Father Elijah

 was an elder and leader of the Mojave Chapter of the Brotherhood of Steel

Background
He went missing during the NCR takeover of the HELIOS One powerplant and was never found. According to Head Paladin Hardin, his becoming an elder was questionable due to his status as a scribe; normally, the ability to become an elder is reserved for Paladins, though in Elijah's case an exception was made due to his high intelligence. Veronica refers to him as still alive as he contacted her after the HELIOS One disaster.

During the quest Still in the Dark, after talking to some of the members of the Brotherhood of Steel, you find out Elijah became an elder because he was a genius. However, the members say he was a strange man and his battle tactics were poor. They then tell you during the takeover of HELIOS One he held them inside the building too long. He kept saying 'something was almost ready'. This is most likely hinting to the Archimedes II.

In the add-on, Dead Money, it is revealed that Elijah discovered the Sierra Madre whilst searching for weapons to eradicate the NCR.

Results of dead money
Elijah is called down to the vault to speak with the player character. Then if the character runs around, Elijah is trapped in the vault forever. HE can also be killed normally.

Appearances
is mentioned in Fallout: New Vegas, and appears in the Dead Money Add-On.