Title text: Even the identity matrix doesn't work normally
Randall is attempting to apply mathematical systems 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 mathematical value, his normal approach is useless. Simply put: He's saying that math has no way of describing love (or more precisely, he has no way of describing love, using only the tools of mathematics.)
From the top, going right, he tries the square root of love; the cosine of love; the derivative of love with respect to x; he left-multiplies love by a 2x2 identity matrix, and finally he defines a function of love as a Fourier transform. These may all be "normal approaches" to solving certain math problems.
The long and the short of the comic is that this might be the thinking of someone who uses math to solve all their problems upon their discovering love, which can't be solved with math. It also echoes the idea that love is not always a rational phenomenon.
 Basic explanations of the functions
- Note: The Wikipedia links will provide far more detailed explanations of the mathematics.
- The square root of x is the number which, when multiplied by itself, equals x.
- Cosine is a trigonometric function which, when given the measure of an angle in a right triangle as an input, outputs the ratio of the lengths of two sides of that triangle (for cosine it is the non-hypotenuse side adjacent to the angle and the hypotenuse).
- A derivative of a function is the rate of change of that function at a given value of x. It is a primary focus of calculus. A basic example is where "velocity" is the rate of change of displacement at a given time, the derivative of velocity is "acceleration" which is the rate of change of velocity at a given time.
- Identity matrices are matrices which consist of only zeros and ones, with zeros everywhere except along the main diagonal. Multiplying a matrix by the equal-sized identity matrix will result in the same output in the same way that multiplying a non-matrix by 1 does not change the original term. The title text suggests that multiplying love by the identity matrix does not return the same "love" value.
- A Fourier transform converts a function from one (sophisticated) function into an endless continuous series of (more simple) functions, where each next part is bringing the equation closer to the real result. This means that you can stop your calculations after a few iterations and you are very close to the real result, and it also can be used to deconstruct signals.
- [Different mathematic equations, all with heart on left side, and all equal question mark. Equations are as follows:
- Square root of heart equals question mark
- Cosine of heart equals question mark
- Derivative of heart with respect to x equals question mark
- Identity matrix of heart equals question mark
- Fourier transform of heart equals question mark.]
- My normal approach is useless here
- This is the fifty-second and last comic originally posted to LiveJournal. The previous comic was 53: Hobby.
- The version used on the t-shirt and in xkcd: volume 0 is slightly different. The derivative is with respect to time (t) instead of x, and the function at the bottom is a Laplace transform.
- This comic was adapted to a wedding cake featured on an installment of "Sunday Sweets", a regular feature on popular blog Cake Wrecks.