Useless
Useless
[Different mathematical equations, all with a heart on left side, and all ending up with question marks.] √♥ = ? cos ♥ = ? d/dx ♥ = ? [1 0]♥ = ? [0 1] F{♥} = 1/√2π ∫ ∞ -∞ f(t)e it♥ dt = ? [Caption below:] My normal approach is useless here.

Randall is attempting to apply mathematics to the concept of love to no avail. Specifically, he is attempting his "normal approach", which is a term used in mathematics for the method one typically uses to solve a certain type of problem. However, as love is not a well-defined mathematical entity, his normal approach is useless. Simply put: he's saying he has found no way of describing love using only the tools of mathematics.
From the top, moving left to right, he tries the square root of love, the cosine of love, and the derivative of love with respect to x. He then attempts to left-multiply love by a 2x2 identity matrix , and finally he defines a function of love as a Fourier transform . These are all "normal approaches" to solving certain math problems.
The message of the comic is that for someone who uses math to solve all their problems, defining love is impossible.  It also indicates that love is not always a rational (or irrational) phenomenon.
This comic has been made into a t-shirt in the xkcd store, with a Laplace transform in place of the bottom integral.
Note: The Wikipedia links will provide far more detailed explanations of the mathematics.
[Different mathematical equations, all with a heart on left side, and all ending up with question marks.] √♥ = ? cos ♥ = ? d/dx ♥ = ? [1 0]♥ = ? [0 1] F{♥} = 1/√2π ∫ ∞ -∞ f(t)e it♥ dt = ? [Caption below:] My normal approach is useless here.
