I have heard many stories of what the equation is.....one of the most popular theories is that Smith and Neo are part of the same equation.....Listen to the way the Oracle says this line "He doesn't understand them, he can't. To him they are variables in an equation. One at a time each variable must be solved and countered. That's his purpose to balance the equation." The Architecht is a mathmatican and his purpose is to balance equations...when the oracle says this she means it in a general sense not to a specific equation....an equation has two sides to it....one side is say the number 3 so the other side must be 3 too, to balance it out...the Architecht says in his infamous speech that Neo is the product of an unbalanced equation....that is the choice factor that was plugged into the matrix....he even says its fundamentlly flawed....to him choice is a variable that he must wait until its solved by the human and then its up to him to counter it just like he would to any other equation, but he can't since he doesn't know what choice really is....he doesn't understand it....he was created perfect....NEO is a product of this unbalanced equation....he has the ablility to do anything he so chooses....and the Architecht even stated hes a "Systemic Anomaly"....Because of this unbalanced equation it creates an Anomaly that is Systemic, creating fluctuations in even the most simplistic equations.....for example, Neo has true choice to be able to have to fly and such, but this is not part of what the system was created for so its a fluctation in the gravity's equation.....so Neo is a product of the unbalanced equation, he is the end result of the all those humans that make choices(Sum of a remainder)... and Smith is the product of the equation trying to balance itself out, he spreads across the matrix to counter all those choices people are making...Neo and Smith now completely complement each other. Neo the product of an unbalanced equation (choice) and Smith is the product of the equation trying to balance itself out (purpose)....