Aesthetic quality of mathematics.

Willowz

First of all I thought that this thread belongs to the philosophy section due to it's ambiguous character (a la, beauty, aesthetics, elegance, order).

Is it possible to express yourself through math? Do you know any people who did express themselves through mathematics? Euclid, Euler, Gauss, Plato..?

Or better yet. Can you express your thoughts about mathematics, as an novice, professional, ect.? How does it seem beautiful or elegant to you?

I'm asking this because I don't yet grasp the beauty of mathematics. I mean, it is just too large for my puny mind. I don't really know how you can 'experience' maths. Dumb me.

Thanks for any input.

Math Is Hard

But a bit too far outside the Philosophy guidelines:

http://www.physicsforums.com/showthread.php?t=459350

http://www.physicsforums.com/showthread.php?t=47294

Moved to General Discussion..

Willowz

Those are some pretty strict guidelines.
Doesn't bother me that it was moved but I wonder whats your axiology on 'adequately defined key terms' such as 'aesthetics'? As I'm guessing this is the reason why the thread was moved.

Proton Soup

i've never understood what people mean by beauty in mathematics. does it involve an element of surprise ? or perhaps it is more familiarity?

pergradus

I think often its a combination of surprise and simplicity.

However, a lot of this "beauty" also arises from the notation involved... if you change notation, a simple expression may become complicated.

HeLiXe

Rene Descartes comes to mind. I did my philosophy paper on him. I'm not thoroughly experienced with philosophy so it is possible that I am not considering beauty, aesthetics, elegance, and order with well defined meaning.

Is it possible that you do not see the beauty in math because it makes you feel belittled? I have helped many people with math in my lifetime and I find that math is a rational subject and the way it is perceived or learned can affect ones understanding, some people prefer a logical approach while others are more empirical and need practical examples to understand. When I was in high school I used to cringe when people asked if they will ever have to use this in real life because they saw no purpose in learning it. The professor would usually answer no, and the disinterest would continue. It could be possible that these students needed a more natural approach to mathematics with real life examples--not just the occasional word problem. I think the beauty of mathematics is something highly personal and cannot be taught like music appreciation. What I mean by this is beauty is not defined by itself but by those who perceive it and appreciate it, so when one discovers the beauty in math, it is sort of like an appreciation they generated within themselves, or even an appreciation of the beauty of their own understanding of mathematics.

Willowz

Hex, yes. I feel that math is so abstract that it cannot even be grounded in experience. In a sense it is beyond such feelings of 'beauty' and such.

For example, I don't understand what (some) physicists mean when they say that "it is almost unreasonable that mathematics describes reality so well". I don't even see how math can be grounded down with reality. I mean sure, these equations do predict the behavior of light and such, but that is not what you call mathematics, is it?

Dembadon

To me, the beauty of mathematics lies in its precision and versatility. I can't think of a language that's more precise or versatile.

I love finding clever ways to use mathematics to express myself. Here's an example of what I'm talking about:

Willowz

So dumb! Must be overlooking something here. Like a grave and horrendous mistake not to see the beauty in math. *Argh*

HeLiXe

lololl
I have actually never heard this expression before but I presume they are saying it because math is considered to be almost (if not totally) pure reasoning, so the fact that it describes the empirical so well can seem somewhat paradoxical I guess.

The way I think of it is that math is sort of like how light is...like light can behave like a particle and a wave, math can be both a language used to describe a process and the process can be interpreted as math in action, so the behavior of things can be described with mathematics and can be interpreted as math. I hope that wasn't a bad choice of metaphor!

HeLiXe

I think you're joking around, but I think that not seeing the beauty in something just has to do with your preference and what you choose to appreciate -- nothing dumb about it. When we were learning solids of revolution in Calculus, I could hardly contain myself at times lol. I mean I was literally so excited that I had to stop doing it and walk away. I actually stayed up an entire night doing them and did not even realise where the time had gone

^^I just wish this video showed the solid forming from the shadow of its revolution--that's like how I was doing it in my mind and it was VERY euphoric for me. To someone else this is just some simple garbage and I am a total weirdo! or MAJOR nerd lol

Willowz

Better joke about it than go crazy over it. :p
Nice video. Hope to see what you were all exited about soon. :)

HeLiXe

Proton Soup

actually, i did think of something today that maybe is beauty in math. once upon a time, i did a fair bit of computer simulations that crunched lots of numbers. beauty there was any mathematical simplification that could take hours off of processing time. double kudos if the answer was more accurate.

there are also some classes of functions with magical properties that make life easier. for engineers, the obvious ones are fourier transforms and the voodoo they do with frequency and time. gaussians are also another versatile tool.