What is the greatest mathematical equation?

Question

What is the greatest mathematical equation and what good is it?

Answer 1

Pythagoras' theorem

Answer 2

2+2=3

Answer 3

It's interesting to see that many of the answerers gave PHYSICS equation. But as a pure mathematical equation, it has to be

e^ix = Cos(x) + iSin(x), of which a special case is e^(iπ) = -1

otherwise known as Euler's formula. This one equation is the lunchpin of a vast body of classical mathematics, tying together complex numbers with trignometric functions, with applications extending into Fourier analysis and even quantum theory.

Answer 4

This is a tough competition.

Pythagoras has precedence: H² = A² + B².
Newton defined mechanics with F = ma and
  gravitation with F = G m₁ m₂ / r₁₂².
Maxwell's equations define electricity:
   ∫ E•dA = q / ε₀
   ∫ B•dA = 0
   ∫ E•ds = -dϕ/dt
   ∫ B•ds = µ₀ i + (1/c²) ∂(∫E•dA)/∂t.
Einstein has relevance: E = mc².

and...

Who is to choose?

Answer 5

In all seriousness, I really think it's the Transitive Property of Equality (given a=b & b=c, then a=c), which gives us substitution.
It's the basis of the Equivalence Properties, which means everything in upper level math is pretty much based upon the transitive property.

Answer 6

E=MC2
As for what good it is, look it up
It is one of the basic building blocks of modern day science today
And for those that don’t think it is a formula based in math try solving it

Answer 7

1+1=2
Enough said.

Maxwell's Equations - four interwoven equations that describe the interplay between electricity and magnetism
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq.html

Euler's Formula - combines rational, irrational and imaginary numbers to obtain zero
http://www.well.com/user/davidu/euler.html

Newton's Second Law - F=ma
http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/newtlaws/u2l3a.html

Pythagoras' theorem - a^2+b^2=c^2
http://www.mathsisfun.com/pythagoras.html

E=mc2
http://www.pbs.org/wgbh/nova/einstein/

Answer 8

0+0 = 0, useless

Answer 9

1 + 1 = 2

Sort of laid the ground work for everything else.

Answer 10

E=MC^2

it is a reletivity equation made by einstien himself.

---------------or---------------------

go here ( http://mathworld.wolfram.com/PiFormulas.html ) for the most complex formula EVER!