/sci/ - Science & Math

the ability to explain why things happen

In the relationships (yes, this is pretty vague).

Yes, it can compare to art. It's pretty beautiful, you just don't know how to read it.

Well give some instances of beautiful math

and maybe even ugly math...? What's the difference

If you keep trying to explain beauty, you might lose sight of it.

I find geometry proofs to be beautiful.

>>2739324
> Can it compare to music, literature and art???
Simply put: no

Mathematics is a tool that allows abstract understanding of the rules that underly reality

It's science, biatch

The beauty of math is within it's irrefuteable truth.

If we ever make contact with an alien species, math will be the first language that we communicate with.

>>2739350

Why are tautologies beautiful? They just seem redundant.

truth is maladaptive in modern society, so it is understandable that mathematical beauty is seldom appreciated

>>2739353
>abstract understanding of the rules that underly reality

lol. most math is just math for math's sake. it makes it no less beautiful.

IMO, the applications of math are beautiful (understanding the universe), but otherwise the proofs and theorems are extremely fucking ugly and boring.

>>2739360

it has to be more than truth, you have to have a sensitivity towards it....

a dog has 4 legs, thats true...but it isn't a beautiful truth
2+2 = 4, but so what

tautologies are boring
where's the beauty in math? show me

this

'The art of using what is known to resolve the unknown'

Mathematics can be elegant. A good idea can give you a simple understanding of a vast and complicated set of seemingly unrelated questions.

An example of ugly maths is having a computer brute force all possible options to get an answer by elimination.

Math
>Objective
Music, Literature, Art
>Subjective

>>2739395
>He doesn't know that math is the most subjective subject in existence since inevitable it boils down to rearrangement and manipulation of axioms which are just magically defined to be true.

>>2739406
> nope.jpg

>axioms
>objective

nope

>>2739406

>trollface.jpg

>>2739358
You don't understand because you can't appreciate truth.

Maybe you will one day though, maybe just before you die, when you realise just how certain death is.

>>2739439
>subjective post is subjective

>>2739439
What is 'truth?' Is the red pill any more real than the blue?

>>2739353

actually no. music is math.

>>2739370
Correct. All the pure math in the world is strictly masturbatory without applied sciences/engineering.

If a particular avenue of math cannot be used to solve a real, physical problem in the world, what is the use?

>>2739330

it doesn't explain how things happen. its just a good model to describe HOW things happen

>>2739465

>it doesn't explain why things happen

whoops, fixd

>>2739375

beauty is subjective. like taste in music.

>>2739350

How?

>>2739458
This is well known fact by all musicians. Obviously no one else here on /sci/ is a musician other than I and I guess you.

>>2739457
This is about beauty, not usefulness. Vanity and beauty go along for a reason.

>>2739452
Truth is that which is definate.

<div class="math">f(z_0)=\frac{1}{2\pi i}\int_{\partial \Omega}\frac{f(z)}{z-z_0}dz</div>
where <span class="math">z_0 \in \omega \subset C[/spoiler], and f is any analytic function. That is some beautiful math right there, people.

>>2739484
I study math, and I've played violin for 17 years. I can tell you that any musician who thinks that his music is comparable to any except the most RUDIMENTARY math (hurr, I'm playing in 3/4 time!) just wants his chosen hobby to sound more technical than it is. It's not the same, and if it was music theorists would be able to make more money than they do, and would be required to take upper division math courses. They are not.

inb4 Josef posts Stokes' for the over 9000th time

>>2739486
Then yes, I do find some mathematics to be "beautiful." But I think it's no better than art if it cannot be used outside of mathematics itself. Much worse than art, really, as it has no real cultural significance outside of the niche of pure mathematicians.

>>2739507
There are algorithims that can predict if a song will be a hit or not, there are also programs that can compose music. Music can be modelled by mathematics, it should not be surprising.

At least you could've said 'for the Nth time'

>>2739520
That isn't the point of this thread. Re-read op's first post.

>>2739531
For the N-th time where <span class="math">\mathbb N \ni N > 9000[/spoiler]

>>2739506
That's the ugliest fucking thing I've ever seen.

>>2739547
It's the idea behind the theorem that is beautiful. (You could've added the derivatives as well in your formula. pff)

Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is.

You realise the beauty of equations/theorems when you understand what they truly mean

>>2739506
This is one of the problems with mathematical beauty. It is even less accessible in many ways than modern art. You have to be at a certain elite level of mathematical knowledge to even be able to understand what that equation means, so that you can fairly judge whether or not that equation is beautiful. It is truly a wonder to me. I find the general idea of residues in complex analysis to just be amazing, but that will only make sense if you are familiar with complex analysis.

>>2739565
I love how Pual Erdős always makes the same face in every picture there is of him

>>2739582
As some with appreciable exposure to Cauchy residue theorem and Mozart, I can assure you that a Mozart sonata is more beautiful. Objectively.

