Can Equations Be Purely Aesthetic?

[Mattematics]

Minimalistic but very pleasing
\nabla^2 = \Delta

 

[micromass]

H_2O
If you don't appreciate it, then you don't appreciate life...

Not really an equation...

 

[micromass]

No Gauss-Bonnet yet??

 

[strangerep]

No Gauss-Bonnet yet??

You still seem to be thinking in terms of beauty-in-meaning, rather than visual beauty.

Actually, it's fascinating how high powered mathematicians like yourself and A. Neumaier (to name just 2 among others in this thread) perceive beauty-in-meaning where others do not, yet have trouble perceiving the visual beauty that others can. Other types of people (e.g., conventional artists) suffer the reverse -- they create beautiful pictures yet cannot even understand how basic percentages work.

 

[ShayanJ]

You still seem to be thinking in terms of beauty-in-meaning, rather than visual beauty.

Actually, it's fascinating how high powered mathematicians like yourself and A. Neumaier (to name just 2 among others in this thread) perceive beauty-in-meaning where others do not, yet have trouble perceiving the visual beauty that others can. Other types of people (e.g., conventional artists) suffer the reverse -- they create beautiful pictures yet cannot even understand how basic percentages work.

I'm not a mathematician nor a physicist, only a physics student, but I still feel like micromass.
Also, let's take a look at others. A good percentage of people posted some explanation along with their equations, which means they had some meaning in mind when they posted it.
The most voted equations are the ones by Samy_A and micromass himself, which are both more about the meaning than the looks.
It seems most of the people actually feel the same as micromass about the equations but they either don't know it or don't want to admit it!
Actually this is reasonable. How people feel about an equation gets stronger and stronger as they work with it and learn more about it and its relation with other equations, to the point that this meaning-induced feeling will over-shadow any feeling related to only the looks of an equation. Even about people who don't know the meaning and are just learning it from the explanations given, the meaning is more exciting than the looks!

 

[mfb]

The most voted equations are the ones by Samy_A and micromass himself, which are both more about the meaning than the looks.

Don't forget the "all 1" formula from @TeethWhitener. It has the most votes currently.
micromass' formula has small and capital pi in it.

 

[ShayanJ]

Don't forget the "all 1" formula from @TeethWhitener. It has the most votes currently.
micromass' formula has small and capital pi in it.

Oh...missed that one!
Anyway, I think even that equation actually seems more interesting to people than beautiful!

P.S.
Aren't they asymptotic to each other rather than equal?

 

[mfb]

Both values are the limit of the shown procedure. Those limits are equal.

 

[micromass]

Don't forget the "all 1" formula from @TeethWhitener.

That one should definitely deserve to be the winner. But let's but honest, would it be as beautiful to somebody who didn't know what division and square roots are? Or to somebody who doesn't realize those are limiting processes? Because it's very hard to suppress this knowledge when judging the formula...

 

[ChrisVer]

Not really an equation...

well before me someone had posted some chemical bonds and the process of electrolysis was shown in the Naturwissenschaften box (I love how this word tickles my tongue! And I love even more the fact that I wrote it correctly without looking at it)

Common, the most beautiful formula is this one:

L = i \bar{\psi}_i \gamma^\mu D_\mu \psi_i -\frac{1}{4} \sum_{b \in \text{adjoint}} \sum_{a\in U(1),SU(2),SU(3)}F^{ab}_{\mu \nu}F^{ab~\mu \nu} + Y^{ij} \bar{\psi}_i H \psi_{j} + + | D_\mu H |^2 + \mu^2 H^\dagger H - \lambda ( H^\dagger H)^2

 

[Kevin McHugh]

∫e^x = f(μ)ⁿ

Here is one I think is beautiful!

 

[mfb]

Now you have to show that it is either generally true in some way or defines something meaningful.

 

[micromass]

Now you have to show that it is either generally true in some way or defines something meaningful.

I think most people would consider it true. I just don't get why this forum allows it...

 

[Ygggdrasil]

∫e^x = f(μ)ⁿ

Here is one I think is beautiful!

Whereas a lot of these equations require an advanced degree to appreciate, this one is one that middle schoolers might appreciate more

 

[Pepper Mint]

http://www.bbc.com/earth/story/20160120-the-most-beautiful-equation-is-pi

 

[epenguin]

As any fule no

 

[samalkhaiat]

You still seem to be thinking in terms of beauty-in-meaning, rather than visual beauty.

Actually, it's fascinating how high powered mathematicians like yourself and A. Neumaier (to name just 2 among others in this thread) perceive beauty-in-meaning where others do not, yet have trouble perceiving the visual beauty that others can. Other types of people (e.g., conventional artists) suffer the reverse -- they create beautiful pictures yet cannot even understand how basic percentages work.

“Beauty” is in “Usefulness” and “Simplicity”. Imagine you are working on extremely important problem with limited time scale, and suddenly the following difficult integral pops up in your face
\int_{0}^{\infty} dx \ e^{-(x^{2} + \frac{1}{x^2})} .
Do you waste precious time trying to evaluate the integral, which is not easy, or use the following “simple” and “extremely useful” inequality to guess correctly its value?
x + \frac{1}{x} \geq 2 .
By the way, the inequality I posted in #4 follows from the above beautiful inequality

 

[Kevin McHugh]

Now you have to show that it is either generally true in some way or defines something meaningful.

No I don't. The rule was it has to be ascetically pleasing.

 

[Kevin McHugh]

I think most people would consider it true. I just don't get why this forum allows it...

Whatsamattta U? What's not to allow?

 

[micromass]

No I don't. The rule was it has to be ascetically pleasing.

This is the rule:

• The equation must be valid and true.

Yours isn't.

 

[Greg Bernhardt]

Yours isn't.

It is literally true, but not mathematically. I didn't really specify

 

[micromass]

It is literally true, but not mathematically. I didn't really specify

I don't think it's true for everybody though...

 

[Kevin McHugh]

This is the rule:
Yours isn't.

Lighten up Francis

 

[Kevin McHugh]

I don't think it's true for everybody though...

Good God man!

 

[micromass]

Lighten up Francis

I got to admit I'm pretty upset because you missed the $dx$...

 

[Kevin McHugh]

I got to admit I'm pretty upset because you missed the $dx$...

OK, now there's a response I can wrap my head around

 

[Ssnow]

... and the domain of integration must be the union of intervalls $C\cup O \cup N \cup D \cup O \cup M$

 

[strangerep]

[...] Naturwissenschaften box (I love how this word tickles my tongue!

That picture reminds me of a joke that circulated during my high school German class: "In dieser Box ist viele Ratschidt gemixt."

 

[strangerep]

It seems most of the people actually feel the same as micromass about the equations but they either don't know it or don't want to admit it!

Don't get me wrong. I, too, can perceive beauty-in-meaning. Indeed, I'm sure I'd enjoy a brief Insights article explaining Micromass's entry more extensively.

But this contest is about visual beauty, as Greg already explained.

 

[strangerep]

“Beauty” is in “Usefulness” and “Simplicity”.

Heh, I see you are from the "Marie Curie" school of beauty and deportment. (IIRC, Einstein said that MC "never smelt the roses".)

But I think you (and several others) misunderstand me. I can also perceive beauty in usefulness and simplicity. My point is that it's not the same thing as visual beauty.