Getting ready for the May 8th episode of LOST it features some action with Horace Goodpseed. Here's some background on Horace to catch us all up.
Horace Goodspeed was a mathematician in the DHARMA Initiative. Little is known about him so far except that he was present in Oregon on the day that Benjamin Linus was born, helped Ben's father to get a job on the Island, and was killed during the Purge. However, on the DVD commentary track for "The Man Behind the Curtain" Damon Lindelof and Carlton Cuse describe Horace and his companion Olivia as factoring significantly in the future "game plan" for Lost.
Before he came to the Island, Horace was driving with Olivia 32 miles outside of Portland when he came upon Roger Linus carrying Emily Linus on the side of the road, right after Ben had been prematurely born. He wanted to take Ben's dying mother to the hospital, but she died before he had the chance to.
On the island, as part of the DHARMA Initiative, Horace was involved in bringing Roger and Ben to the Island roughly ten years after Ben's birth. His DHARMA jumpsuit identified his role as "Mathematician". He also wore the Arrow logo. After a shootout with the Hostiles, Roger confronted Horace, demanding that he be paid more for such a dangerous job.
Horace was in the Barracks at the time of the Purge; he died while sitting on a bench. Ben discovered his body after coming back from having killed his father and showed his respect by closing Horace's eyes, a respect which Ben didn't pay to any of the other deceased.