LONDON — The first thought that struck me about the Serpentine Gallery’s exhibition of Swedish artist Hilma af Klint, Painting the Unseen, was: Thank goodness — finally a solo show starring a female artist! And not just any female artist: Hilma af Klint is a brilliant choice. Few people beyond the art world have heard of her, and the work on view here proves that she was such an intriguing individual and artist, this show is so much more than the product of tokenism.

Upon entering, you’re greeted with enormous, geometric murals in flat blocks of color, instantly recognizable as in some way spiritual, even occult. Glance at the date and you see that af Klint effectively ventured into the principles of abstraction well before its more famous exponents (Kandinsky, Mondrian, and Malevich), something the publicity material takes pains to emphasize. Even more fascinating is that the abstract works here were apparently made secretively, withheld from exhibition at her own instruction for 20 years after her death.

Af Klint was trained in portrait, landscape, and botanical painting at the Royal Academy of Fine Arts, Stockholm, from 1882 to 1887. From the late 1880s on, however, she rejected these disciplines, joining four other female artists to form the group De Fem (The Five), which conducted weekly séances and engaged with esoteric religious philosophies.

This side of her work — presented here as the primary side, the academic pieces completely discarded — was thus wholly rooted in spiritual concerns. She used painting as a medium (pun intended) through which the secret language of nature, whether cosmic or earthly, could be manifested, as well as early experimentations with automatic drawing. This may be the crux for understanding why her art has for so long been ignored: The level of finish (or distinct lack thereof) evidenced in the works, combined with a penchant for unplanned, experimental sequences including meandering lines and automatic drawing, indicates that the physical paintings, for af Klint, really were planes on which she communicated with immaterial and spiritual forces. They are far removed from the traditional, Western notion of not only representative art, but also, crucially, anti-representational art. In a way, to mention her work in the same breath as any of the Modernist abstraction movements is misleading, undermining real efforts to understand her real purpose.

Af Klint’s paintings appear as a series of sequences, in which one visual theme is explored in limited but specific directions, in a surprisingly methodical manner. So the works in Primordial Chaos Group I (Nos. 1 to 25) (1906–7) are restricted to a limited color palette and are of uniform size, as are those in Seven Pointed Star: Evolution (Nos. 1 to 16) (1908). The psychedelic, formless shapes and squiggly brushmarks look like they might have been made by someone in a trance or possessed, which is perhaps exactly the point. Three versions of “Altarpiece” (1915) are more monumental with solidly blocked-out color, exploring chromatic shading combined with the hard, basic geometric shapes of a triangle and circle. These look more like charts, their meaning mysterious and elusive while simultaneously simple and — in their own curious, restrained way — logical. It is staggering to think that these were completed in 1915; viewed in isolation, and without looking at any wall text, you would be hard pressed to place them historically.

Most striking are the enormous depictions (if they can be called that) of the stages of life in her The Ten Largest sequence. These jumble together vaguely feminine motifs of eggs, flowers, and swirls in distinctly pastel shades of pink, orange, and blue. Again, the meaning is mysterious and elusive, but here unmistakably fecund. They should be treated not as artworks expressing inner thought or narrative but mystical charts into other planes. They suggest a 20th-century equivalent of the maps and diagrams we see in Medieval manuscripts, created by writers, philosophers, cartographers, and scientists who were trying to make sense of the world around them.

Presenting her as an undiscovered artist is perhaps the wrong way to consider Hilma af Klint. Much is made of her modernism because we are mistakenly viewing her through the prism of defined art movements. In this light, we may be more critical of perceived shortcomings, like some figurative representations and automatic drawings and texts that appear clunky and awkward. High finish and polished, considered design — the hallmarks of Modernist abstraction — were not her concern in her quest to connect with the spiritual. Instead, she should be admired for what she was: as a wonderfully refreshing and unique presence in art history.

Hilma af Klint: Painting the Unseen continues at the Serpentine Gallery (Kensington Gardens, London) through May 15.