Edge's "World Question Center" debuted a project where they asked scientists "What is your formula? Your Equation? Your Algorithm?"
Here are the responses that they collected. The overwhelming responses from physicists are as expected: something in string theory, cosmology, or quantum gravity. But there is one real exception that caught my eye: Freeman Dyson's response is a five-fold symmetric representation of the tau function that he discovered.
Surprisingly, for a "question" about "formulae and equations", only one mathematician was interviewed: Shing-Tung Yau. His response: a parabolic Harnack inequality which can be applied to give some bound on the Ricci flow (I never really studied Ricci flow so I am not quite sure of the significance of that inequality he demonstrated.
Some others that I really like: George Dyson (son of Freeman) gave a equation about lift coefficient of a kayak; Marvin Minsky's is kind of neat, even though it is stretching the question a bit (I guess the picture counts as some sort of algorithm).
Lisa Randall's is cute, but it is about five dimension gravity, which I personally think is a rather crazy idea (but it seems that Sergiu has some interest in it now... and what do I know, I am just a grad student...)
But my overall favourite has to go to Benoit Mandelbrot. It is simple, elegant, and classy. Just one line "Z to Z2 + C" and signed "B.Mandelbrot".
What would I answer? I have no idea. I am now really working on Einstein's equation. But that's his equation, and not mine. Though hopefully I'll have an expression of my own once I figure out exactly what this business with Kerr-Newman metric is like.