Gårding was born in Hedemora, Sweden but grew up in Motala, where his father was an engineer at the plant. He began to study mathematics in Lund in 1937 with the first intention of becoming an actuary.
His doctorate thesis, which was written under supervision of Marcel Riesz, was first on group representations in 1944, but in the following years he changed his research focus to the theory of partial differential equations. He held the professorship of mathematics at Lund University from 1952 until retirement in 1984.
His interest was not limited to mathematics, but also in art, literature and music. He played the violin and the piano. Further, he published a book on bird songs and calls in 1987, a result of his interest in bird watching.
