The paintings are brown and grey, with spaces of white canvas turned cream with time. They are almost 100 years old. In the museum, you tend to pass them by. There are so many modern movements that are easier to enjoy than cubism. In the next room, those crazy Italian futurists offer a more spectacular, understandable theatre of time and space. The Dadaist Duchamp's bicycle wheel conveys the enigma of the universe. The surrealists display their sexualities. And so it goes.
We tend to see ourselves as more sophisticated than our great-grandparents. Many of the assumptions of the world a century ago have been so overturned that you would think the paintings Pablo Picasso and Georges Braque, produced between 1907 and the first world war, would make perfect sense today, and even appear a little naive. Yet their difficulty is not of a type that recedes with familiarity. Cubism is like a maths exam at the gateway to modern art. The paintings are uniquely unyielding.
But modern art in its later manifestations is no longer unpopular; most of us can enjoy or at least be provoked by it. This is because its language is democratic. You can decide if you do or don't like the candidates for this year's Turner prize without having to bring anything to them except your intuitions; the vocabulary of contemporary art is that of everyday experience. So is that of cubism - in a different and far more threatening way.
Art today is made from the building blocks of ordinary life. Cubism took these building blocks, or working premises, apart. Most art confirms our sense of who we are and how we live. Cubism suggests that our real existence eludes the images and stories we constantly make of it. "I went to the cafe" - cubism asks what a cafe is, what it is to go, and, most provocatively of all, who the hell you are. It is philosophical. This is why it remains undomesticated, while all other avant gardes can be turned into decoration or romance.
Paradoxically, cubism is difficult not because it is abstract but because it is descriptive. If it were abstract, we could let go, relax, be moved. But Picasso and Braque were not abstract painters, and cubism claims not to be beautiful, but true. It takes seriously the avowed aim of every painter since the Renaissance to depict the world as it is. Yet in trying honestly to account for humble, everyday experiences such as looking at a bottle, a pipe and a newspaper on a table, or at a friend or lover sitting in an armchair, the cubists discover complexities so exhausting that modern art has largely turned away from them ever since. We just don't expect art to make us work as hard as this. It is one thing to like or dislike an avant garde work, to "see something" or "see nothing". It's quite another to be told the world is profoundly different from the way we assume it to be. There's a fundamental difference between cubism and later modern art.
Most modern painting is stylish. It uses geometrical forms rhetorically. In revolutionary Russia, black squares and suprematist constellations of bars and pyramids became a shorthand for a new society. In Mussolini's Italy, futurist images of bodies hurtling through space became icons of militarism. Today, such modern geometries are as likely to be found on an album cover as in an art gallery.
Cubism was never a style in that sense. It was an inquiry. Picasso and Braque were lucky enough to be young - Picasso was 28 in 1909, Braque 27 - at a time of intellectual revolution. Habits of perception and assumptions about the nature of things that had been stable since the 17th century were falling away. Arthur I Miller's 2001 book Einstein, Picasso: Space, Time and the Beauty that Causes Havoc demonstrates how uncannily Picasso's discovery of cubism parallelled Einstein's contemporary theories of special and general relativity. In science, mathematics and philosophy, the laws of a clockwork universe established by Sir Isaac Newton in the Baroque age were giving way before the first world war to extraordinary notions - that time and space are one, that light waves curve, that no two observers ever see exactly the same thing.
Picasso and Einstein, Miller has shown, were both influenced by the French thinker Henri Poincaré, who published his book La Science et l'Hypothèse in 1902. In it he argued that, far from being universally or absolutely true, the Euclidean geometry that had defined mathematics since ancient times was only one of many possible systems, its three dimensions nothing like the only ones that could be conceived. But, said Poincaré, Euclid's is the most "convenient" set of assumptions with which to negotiate life. Thinking in three dimensions is practical, it seems to match our experience and speculation about a fourth does not help you to bake a baguette. Einstein, speculating on the basic premises of physics while working in the patents office in Bern, found Poincaré's relativism liberating.
