As any knowledgeable computer programmer knows, it takes more then just a keyboard to create a program. It takes a lot of math. The Matrix as presented in the movie series is nothing more then merely a program written by the "architect" as referred to in the movie. Many common and detailed math concepts apply to the Matrix and the Matrix Reloaded like equations, axioms, tessellations, and many other ideas on a more toned down level.
The Matrix is just one very large set of equations generated by the computers as derived from their own regulated set of equations. Thus one is then suppose to be able to get all the other problems from this main set of equations, which serves as the operation system, also known as the matrix. This main set of equations is the axioms, which cannot be changed or broken. Any derivation can be changed or broken if the equation systems are changed. .
The movie itself is also highly versed in computer animation and effects. All computer animations and effects are created using tessellations and mathematics. To create stunning special effects the frames per second, animation movement and design have to be mathematically coordinated. Math is the basis for the dramatic increase in stunning special effects over the past decade, and will continue to be. .
On smaller levels, many events in the movie involve mathematics. All of the stunts and animations during the fight scenes, car chases, etc. are highly related to physics and motion. To calculate times, distances, velocities, etc. they must use math. The matrix itself is a set of huge equations. The passwords in the movie are also binary strings of information which are only interpreted through mathematics. .
The Matrix movie series is probably related more to mathematics then it is the plotline. Basically everything in the movie can be applied to some aspect of mathematics, be it simple equations, tessellations, axioms, etc.
