MoMA audio guide,
five stops, free.

Most people's first thought is that it is smaller than they imagined. Seventy-four centimetres by ninety-two, not much bigger than a window, which is fitting, because a window is where it started.

In 1889 and 1890 Vincent van Gogh spent twelve months at the asylum of Saint-Paul-de-Mausole in Saint-Rémy, in the south of France, trying to find some relief from his mental illness. His bedroom window looked east. He painted that view twenty-one times. This is the only version set at night.

In early June he wrote to his brother Theo: this morning I saw the countryside from my window a long time before sunrise, with nothing but the morning star, which looked very big. Find it now. It is the brightest light in the sky, just left of centre, next to the dark cypress, ringed in white and yellow. That is Venus. Astronomers have checked, and in the spring of 1889 it really was visible at dawn over Provence, close to as bright as it ever gets.

So part of this is observation. A lot of it is not. It is a night scene painted in daylight, in several sessions. The village below the hills could not be seen from his window at all; he took it from other views. The cypress on the left was much further away than this, and he pulled it forward until it almost touches the top of the canvas. And look at the church steeple, thin and sharp. That is a steeple from Holland, where he grew up, not from the south of France.

Then there is the paint. The sky fills three-quarters of the picture and it is built of short, heavy strokes that you can see from where you are standing. When scientists at the Rochester Institute of Technology and at MoMA analysed it, they found ultramarine and cobalt blue in the sky, and for the stars and the moon a rare pigment called Indian yellow, mixed with zinc yellow.

Van Gogh was not proud of it. In September 1889 he listed it as a night study among a batch of paintings for Theo, and said most of that batch told him nothing; when he held back three canvases to save on postage, this was one of them, and it only went to Paris on the twenty-eighth of September. In a letter to the painter Émile Bernard at the end of November he called it a failure. But he had once written down exactly what night skies meant to him: just as we take the train to go to Tarascon or Rouen, we take death to go to a star.

MoMA acquired it in 1941 from the dealer Paul Rosenberg, by exchange. According to the museum's director Glenn Lowry, the price was two paintings by Cézanne and one by Toulouse-Lautrec. The museum almost never lends it out, so for more than eighty years the place to see this sky has been Midtown Manhattan, not Provence.

Nearly four metres of canvas, and four colours. Blue for the sky. Green for the hill. Pale pink for the five bodies, and black for the hair and the outlines. That is the whole painting, and it is enough to make the room feel as if it is turning.

In March 1909 a Russian businessman and collector named Sergei Shchukin commissioned two large decorative panels from Henri Matisse, one called Dance and one called Music, for the staircase of his house in Moscow. Dance was to hang on the landing. Matisse painted this canvas first, quickly, as a study to work out the composition. The finished Dance, painted in a strong, hot red, was shown at the Salon d'Automne in Paris in 1910 and hung on Shchukin's staircase until the Russian Revolution of 1917. It is in the Hermitage in Saint Petersburg now. The study is the one in front of you.

People hated it at first. The bodies were so simplified and the space so flat that critics called it inept, or crude on purpose. Matisse's answer was that it had life and rhythm, and he meant it as a deliberate choice. That same year he said that photography could now record details a hundred times better and more quickly than any painter, so the painter no longer had to bother. What was left for painting was the thing a camera could not catch: movement, feeling, the swing of a line.

Follow that line. The figure on the left is one continuous curve from her raised arm down to her back foot. Now look at the front of the circle. Two dancers are stretching for each other's hands and they have not quite made it. The ring is open, right where you are standing, as if there is a place for one more.

Matisse thought highly of this first version. He painted it into the background of another picture, Nasturtiums with the Painting Dance I, in 1912. Nelson Rockefeller later gave it to MoMA in honour of Alfred Barr, the museum's first director, whose name is on these galleries. The gap between those two hands has never closed.

Nearly thirteen metres of pond, in three panels, and nowhere in it is there a horizon. That is the first thing to notice, and the reason this room feels different from every other room on the floor. There is no edge of the water, no bank, no sky overhead. The only sky is the one reflected in the pond, clouds turned lavender and floating among the lilies. Your eye has nowhere to stop, so it keeps going.

Walk the length of it. In the centre panel the lilies float in a bright pool of green and blue. On the left, thicker, darker strokes seep in from the edge. On the right, sky and water are swallowed up by reddish-green vegetation. MoMA's own description is that the whole thing hovers at the threshold of abstraction, and standing here it is easy to forget that this is a real pond, in a real garden, at Giverny in northwestern France.

Claude Monet spent the last years of his life painting that pond. He called these canvases his grandes décorations, and in 1915 he built a large new studio near his house to make them. From 1914 until his death in 1926 he produced some forty of these huge panels and kept reworking them, many while he was suffering from cataracts. After he died, twenty-two of them were installed on the curved walls of the Musée de l'Orangerie in Paris, his gift to France. The rest stayed in his studios until the late 1940s.

What brought them back was New York. In 1955 MoMA became the first museum in the United States to buy one of the big panels, and the reason had as much to do with the present as the past. Jackson Pollock and the Abstract Expressionists were making enormous paintings with no single focal point, and suddenly an old Impressionist's lily pond looked like the future.

Then, on the fifteenth of April 1958, a fire broke out on MoMA's second floor. Workmen installing air conditioning had been smoking near paint cans and sawdust. One of them died. The fire destroyed an eighteen-foot Monet Water Lilies. This triptych was acquired shortly afterwards, as its replacement. So the painting in front of you exists here because another one burned.