Everything is art because all is vanity. The world is but an blank canvas. Man colors the world with his will; he molds it into something that is pleasing to his aesthetic sense--and he lives it. Math is both a tool for art, as used in the sciences, and a medium,when pursued as an end in itself. It's a shame that the popular appreciation of math qua art, as it was known to the greeks, declined during the christian periods and fell to nothing in our age of tedious realism. Math can be beautiful, but only if you are capable of knowing it to be beautiful.

This guy: >>2739565 seems to have the right idea.

numbers aren't any more beautiful than letters, they are just symbols that point to something

there isn't much to them

is 3 more beautiful than 5? gtfo

math isn't beautiful, otherwise people would buy math art, but there is nothing artistic in math

there are no math museums where math is put on display to be gawked at

>>2739601

erdos was a stinky old man, apparently he never showered and was homeless most of the time

Math is the only absolute truth in the entire universe.

>>2739900

I think they're opening a math museum somewhere quite soon, actually. Too lazy too Google it.

>>2739910

No it's a language like any other. All expressions are eternal if math is eternal.

It really depends on the math but sometimes i do find it as beautiful as music and art. For example when i first realized the importance of irrational numbers in everyday math, and even in everyday life.
--the number PI for example is always irrational no matter what base number you use because of its ratio of circumference and diameter.
-- even further the relationship of any irrational number and trigonometric expressions. EVEN though the numbers are irrational, without those irrational numbers our world would look very unsymmetrical ( from our perspective at least )

--TLDR:
irrational numbers are beautiful, so is trigonometry+ relationship with geometry.

>>2739476
most people seem to believe that music and art are subjective. Their proof for subjectiveness is flawed because the proof itself is the fact that people have different tastes (subjective). They therefore assume that art/music is subjective. THIS IS CIRCULAR REASONING!! A is B because A is B. Hurrrrrr

Anyways, No one has quantified the brain's interactions with what we see as reality. As in, no one has really found out what gives us the ability to name objectively what is beautiful and what is not. THIS FACT is also a reason for why we immediately assume music/art beauty is subjective.

We cannot jump to that conclusion.
Everyone already is preprogrammed to find things beautiful. A person does not have the capability to think of something to be beautiful.
Some one said in this thread that the more you try and think about why something is beautiful the more and more you move away from the beauty and "lose sight". That is true.


TLDR: Beauty is complex because we do not yet understand it. (i.e. a quantification of what makes beauty)
-- Math is beautiful because i have had the same feelings about some MATH as i had about some ART and MUSIC.

The beauty of math is when I use it in computer science to make some badass shit. Math in its pure form is shit:)

>>2740049
i agree, its all about the application of the tools in the world that make the tool itself beautiful. XD

>>2739900
You're only talking about the symbolic representation of math; you're retarded and have no idea what math is.


It doesn't matter what language you do math in, the concepts are always the same. You will always have the fundamental mathematical operations of addition, subtraction, division, multiplication, exponentiation, differentiaon, integration etc. These transcend any other form of human thought, and really are the closest things to god, in this universe.

I think the beauty of math lies in the elégance and ideas people can have. With math, you can make sense out of pretty much everything as long as your axioms lead to a consistent building.
Some beautiful math to me would be the Cauchy theorem and Stokes stated ITT, but I don't consider numbers to be beautiful. At least the natural numbers seem so obvious that I don't really see it.

Also, I can not agree that mathematical beauty only comes with application, since I thing a big part of what is fascinating it how you can see things in a bigger picture (like when you invent functional analysis or cartan geometry) and this doesn't really change how you compute things in an applicational context.
Lastly
>>2740049
I have never seen or heard of any interersting implementations in computer sciences, other than maybe information theory. When it comes to the cool stuff, the strong theorems, then it's always big numerics going on. It's tricky how to organize the interiour of a machine and software, but the math used in cs application (not necessarily talking about logic here, which can be crazy) is always far away from pure beautiful integral identities of say...some geometric ideas. I don't blame people for it though, abstract algebra systems are pretty young stuff, the last 50 Years it was only Fortran and C :P

>>2740271

> cartan geometry

lol learn to spell retard

>>2739565

>>2740323
?
You want me to write it with a big C or what do you mean?

You want to see mathematical beauty?

Differential and Integral calculus will blow your mind.

Using limits, you can find exact answers to places where a function is undefined. Using that, you can find the exact slope of any point on a graph.

Using the inverse of this, you can find the exact area between the graph and the x-axis, even if the graph is agonizingly curved.

That is beauty. Exact truth from something seemingly indecipherable.

Maths is a tool.
A hammer is a tool.

Sure you can get a fucking beatufiul hammer but its beauty is limited by its functionality. It cannot be made of gold because then it no longer hammers. Same with math.

>>2740946
don't know if serious.
eighter troll or you just haven't been introduced to some elegant solutions and consequences in abstract terms (like say Cartan geometry to name an example from this thread)

>>2740946

A painting must have certain qualities to be a painting. Does this make paintings inartistic?

