This paper presents an approach in contemporary, abstract art for a new way of experiencing modernist abstraction. This has not been possible until now, about 40 years after the postmodern turn against modernism in art, and the closely connected formalism. This new approach is represented in this paper by the Swedish contemporary artists Ann Edholm and Jacob Dahlgren. Modernist artists such as Kasimir Malevich and Piet Mondrian receives a new relevance to contemporary abstract art. This opens up for a new, more complex and more dialectical understanding and re-evaluation of modernism and its abstract art.This is shown by a historical and chronological investigation which highlights modernist abstract art, formalism, and the critical and post-modern Neo-geometric ?abstraction? of the eighties.