The most beautiful formulae in maths & science

[George Jones]

Yeah, but I think gravenewworld is right, Ramanujan wouldn't write [post=1636702]what you posted there[/post], which currently shows an infinite summation that doesn't converge on a limit being equal to -1/12.

Before I checked humanino's link, I thought to myself, "This seems like exactly the type of thing that Ramanujan would write." Checking the link "confirms" that he did write this.

And oblique name dropping is more of a vice than referencing Wikipedia, btw.

Oblique writing often is meant to be taken in good-natured way as a puzzle for the reader to solve.

Let me have a go at it!

A Swiss mathematician (and an all-time great), after whom an equation is named that has a special case given above, also wrote (hundreds of years ago) the same equation that humanino did. And the Indian genius's English mentor wrote a whole book on such things.

 

[Jimmy Snyder]

Oblique writing often is meant to be taken in good-natured way as a puzzle for the reader to solve.

Let me have a go at it!

A Swiss mathematician (and an all-time great), after whom an equation is named that has a special case given above, also wrote (hundreds of years ago) the same equation that humanino did. And the Indian genius's English mentor wrote a whole book on such things.

Spoiler for obliquophobes: hilite the blanks with your mouse to see the hidden text below.
The English mentor's name is well known: Hardy. He wrote a book on Ramanujan, but I'm guessing that's not what you mean by 'such things', so I'll guess it's his book on number theory. As for the equation of which humanino's equation is a special case, I think it's a special case of the Riemann zeta function, but that's not Swiss, it's Greek, unless you count the German part.
The special case is covered extensively in a problem in Zwiebach's book 'A First Course in String Theory'. The follow on book 'A Last Recourse in String Theory' has not yet been written. He uses the equation to prove that the world has 26 dimensions. In my opinion, this does not reflect well on Ramanujan.

 

[tribdog]

Does the equation have to be difficult to be beautiful? Can't the most useful equation in the world be beautiful? a squared plus b squared equals c squared.

 

[George Jones]

Hardy congratulations for Hardy.

I'll guess it's his book on number theory.

Nope.

Also, "a special case given above" and "humanino's equation" don't necessarily refer to the same thing.

He uses the equation to prove that the world has 26 dimensions. In my opinion, this does not reflect well on Ramanujan.

 

[Schrodinger's Dog]

Does the equation have to be difficult to be beautiful? Can't the most useful equation in the world be beautiful? a squared plus b squared equals c squared.

Not at all, the most simple are often the most beautiful.

e^{i\pi}+1=0

Being a perfect example. Wonderfully simple, and extraordinarily convenient.

 

[tribdog]

Not at all, the most simple are often the most beautiful.

e^{i\pi}+1=0

Being a perfect example. Wonderfully simple, and extraordinarily convenient.

never used it

 

[Schrodinger's Dog]

never used it

It can be used to derive every trigonometric function. So it's pretty up there. It also contains 9 basic rules of maths in one. exponents, imaginary numbers, addition and so on.

 

[Poop-Loops]

God, this is almost like poetry. On the surface, you just go "WTF? This is crap.", but when you look deeper, you get all the stuff Schrodinger's Dog came up with.

 

[Jimmy Snyder]

Nope.

In that case, I owe you a number of pure apologies for the inequalities in the qualities of my response. Here is another wild guess: Divergent series?

Also, "a special case given above" and "humanino's equation" don't necessarily refer to the same thing.

Indeed. In that case the mathematician in question is: Euler. (that is Leonhard, not his younger brother Houston).

 

[Moridin]

\neg (p \wedge \neg p)

 

[humanino]

\neg (p \wedge \neg p)

(This entire sentence is a false statement), OR (you will give me one million dollars).
I wonder how many people will read the previous sentence... [/size]

 

[Jimmy Snyder]

(This entire sentence is a false statement), OR (you will give me one million dollars).

This is more beautiful: (This entire sentence is a true statement), AND (you will give me one million dollars.)

 

[humanino]

This is more beautiful: (This entire sentence is a true statement), AND (you will give me one million dollars.)

Ah but it does not work ! For your entire statement to be

• true, both parts must be true. Fine, the only way is that we all give you one million.
• But there is nothing wrong with the entire statement being false ! Either part can be wrong, or both...

