Mathewson was born in Lerwick, Shetland Islands, into an unusually musical household. At eight years of age, he was studying classical piano.[2] He continued to study and perform classical piano until he reached the age of 16, having started playing bass guitar a year earlier.[2] His talent was noted and encouraged by the Shetland musician Peerie Willie Johnson.
In 1962, Mathewson was in Germany, playing professionally with a band that played Dixieland music. In London, he performed with various jazz and R&B bands throughout the early 1960s. Around this time, he was also a member of The Kenny Clarke-Francy Boland Big Band.[2] In 1966, Mathewson became a member of the Tubby Hayes band, with which he performed until 1973.[2] From 1975 on into the 1990s, Mathewson was frequently a participant in Ronnie Scott's recordings and concerts.[2] In 1983, he appeared on his old friend Dick Morrissey's solo album, After Dark, with Jim Mullen, John Critchinson, Martin Drew and Barry Whitworth.
On 11 February 2007, a benefit concert was held for Mathewson, who was reportedly recovering from two broken hips, a broken wrist and a ruptured artery.