Abstract art does not just mean painting freely and wildly, putting it out there with abandon. If it did, any old doodle or curtain fabric would be abstract art. But modernist abstract painting in the 20th century found meaning in the colours, logic in the lines, discipline in freedom. The greatest abstract paintings convince you they are inevitable, because they have such inner coherence. The paragon of this art is Piet Mondrian. A model of his apartment in New York, where he spent the last few years of his life, in Tate Modern’s show is a glimpse into a world of intercrossed grids and pulses of colour, floating in space with musical harmony and tranquil conviction: a utopian vision just under the surface of every day life.
To reach this vision, Mondrian had to go through a series of inner and outer changes, stimulated by encounters with the revolutionary art movements of his time. Yet his closest allies, the De Stijl movement, who shared his love of primary colours and black lines, don’t get a look-in here. Instead, Mondrian’s art is hammered into his mystical religious interests, because this is all he shared with the Swedish medium and artist Hilma af Klint. She gets equal billing with Mondrian for her paintings that illustrate the ideas of the spiritualist movement and her own transcendental experiences. She would look better in another context – she has been rediscovered partly because she resembles 21st-century artists – but putting her next to one of the very greatest modernists does her no favours.
It’s a cruel way of showing Af Klint and a highly eccentric view of Mondrian. We don’t get Gerrit Rietveld’s 1917 De Stijl Chair, but we do get drawings and writings by the spiritualists Annie Besant and CW Leadbeater. The art is missing from this version of art history. Spiritualism explains Af Klint’s works because she really was finding ways to visualise mediumship and revelation. But it is a misguided way to look at Mondrian.
In a room dedicated to their flower studies, Af Klint’s are dry, pedantic drawings. His are captivating reveries. In Mondrian’s 1908 painting Metamorphosis, a white bloom seems to change into a human skull. The centre of a sunflower seems to become a bleak cyclops eye, in his Dying Sunflower I and II, from the same year.
Didn’t the curators think, when they were gathering such works: “Hang on, isn’t Mondrian obviously the better artist?” For they have borrowed some superlative examples of his art as if to systematically demonstrate that. The Blue Tree and The Red Tree, both painted near the end of the 1900s, develop the expressionism of his sunflowers into romantic gnarled claws of trees in pulsing skies: the visible world on the threshold of apocalypse. Is this a religious intimation shaped by the spiritualist movement? Maybe, but it is also a brilliant extrapolation from the development of modern art to that moment: you can see he is looking hard at Van Gogh’s trees and Cézanne’s mountain. Then he sees the revolutionary cubist paintings of Picasso and Braque in Paris, and takes their cue to dismantle reality into shimmering chunks and opal intuitions in his 1912 work The Flowering Apple Tree: from here, he steps further through the looking-glass, seeing pink and blue squares materialise from nowhere and crosses floating in the void. Nearly in the pure utopian place he’s searching for – nearly, nearly.
By contrast Af Klint has no hesitation. She is drawing flowers and landscapes one minute and the next is depicting the fantastic realm of the Tree of Knowledge in her 1913 W Series. By 1920 she is painting multicoloured tower-like forms with pointy tops.
So, did she pioneer abstract art before Mondrian as her enthusiasts claim? It’s a question badly put because they were not the only two abstract artists of their age. This exhibition ignores Russia’s abstract artists who also had mystical interests: surely if anything Malevich’s Black Square, painted in 1913, has priority. It’s going a bit far in boycotting Russia to exclude it from the story of modern art: to me, Af Klint’s pointy towers seem influenced by suprematism and constructivism. But the real breakthrough was cubism, as Mondrian so clearly sees in his 1914 Composition in Oval with Colour Planes 2, in which the typical “cubes” of a Braque or Picasso still life have been cleansed of any reference to real objects: the void beckons, beautifully.
The real reason it’s daft to argue about priority is that, as this show exposes, it isn’t what you do, it’s the way you do it that counts. If Af Klint and Mondrian are both painters of an invisible world, this does not make them artistic peers. It’s the very caution in Mondrian’s adventuring, his determination to proceed with intensity and truth into a new world, that makes his art so engrossing and profound. Whereas you don’t get a sense of artistic questing with Af Klint.
Any saving graces this show might have are blown apart in its later rooms that give short shrift to Mondrian’s mature Platonic paintings and lots of space to Af Klint’s, not to mention various obscure esoterica. Just for a minute, I thought they might have borrowed Mondrian’s joyous last testament Broadway Boogie Woogie from MoMA. But no such luck. No way is Mondrian going to be allowed to dance out of here alive.
• Hilma af Klint and Piet Mondrian: Forms of Life is at Tate Modern, London, from 20 April to 3 September.