Musée d'Orsay audio guide,
five stops, free.

Stand close enough that the crowd breaks up into blobs of paint, then take three paces back and watch it reassemble. That is the trick of this canvas, and Renoir knew what he was doing.

It is a Sunday afternoon in 1876 at the open-air dance garden of the moulin de la Galette, up on the butte of Montmartre, and he painted it on the spot, outdoors, the rule the Impressionists had set themselves. His friend Georges Rivière, who is somewhere in this picture, wrote later that the wind kept threatening to carry the canvas away.

Nobody here is a professional model. Every face belongs to somebody Renoir knew: painter friends, and young working women of Montmartre whom he paid to sit. Rivière published his memories in 1921 and named them. Henriette Anna Lebœuf, called Margot, who was very close to Renoir and who died three years after this, aged twenty-three. Two sisters, Jeanne and Estelle, both seamstresses. The painters Franc-Lamy and Norbert Gœneutte. Paul Lhote and Pierre-Eugène Lestringuez, who would both stand as witnesses at Renoir's wedding.

Now look at the focus. Most painters keep the front sharp and let the distance dissolve. Renoir blurs the whole thing, front to back, and gives you depth only by making people smaller. The one thing he really describes is light: pale patches scattered unevenly across a bluish ground, as though they had dropped through the leaves onto a hat, a shoulder, a patch of dirt. Find the couple at the left. They are standing in a pool of it, and her pale pink dress pushes them out of the crowd towards you.

Rivière reviewed it at the third Impressionist exhibition in April 1877 and called it a page of history, a precious monument of Parisian life, rigorously exact. Two years later Gustave Caillebotte bought it, and in a self-portrait of that same year painted himself at his easel with this canvas behind him. He left it to the French state when he died in 1894.

There is a second version, smaller, almost identical, painted more loosely, and nobody knows which of the two came first, because the 1877 catalogue printed no dimensions. In May 1990 the smaller one sold in New York for 78 million dollars to a Japanese paper magnate, who announced the following year that he meant to have it cremated with him. It did not come to that: his companies ran into serious trouble, and the bankers holding the picture as collateral arranged a quiet sale instead. It is thought to be in Switzerland now, in a private house, where nobody gets to step back three paces.

He is walking. All four legs are in motion and the weight is carried forward, which is why the English title is often Polar Bear in Stride rather than anything about a bear standing still.

Now look for the fur. There isn't any. François Pompon smoothed the entire surface flat, and that was the whole point. From 1905 he set about simplifying his animals, taking off everything he called falbalas, frills, until what was left was a shape and the way light travelled over it. In 1922 he put a large white bear into the Salon d'Automne, and it cut straight across every other thing in the room, because everything else was still nineteenth-century sculpture.

He was sixty-seven years old. That is the part worth carrying out of this hall. Pompon was born at Saulieu in Burgundy in 1855, the son of a cabinet maker. At fifteen he was apprenticed to a firm in Dijon that carved funerary monuments. He then spent most of his working life as somebody else's hands, a craftsman for Antonin Mercié and Alexandre Falguière, then in Auguste Rodin's studio from 1890, running it by 1893, and after that nearly twenty years with Saint-Marceaux. Rodin looked at a piece of his and told him he would be a great artist. He first showed at the Salon in 1879, with a figure of Victor Hugo's Cosette. It then took another forty-three years.

This is not the bear from the Salon; that plaster is at Valenciennes. The French state commissioned this one in 1927, for twenty-five thousand francs, for the Musée du Luxembourg. It was cut by a praticien, a professional carver, named Jean-Joachim Supéry, working under Pompon's supervision, and delivered on the sixteenth of February 1929. And whatever the guidebooks tell you, it is not marble. It is pierre de Lens, a limestone, which is why it holds that soft chalky light in a hall otherwise full of bronze.

The applause of 1922 finally let him work for himself. He made a monumental stag for a square at Arnhem in the Netherlands and a bull for his home town, and before he died in 1933 he gave nearly three hundred of his own plasters, terracottas and bronzes to the museum at Dijon. Other foundries seized on the name and turned out fakes, a lot of them very poor. Brâncuși was paying attention.

One last thing to notice while he walks past you. The Sèvres factory began issuing him in porcelain in 1924, and in 1925 the designer Jacques-Émile Ruhlmann put him in two rooms at the great decorative arts exhibition in Paris. This animal was a piece of furniture in fashionable France before he was a museum piece.

She is looking at you. Not past you, not down, not into the middle distance where a nude is supposed to look. Straight out, level, with an expression that gives nothing back. That is the scandal. Everything else in this painting is an argument about that one decision.

Manet finished it in 1863, did not show it until the Salon of 1865, and when he did, Paris lost its temper. Two years earlier Alexandre Cabanel had exhibited a Birth of Venus and nobody had objected to any of it. The medal of honour went to Cabanel; the scandal went to Manet. In 1863 a naked woman was entirely acceptable so long as she was a goddess, or somewhere agreeably far away, and so long as she seemed surprised rather than posed. This woman is neither. She is a particular person in a Paris bedroom, and she is showing herself on purpose.

The picture is built on a famous one. Manet went to Italy in 1853 and copied Titian's Venus of Urbino five times over, and the arrangement here is Titian's, down to the way the background splits in two behind her. Titian's Venus curls her left hand in a way that invites. This left hand is flat and shut. And where Titian put a sleeping dog to stand for fidelity, there is a black cat, awake, back up, tail up.

The details point the same way. Olympia was a working name for a Paris prostitute in the 1860s, and the title probably came from Manet's friend the critic Zacharie Astruc, whose verses were printed with the picture in the catalogue. The bouquet is a florist's, and it means a client has arrived. The maid holding it was modelled by a woman known only as Laure, and for a century art historians wrote at length about the white figure and barely mentioned the black one. The woman on the bed was Victorine Meurent, nineteen, and not only a model: her own paintings were accepted at the Salon in 1876, 1879, 1885 and 1904.

The critics were vicious. Paul de Saint-Victor called it Monsieur Manet's high, gamey Olympia. Baudelaire and Zola defended him and it still knocked him flat. Zola's line is the best summary anyone managed: when our artists give us Venuses they correct nature, they lie; Manet asked why lie, and introduced us to a girl of our own time, the kind you meet on the pavement.

Look at the light before you move on. Michel Foucault pointed out that it falls on her from exactly where you are standing, so that the beam and your gaze are the same thing, and the painting hands you the undressing. Then her right wrist: Manet's niece Julie said the gold bracelet was his mother's, with a lock of his own childhood hair inside the locket.

The rest is a rescue. At the sale of Manet's studio in 1884 the scandal was still warm enough that his widow Suzanne bought the picture back herself. In 1888 John Singer Sargent warned Claude Monet that she was in difficulty and might sell to an American, and Monet spent a year raising the twenty thousand francs she was asking, by public subscription. Twenty thousand was cheap: Millets were fetching seven hundred and fifty thousand at the time. The Louvre still did not want her, and a misunderstanding in the press ended with Manet's oldest friend, a former arts minister, challenging Monet to a duel. The compromise was the Musée du Luxembourg, in 1890. She reached the Louvre seventeen years after that, and this building in 1986.