>>2740271
>>2740972
more and more reasons to pick up my spivak book.

>>2740988
it's the joy of learning that using bundles more or less everything you know which is smooth (from Lie Groups to Riemannian Manifolds) can be threatened in one big picture.
Although for example, if you don't know say Riemann geometry beforehand it's a bit weird.
Quotient spaces, quotient spaces everywhere.

you have to be a genius to appreciate the beauty of math, like on the level of perelman and terence tao,

regular Phds can't appreciate it at all because they don't actually create new math

the only one's who see the art in math are the mathematical artists, like Gauss, and Von Neumann, the genetic geniuses

the rest, the hard workers and regular mathematicians just can't do it

no one on 4chan can see the beauty in math either, even if they claim they can--their brains just don't process it, because they've never engaged in the process of producing New math

everyone else is just tracing lines, only a handful have become math artists

>>2741107
This argument is retarded. Just because I can't compose music like Mozart or Beethoven, doesnt mean I can't enjoy their music, and the same is true about math.

>>2741168

But it does mean you lack a deep enough enjoyment of both music and math to create your own unique piece.

>>2741179
enjoyment =/= productivity. Also, it isn't only geniuses that write music or produce new math, and you don't have to be a genius to invent or prove stuff in todays math research.

Math (in particular, fractals) has always held some sort of beautiful. I find the amazingly small, well, amazing, and seeing a fractal go on, and on, and on, *forever*, just completely blows my mind and reminds me of the absolutely mind blowing scale of the universe.

>>2741205

That's a falsehood; people most certainly are productive towards what they enjoy. If what you said were true then having hobbies would be kind of pointless. More to the point it does take a type of genius to be a successful musician. Similarly it takes a type of genius to be a successful mathematician.

The scales may be different (an unsuccessful musician may well starve while an unsuccessful position may simply have to route his mathematical skills towards mundane tasks) but the idea is very much the same.

Fractals are mathematical art

And they can be very beautiful, and infinite in their complexity yet expressed through the simplest of formulas

There are many mathematical objects that I find beautiful: The butterfly curve, spirographs, Various spirals, Tautochrone curve

>>2741168
>This argument is retarded. Just because I can't compose music like Mozart or Beethoven, doesnt mean I can't enjoy their music, and the same is true about math.

that isn't the argument, the argument is that you can't produce ANY math, you are just regurgitating and tracing lines that are already there---hence, no production, no art, no beauty

it's all just being recycled, only 5 or 6 mathematicians in the world can appreciate it's beauty, the 5 or 6 who are breaking new boundaries

>>2741324
you really, REALLY underestimate how many mathematicians there are

Mathematical relations are OBJECTIVE. Beauty is SUBJECTIVE. The beauty comes from how close our subjectivity is so directly mapped onto the objectivity- how our very perceptions can somehow coincide with this system.

>>2741324
appreciation is entirely fucking subjective you stupid fag.

The person that understand math the best might as well think it's fucking ugly and some preschooler might think it's absolutely beautiful. All in the eye of the beholder.

>What is the beauty of math?
We are surrounded by it.
It is pure logic.
It's simple.

>>2741431

What's so beautiful about A=A

lol, gtfo

>>2741441
Beauty is perceived subjectively
What do you find beautiful, anon?

>>2741451

boobs

>>2741498

artistic boobs even

The general shapes that humans find most aesthetically pleasing to look at are represented in geometry by the most even numbers and ratios. Even without knowing the math behind it, almost anyone would find a 1 x 1 square more pleasing to the eye than a 1.23845 x 1 square. 90 degrees is by far the most common angle to use in any kind of design, which has a very even ratio to a full circle. Perfect symmetry is also a concept that is impossible to realize without mathematics, but when executed, anyone would be able to see the beauty in it, regardless of whether they were at any point taught mathematics.

In tonal music, the most harmonious intervals are the ones corresponding to the simplest mathematical ratios, and anything we interpret as rhythm must also have a mathematical evenness, and will be easier to follow the more evenly the beats are divided.

Basically, numbers can represent the perfection the physical world lacks and can only approximate. And humans find beauty in perfection.

>>2741551
>almost anyone would find a 1 x 1 square more pleasing to the eye than a 1.23845 x 1 square
>golden ratio

>>2741441
Isomorphisms.

>>2741498

There's a lot of complicated mathematics to boobs. Smooth manifolds specify the shape of breasts, the partial differential equations specify the jiggling of breasts, and the set of all possible breasts can be described as a many-dimensional affine space.

>>2741551

"Even without knowing the math behind it, almost anyone would find a 1 x 1 square more pleasing to the eye than a 1.23845 x 1 square."

You sure bout that Tim? I think the 1.23845" by 1" canvas is much more pleasing.

>>2741623
Because of the ratio between the objects on the canvas and the canvas itself.