High range … Cézanne's mountainous masterpiece, Mont Sainte-Victoire, 1904-06 (oil on canvas). Photograph: Paul Cezanne/Getty Images/The Bridgeman Art Library
The 20th century began with a manpaintinga mountain. Cézanne's ultimate masterpieces of the 1900s pick apart the process of looking and reveal the infinite complexity of experience. Each brushstroke contains a novel. The intellectual revolutions of the modern age, from Freud to Einstein, all find their mirror in the tough revolutionary eye of Cézanne.
Masterpiece of mayhem … Picasso's Les Demoiselles d'Avignon (1907) at New York's MoMA. Photograph: Stan Honda/AFP/Getty Images
Picasso's most endlessly provocative painting still rattles and dazzles. It bursts out of the confines of pictorial space with a jagged madness. Flesh erupts from a blue crystal cavern. Faces are masks. The "primitive" art Picasso was looking at when he painted this masterpiece of mayhem licenses him to outdo surrealism, before surrealism ever began. Look into the eyes of his formidable whores, and be blinded.
Primitive sophistication … a visitor takes a picture of Matisse's The Dance at the State Hermitage museum in St Petersburg, Russia. Photograph: Sean Gallup/Getty
Matisse makes revolution look eternal. This abstract blaze of bodies in space looked like nothing else when it was created, was utterly new, and yet must also have appeared as timeless as it does today. Matisse takes the "primitive" passions that stirred his time and translates them into a casually sophisticated language steeped in art's long history. The result is a cave painting designed by Poussin. In this wildness the classical conceals itself.
This was painted when Braque and Picasso were "roped together like mountaineers", as they put it, to explore a new tactile universe. Cubism – as their revolution was nicknamed – rejected not just the convention of painting pictures, but the very expectation that art must be about the visible surfaces of the world. This and other Cubist paintings fumble for the form of things, trying to grasp the weight and heft of reality. In that attempt to know all the richness of experience, neat fictions of tidy portrayal disintegrate in a dark tumult of perceptions.
This hymn to speed, energy and athleticism comes from a time when the world was striding forward, convinced of the reality of human progress. Boccioni is the greatest artist, by a long chalk, of the Futurist movement. Like all Futurist art, this is a kind of propaganda, a deliberately brutal hymn to the new. But in imagining a soldier of the future, Boccioni creates a vision of the self stretched out in a cloud of spatial distortion, the ego vanishing in space-time.
The ultimate, most extreme and simplest work of abstract art painted in the early 20th century is a black square. Just that. Crackling with time, it survives as a baffling, unforgettable icon. Malevich, like other abstract artists including Kandinsky and Mondrian, had a quasi-religious vision. His black square has the terse authority of some unnameable revelation.
Réne Magritte – The Treachery of Images (1928-29)
For the surrealist movement, reality was a lie to be pierced by the truth of dreams. Magritte was the movement's resident philosopher. This is his most succinct demonstration that images are deceptive, names are arbitrary and objects themelves not the familiar things we expect, but incomprehensible stuff to which we give meaningless labels.
Mutt's nuts … Marcel Duchamp's 1917 work Fountain at the Pompidou centre in Paris. Photograph: AP
The century was not yet out of its teens. For most of the small minority aware of the experiments of modern art, the bright colours of Matisse were still shocking and Picasso's assaults on beauty were beyond the pale. What was anyone to make of the porcelain urinal Duchamp submitted to a New York art exhibition? Yet it took. Fountain, with its signature R Mutt and the date 1917, was photographed and remembered. It became art, and so changed art forever.
This epic constellation of visual jokes and scathing political jibes – its references to Weimar politicians and celebrities make it as dense to read as a Georgian political cartoon by Gillray – packs the punch of Dada, the most aggressive and yet the most human art movement of the 20th century. Directly rooted in everyday life ("cut with the kitchen knife") and happy to be part of the mix of media images the modern world pumps out, it nevertheless has the intensity of an abstract painting.
For a brief moment, the troubled and confused Pollock painted like an angel, seeing the crystalline web of the universe, the veins behind the eye. His labyrinths of raw paint lead the imagination inward, towards the unconscious depths, and outwards, to the limits of space. All art since is born out of his freedom.