Hilma af Klint did not trust her peers to understand her work. She sensed her paintings were too weird and too radical for her fellow Swedes. As a star pupil of Stockholm’s Royal Academy, she made a living selling impressionistic landscapes. But she worked privately and passionately on a staggering array of canvases that strove to represent the spiritual world in visual terms.

When af Klint began making abstract paintings in 1906, her departure from realism was unprecedented. It would take almost a decade for Sweden to exhibit the work of Vasily Kandinsky, a Russian long credited with pioneering abstraction, though his experiments in the form began after af Klint’s...