Richter: You said they'd be killed publicly.
Robert Langdon: Yes, revenge. For La Purga.
Richter: La Purga?
Robert Langdon: Oh geez, you guys don't even read your own history do you? 1668, the church kidnapped four Illuminati scientists and branded each one of them on the chest with the symbol of the cross. To 'purge' them of their sins and they executed them, threw their bodies in the street as a warning to others to stop questioning church ruling on scientific matters. They radicalized them. The Purga created a darker, more violent Illuminati, one bent on... On retribution.
Robert Langdon: The Illuminati did not become violent until the 17th Century. Their name means 'The Enlightened Ones'. They were physicists, mathematicians, astronomers. In the 1500's they started meeting in secret, because they were concerned about the church's inaccurate teachings. They were dedicated to scientific truth. And the Vatican didn't like that. So the church began to, how did you say it? Oh, hunt them down and kill them.