Roger Butts was a former child math prodigy who finished high school at the age of 10 and finished college at 13.
At the start of the series, he was 40 years old and still enthusiastic as ever about math to the point in which it had caused him significant physical damage; he suffered from a back injury he obtained from jumping up on (and falling off of) a student's desk after the student finally grasped a theorem which had been eluding her for months. He may or may not have been on some form of amphetamines.
He swore himself to a life of celibacy since he witnessed his father and stepmother get hit by lightning when he walked in on them engaging in coitus on a camping trip in the Adirondacks, although he identified as somewhat asexual before the incident.
He dated Jillian Jordan on and off when she was "on her breaks" from Robert Fry. While they were good friends, there was no romantic attraction; this was a relationship of convenience meant to secure an inheritance from his wealthy grandmother Patricia (she had no such rules for her favorite grandchild, Roger's older sister Ophelia).
He met an unfortunate end in Season 9.