[1] Born in Copenhagen, Geertsen first trained as a gardener (1934–39) before concentrating on art in which he was self-taught.
In 1937, he associated with Thorvald Hansen and other painters from Aalborg, developing an interest in Naturalism and painting dark still lifes and landscapes inspired by Paul Cézanne and Amedeo Modigliani.
[2] In 1943, he moved to Copenhagen adopting a more spontaneous impasto, surrealistic technique in his painting.
In 1947, he was a co-founded of the Linien II artists association, which concentrated on concrete art.
Later he created a variety of mobile and hanging works, decorating the Ministry for Foreign Affairs (1980) and the concert hall in Statens Museum for Kunst (1998).