The ultimate formula to date?

Question

What scientific/mathematic formula is so far the best formula in your opinion?

Answer 1

There is no best formula. They are all useful in different situations. But the ones I use the most often are the pythagorean theorem, quadratic formula and fundamental theorem of calculus.

Answer 2

There are many important formulae, but perhaps a good contender would be either the Cauchy-Riemann Equations for determining whether a function of a complex variable is analytic, or the Cauchy Residue Theorem which allows for determining the integral of a meromorphic function around a closed loop, given a side condition.

(Even though I would not rate it as number one, I also would rate the Prime Number Theorem,

#{primes p not exceeding x} = (x/ln x)(1 + o(1)) as x approaches infinity

as an extremely important result, which ultimately led to a lot of nice mathematical research and the development of many new techniques)

Answer 3

Mother's milk.
It beats the hell out of all of the commercial formulas on the market.

If you meant in mathematics - I'd have to go with E=MC^2. It's simply the one formula that's quoted the most, had the largest impact on science and after over 100 years, it still boggles the mind!

Answer 4

I'm fond of Heron's formula. It allows you to get the area of a triangle from just the lengths of the sides, without using the law of cosines or any trigonometry.

Answer 5

Pythagoras' right angle triangle theorem!
a^2 + b^2 = c^2

Answer 6

the formula for a hyperbola with the center on th origin:

Answer 7

The quadratic reciprocity law:
(p/q)(q/p)=(-1)^{[p-1)/2] *[(q-1)/2]}
for p,q natural numbers and (./.) the Legendre symbol.

It has hundreds of proofs.

Answer 8

euler's formula

e^(iπ)+1=0

Answer 9

E=MC^2

Answer 10

breath in and breath out. it keeps me alive.
I dont know if they that written in a formula, but I find it a great credo.