The Illuminati are an underground organization on scientists who hold a grudge against the Catholic church for suppressing them and science in general. The Church has been an outspoken opponent to science for all of its history.
The original crime against science was the suppression and denial of Galileo and his ideals. When the church made him refute his beliefs and put him under house arrest, the Illuminati became committed to achieveing retribution for Galileo.
Though today they are said to be extinct, many still believe in their fight against the opressive church.