F/L Matheson joined the RAF on a short-service commission in October 1936.
On 16th January 1937, he was posted to 10 FTS at Tern Hill, and on 7th August he joined 41 Squadron at Catterick.
On 12th October he was promoted to Pilot Officer, and on 12th July 1939 to Flying Officer.

In early July 1940, Geoffrey was with 222 Squadron at Hornchurch.
On 30th August he claimed a Bf 109 destroyed but was seriously injured when he was shot down in Spitfire P9443, and crash-landing near Sittingbourne.

On 3rd September he was promoted to Flight Lieutenant.
Later that month, on 30th, he was shot again, and again he crash-landed near Sittingbourne. He escaped the wreckage before it exploded. He was unhurt.

On 1st December 1941 Geoffrey was promoted to Squadron Leader.

On 24th August 1943, Geoffrey was operating Mosquitos with 418 Squadron from Ford when he was killed.

He is remembered on the Runnymede Memorial, Panel 118.