Arvin first appears in "In Your Head" when Haley sneaks into Alex's class to get her to read over her writing sample before she goes to an interview at Nerp. Haley ends up interrupting the class before Alex rushes her out. Arvin later finds both of them in the school yard and tells Haley that the two of them will get married one day, that he doesn't understand it but he just knows because all the probability scenes he's been running in his head end up with the two of them marrying. Haley later uses a similar speech to get the job she's applying for and later ends up accepting his contact request. It's unclear whether Arvin actually believes this or if it's just a clever pick-up line.
Arvin is a two-time Vanderscoff Grant winner, one for philosophy and one for geometry.
In the series finale, he and Alex are in a relationship.