There aren't any mathematical tricks, rather how the real world (generator) translates to math.

The generator at the power company has 3 stators that are on equal distance between each other on a circle. As the rotor rotates, it induces AC voltage at each of them.

Because the rotor rotates at a stable speed, the AC voltage follows a sine function.

Because the stators are placed 2/3pi apart, their sine waves have a phase difference of 2/3pi.

Because 2/3pi+2/3pi+2/3pi=2pi, if you add them all together then you get 0 (sin[2pi]=0) and this is your neutral wire.

Quite honestly I learned that very late in the university which is a pity. Once you see how the real world translates to math, many things (like euler's formula which is of utmost importance for engineers) fall in place.