Mathews has contributed to many sketch shows, including Harry Enfield and Chums, The All New Alexei Sayle Show and, notably, the Ted & Ralph segments of The Fast Show.
However, it was with Father Ted that Linehan and Mathews made their biggest splash on the public imagination.
Both Linehan and Mathews worked on the first series of sketch show Big Train but only Mathews had a hand in the less fondly remembered second series.
Nevertheless, Mathews has continued to provide material for many of the shows respected by hard core, thirty-something, comedy junkies, particularly Brass Eye and Jam.
In 1999 Linehan and Mathews created the sixties-set sitcom Hippies, but the six-part series (which starred Simon Pegg and Sally Phillips) was written by Mathews alone.
Mathews contributed to only one episode of the first two series of Black Books, whereas Linehan had a hand in six.
In late 2003, the writing duo were named one of the 50 funniest acts to work in television by The Observer.
In 2005, Mathews, with Michael Nugent and Paul Woodfull, co-wrote I, Keano, a comedy musical play about footballer Roy Keane leaving the Irish national football team before the 2002 FIFA World Cup.
It is presented as a mock-epic melodrama about an ancient Roman legion preparing for war. In its first two years, over half a million people watched it, generating €10m ($13m) in ticket sales. In January 2007, it began its third year of performances.
Mathews has written two books:
- Well Remembered Days: Eoin O'Ceallaigh's Memoirs of a Twentieth-century Irish Catholic -- Arthur Mathews (Paperback - Macmillan - March 9, 2001) ISBN 0-333-90163-0. This book received many positive reviews.
- "Father Ted": The Complete Scripts -- Graham Linehan, Arthur Mathews. (Paperback - Boxtree - October 20, 2000) ISBN 0-7522-7235-7
Mathews has had two cartoon series published:
- Doctor Crawshaft's World of Pop, in NME, from 1992-1993
- The Chairman, in the Observer Sports Monthly, from 2003-2004
Both Linehan and Mathews have made cameo appearances in programmes they have written.
They also made a rare appearance in the sitcom I'm Alan Partridge as two Irish men considering Alan Partridge (Steve Coogan) for a contract. In the absence of a picture, Mathews is the fairer haired of the two in the scene mentioned.
Typically, they went away with a strong urge to employ somebody else (Partridge: "‘Sunday Bloody Sunday’. What a great song. It really encapsulates the frustration of a Sunday, doesn’t it? You wake up in the morning, you’ve got to read all the Sunday papers, the kids are running round, you’ve got to mow the lawn, wash the car, and you think "Sunday, bloody Sunday!").
Mathews also starred in I Am Not An Animal, an animated comedy series about talking animals written by Peter Baynham. He voiced a rabbit called Niall who had had his brain replaced with that of a call centre worker.