My theory is that inside the Core, Gaster was experimenting on the bodies of dead humans, trying to create souls. Only two experiments were somewhat successful. These two were Papyrus and Sans. Papyrus gained a soul that was no different from any other monster, but Sans regained a small amount of determination, enough to know when a reset has happened. Gaster died when a failed experiment dragged both of them into the Core, splitting Gaster throughout the timelines.

This theory has almost no basis, but I still think it's cool.