Picasso learned about his ideas through the mathematician Maurice Princet, who was a regular at Montmartre cafe tables. Picasso's friend André Salmon wrote that Princet "preoccupies himself especially with painters who disdain ancient perspective. He praises them for no longer trusting the illusory optics of not long ago... "
Mathematicians, philosophers and physicists at the beginning of the 20th century were recognising that many absolute truths were convenient caricatures of a universe that might be far stranger, far further from common sense than anyone thought. Western painting had its own scientific assumptions, established in the Renaissance. Picasso and Braque unmasked these as conventions. The concepts of absolute gravity and time that gave way to relative ones in the early 20th century had been established by Newton in the 1600s. The doctrine of single-point perspective, whose inadequacies Braque and Picasso exposed, had been asserted by Leon Battista Alberti and Filippo Brunelleschi two centuries before.
The perspective system invented in Florence in the 15th century was a shorthand for the way things looked, a brilliantly usable fiction of the appearance of the world. Our sense impressions are complicated, chaotic data that the brain has to make sense of. Seeing in pictures appears to be necessary in our lives. Alberti and Brunelleschi showed how those pictures can be made consistent and logical by fixing a distant point towards which objects recede - what's further away looks smaller than what's near. The inventors did not make their intellectual revolution against this centuries-old system in a cool, considered mood, but with turbulence and fury. There was a violence in their assault on perspective.
Picasso's first essay in the new painting, Les Demoiselles d'Avignon (1907), associates the death of the picture with sexual aggression and "primitive" release. It is an overturning of civilised lies, one of which is the neat illusion of perspective. Braque put his anger into words. "The whole Renaissance tradition is antipathetic to me," he said. "The hard-and-fast rules of perspective, which it succeeded in imposing on art, were a ghastly mistake... "
Picasso painted the Portrait of Daniel-Henry Kahnweiler, the art dealer whose brother's collection of cubism goes on view shortly at Tate Modern, in Paris in the last months of 1910. Hanging today in the Art Institute of Chicago, this is one of the definitive masterpieces of cubist painting. There is, plainly, no deep or orderly pictorial space receding to a single vanishing point in this picture. And the word "picture" seems highly inappropriate. It is not hard to see a human figure in the painting: Kahnweiler's hair and nose, his crossed hands, are crisply cartooned. And yet, when you look again, they're not there at all. What seemed to be an eye is just a triangular interstice in the multiplicity of unfinished planes that form the painting. This is not an image of someone, but an exposition of everything that is suppressed in recognising an image. In place of hair colour, habits, clothes, that smile, Picasso paints the rubble of perceptions that are glimpsed and held just for a second, that any abstraction of experience must suppress as irrelevant.
What Picasso's Portrait of Daniel-Henry Kahnweiler is emphatically not is a cold, logical puzzle to be solved. The name "cubism" was coined by a hostile critic and tells us nothing about the real flavour of these paintings. Kahnweiler inhabits not a geometrical diagram but a dense drawing of many textures. Picasso was a very physical, emotional man, and his cubism is not an attempt scientifically to account for the world so much as to experience it more fully. Braque hated the way traditional perspective "forces the objects in a painting to disappear away from the beholder instead of bringing them within his reach, as painting should". Picasso's Kahnweiler is a complicated object whose contours elude us, yet whose mass we intuit. He is as real and baffling as the universe we inhabit.
We can't go around every day acknowledging that space and time are a continuum. We know clock time is a convention but that is no help when you're late for a meeting. In the same way, the insights of cubist painting are useless. It doesn't help to know that the form you call a bottle is really a little universe of hardness, transparency, tubular geometry, containing taste, memory, and all the other things a cubist painter finds in a bottle on a cafe table. Cubism is as spiritual as it is scientific. To live the cubist way would mean to be alive to the texture, weight and fragmentary beauty of the world. It would take for ever to appreciate a bowl of fruit.
But we haven't any more time to live that way than the Victorians had. Because it can never be completed, the cubist revolution will never end. Cubist paintings will always be the least assimilable, and greatest, paintings of the 20th century. They will always contain a universe of expanded possibility.
· Cubism and its Legacy: The Gift of Gustav and Elly Kahnweiler is at Tate Modern, London SE1, from Monday May 24. Details: 020-7887 8008.