Now with

(This entire sentence is a false statement), OR (you will give me one million dollars).

we have :

• fasle only is both are false, but then first part makes self contradictory
• true if at least one is true, but then first part cannot be true, so second part must be true

Not sure I can find a better formulation right now... Am I out of my mind ?

EDIT
In the end, the all thing goes down to the old "paradox"

• This sentence is true can be true or false, no problem
• This sentence is false is self-contradictory and cannot be evaluated true or false consistently.

 

[Jimmy Snyder]

Fine, the only way is that we all give you one million.

Beautiful.

 

[humanino]

Beautiful.

I am not arguing anymore

 

[Schrodinger's Dog]

I am not arguing anymore

I'm just glad I don't understand the terminology behind logical arguments, because I don't have 1 million to give.

I disagree on the grounds that I have no clue what you are going on about.

 

[tkjacobsen]

What about:

<br /> \Delta A \Delta B \geq \frac{1}{2}\left|\langle[A,B]\rangle\right|<br />

 

[humanino]

What about:

<br /> \Delta A \Delta B \geq \frac{1}{2}\left|\langle[A,B]\rangle\right|<br />

Oh it's merely Cauchy–Schwarz inequality

Mathematics Is Beautiful

 

[gravenewworld]

Treatment for cancer

http://www2.mrc-lmb.cam.ac.uk/personal/sl/Html/Graphics/Syntheses1.gif

http://www2.mrc-lmb.cam.ac.uk/personal/sl/Html/Graphics/Syntheses2.gif

 

[Schrodinger's Dog]

Now you see gravenewworld not only is that beautifully written and a lovely little chemical equation. But it's beautiful on many levels.

 

[Pythagorean]

It can be represented by either \nabla^2 or \Delta and technically it should be \Delta f but I left it out because I am in fact quite mad/evil.

yay, new notation. I was as equally excited by the d'Alembertian, square as it is.

my simpleton contribution to this thread:

I was very excited when (during the course of my education)

F = ma

evolved into
F = m \frac{d^2x}{dt^2}

and further to
F = \frac{dp}{dt}

I really like the continuity equation too:

 

[EL]

I was very excited when (during the course of my education)

F = ma

evolved into
F = m \frac{dx}{dt}

Wow, so F=ma has evolved into F=mv...

 

[Pythagorean]

haha, my bad, editing...

 

[slider142]

Stokes's theorem: \int_Md\omega = \int_{\partial M}\omega
Elegant, concise, obvious once the components are properly defined, and pops up in cute places in classical physics and differential geometry.

 

[rohanprabhu]

One of the most ridiculous and ugliest equation ever:

<br /> N = R^* \times f_p \times n_e \times f_l \times f_i \times f_c \times L<br />

This is the 'Drake equation' where N is the number of civilizations in our galaxy with which we might hope to be able to communicate.

and some estimates even give the value as '10'...

 

[EL]

One of the most ridiculous and ugliest equation ever:

<br /> N = R^* \times f_p \times n_e \times f_l \times f_i \times f_c \times L<br />

This is the 'Drake equation' where N is the number of civilizations in our galaxy with which we might hope to be able to communicate.

and some estimates even give the value as '10'...

True! There's no reason to have a special name for that kind of equations.

 

[tribdog]

True! There's no reason to have a special name for that kind of equations.

Equations should be equation, singular. I'm only pointing this out because you asked.

 

[Schrodinger's Dog]

One of the most ridiculous and ugliest equation ever:

<br /> N = R^* \times f_p \times n_e \times f_l \times f_i \times f_c \times L<br />

This is the 'Drake equation' where N is the number of civilizations in our galaxy with which we might hope to be able to communicate.

and some estimates even give the value as '10'...

Well as I said on the thread where I used this it's meant to be a starting point for discussion, where people can suggest their own values; it's entirely hypothetical; it's parameters are meant to be unknowable, and any conclusions based on it are by these criteria, purely speculative. So I would say yes its ugly but I don't think it's ridiculous, after all it is meant purely to encourage discussion on life in the Universe, not as an accurate measure of such.