university textbooks in my free time.

I can honestly say that applications of vector calculus are definitely one of the most fascinating parts of mathematics I have seen yet. I just finished reading basic vectors , but vector calculus was just so interesting.

Just out of curiosity, for any graduate students who have done vector calculus and applications in university, how difficult is it compared to other applied mathematics?
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Postby japanese_jew » Mon Jul 16, 2007 3:35 am UTC

There was one proof for the pythagorean theorem that I thought was really pretty. Don't actually remember it though, which is a real pity. Graph theory is pretty interesting too, although I don't actually know anything about it beyond what I've read in Nexus and the book about Erdos.

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Postby bonder » Mon Jul 16, 2007 7:17 am 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.


Every hear of Galois Theory? Set Theory? Graph Theory? Number Theory?

Anywho, my favourite kinds of math are number theory and combinatorics (more specifically graph theory). Combinatorics is nice because it is accessible even if you haven't had a whole lot of advanced math, so is elementary number theory.

Close runners up would have to be abstract algebra and complex analysis. Complex analysis is one of the most beautiful branches of math that I've studied so far. When I first saw how you can evaluate a definite integral (over the real line) by extending the function to the complex plane and then evaluating a contour integral (in the complex plane) and then extracting the solution to the original integral, it blew my mind. And abstract algebra is great because you get to see what goes on behind the scenes, so to speak, but looking at the rules that govern sets that behave like numbers. These two are a little less accessible if you haven't had some advanced math, but still worth looking into.

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Postby MathBOB » Mon Jul 16, 2007 5:54 pm UTC

While I've found analysis to be overall very pretty, I have to admit I've never been very good at it. I understand it intuitively, but just get caught on proofs. Grr.

The most abstract type of math that I've run into - and therefore, in some wierd part of my head, the most beautiful - is noncommutative algebra. Starting with Category theory, work your way into groups, rings, and fields, and then construct modules and algebras out of those. It's just so awesome how quickly things compound upon each other. The course I took focused on Central Division algebras and worked its way into the definition of the Brauer group. I was also amazed at how often you could make statements of the form:
"If object of type A has property B then all maps of type C have property D"
without ever stating whether or not an object of type A can even *have* property B, or giving a concrete example of such an object with such a map.

Most recently, I've been delving into differential geometry, trying to understand higher-level mathematical physics, and I have to say that it's the most beautiful type of math I've seen so far. Chart-independent formulations are among the most elegant formulae I've ever seen.

jtin
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Postby jtin » Fri Jul 20, 2007 9:08 pm UTC

Perhaps you could have a look ata few "elegant" textbooks and see which kind of math you like?

Calculus by Michael Spivak
Topics in Algebra by I. N. Herstein
Mathematics Applied to Deterministic Problems in the Natural Sciences by Lin and Segel

I'd be interested in other people's suggestions.

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Re: Most interesting/beautiful math

Postby Monox D. I-Fly » Sat Jun 11, 2016 4:45 am UTC

The most interesting/beautiful math for me is that pi and phi, two irrational numbers which people in my country keep mistaking with one another, are related. Namely, cos(pi/5) = phi/2.
Finally found one comic mentioning a Trading Card Game:
https://xkcd.com/696/

PsiCubed
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Re: Most interesting/beautiful math

Postby PsiCubed » Sun Jun 12, 2016 10:38 pm UTC

Monox D. I-Fly wrote:The most interesting/beautiful math for me is that pi and phi, two irrational numbers which people in my country keep mistaking with one another, are related. Namely, cos(pi/5) = phi/2.


Ah, the close relationship between Pi, phi, 2 and 5.

Also note that:

(1) phi = [sqrt(5)+1]/2
(2) cos(2*pi/5) = cos(pi/5)+1/2

Once again, 2 and 5. Beautiful indeed. :)
Image

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Re: Most interesting/beautiful math

Postby Monox D. I-Fly » Mon Jun 13, 2016 3:56 am UTC

PsiCubed wrote:Once again, 2 and 5. Beautiful indeed. :)


Make a peace symbol using your index and middle fingers. It can be interpreted as either 2 (because there are two fingers) or 5 (Roman numeral). It can also be interpreted as 7, though (Arabic symbol), which is the result of 2 + 5.
Finally found one comic mentioning a Trading Card Game:
https://xkcd.com/696/


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