Physics World magazine presents its candidates for the 20 greatest equations of all time. The equations are divided into two groups–those from pure mathematics, and those from physics (there apparently being no worthwhile candidates in fields like chemistry or engineering).
Making it from the mathematics side is my personal favorite, Euler’s equation, exp(i*pi)+1=0, uniting the five most important numbers in one simple formula. Others include the formula for the circumference of the circle and “1+1=2,” which Bertrand Russell strove mightily to prove from first principles in his Principia Mathematica–an endeavor that he maintained cost him some of his sanity.
From the physics roster we have Maxwell’s equations in their vector form, Newton’s second law (F=ma), the ideal gas law (PV=nRT), Einstein’s equations, and several others, most of which carry the name of their discoverer. They’re enough to fill a book, and in fact someone has written it: Five Equations that Changed the World, by former ABC News science journalist and Raelian clone investigator Michael Guillen. He sure fell off the map, didn’t he?