The Illuminati, or People of the Light, was orignially a secret society founded by Galileo himself. The Christian church was persecuting scientists in his time, and he and his people went underground, but their ultimate goal was to unite religion and science in harmony. But the church, threatened by their studies that were controversial to their teaching, rooted out the Illuminati and killed them all (decades after Galileo's time). Later, the Illuminati returned, but the new leaders wanted no harmony. They became a Satanic cult that was wholly opposed to the church, and began killing priests.
The Illuminati believed in symmentry, the belief that everything had an opposite. Dark/Light, Sun/Moon, Fire/Water, Earth/Air, even in scientific proportions, like Protons and Neutrons, Matter and antimatter.
They have since faded out and are no longer, as far as anybody knows