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[Virex]

I'd probably go for the theory of thermodynamics:
dU = dQ + ΣdW_ⁱ
TdS = dQ
pdV = dW_pr
Σμdx = dW_chem
PV/RT = Z           (You can actually derive this one, but it was first determined experimentally. Besides that you'll need a bit of quantum mechanics or you end up with a wrong factor)

Should be enough for most applications (though you may need a few extra W-terms if you're working with sources of energy besides heat, pressure and chemical). Most other thermodynamical properties can be derived from this small set of equations.

[Poltifar]

Phi, the most awesomest ratio ever.

And the Fibonacci sequence whose consecutive terms' ratios tend to Phi as the sequence tends to infinity.

I find complex math and physics equations intriguing and all, but sometimes I find the prettiest things to be some of the simplest concepts. For example, prime numbers really fascinate me. Of course, even the simplest of concepts can be taken further with some work, such as the work being done on factorizing very large numbers, the dispersion of prime numbers among the set of natural numbers, and ultimately finding some sort of function that can determine all prime numbers efficiently. And from there we can follow a tangent to arrive at the amazing field of cryptography, and then we might suddenly find ourselves at quantum computing...

I guess my problem with the many pretty equations, theories, and fields of work in general is that I never manage to focus on one long enough to appreciate its full beauty.

[Darvi]

Euler's identity,

[MonkeyHead]

Maxwells equations...

well, them, or:

[Darvi]

Ya they're nice too.
 
Just imagine, Maxwell doing his equations, and when he's done, he stads up, runs out of his house to the nearest podium shoutig "I have seen the light!"

[Leafsnail]

First law of thermodynamics.

e^(pi)i + 1 = 0.

Fixed for even more mathematical beauty.

...I had to have this explained to me.  Now I know it's because it links 5 fundamental numbers (0, 1, e, pi, i) and 4 fundamental operators (powers, multiplication, addition, equals).

[Strife26]

Woah, it does link a lot of fundamentals, doesn't it? Cool.

[Darvi]

First law of thermodynamics.

e^(pi)i + 1 = 0.

Fixed for even more mathematical beauty.

...I had to have this explained to me.  Now I know it's because it links 5 fundamental numbers (0, 1, e, pi, i) and 4 fundamental operators (powers, multiplication, addition, equals).

e to the power of imagiary pie is minus one. Euler's idetity.
 
It's because e^i*x=cos(x)+i*sin(x)
 
and since cos(pi)=-1 and sin(pi)=0, well...

[Leafsnail]

No, I know what it means.  What I didn't understand before I checked a poster on the wall of my maths class is why writing it in that manner is significant.

[Darvi]

Oh. It isn't significant. As she said, it was for "mathematical beauty". Aesthetics.

[Leafsnail]

Yes - aesthetic significance.

[Darvi]

Eh, YMMV.

[Dr. D]

I like Laplace transformations. They are very useful. The only problem is that if you multiply the Laplace transformations of two functions together and inverse Laplace it, the result gets a little convoluted.

Spoiler (click to show/hide)

Yes that was a joke.

[Miggy]

In mathematics, I was pretty intrigued by infinite series and sequences. Taylor polynomials in particular are awesome.

In chemistry, enzymes. The closest to real-life magic that we'll ever come.

No, these are "theories" per se, but they are phenomenons and they are awesome.

[Virex]

On the field of chemistry, one interesting field that's being worked on is the field of supramolecular polymers.