Michelangelo once made a snowman. It's recorded by the art historian Giorgio Vasari that "one winter, when a great deal of snow fell in Florence, [Piero de' Medici] had him make in his courtyard a statue of snow, which was very beautiful". Nothing else is known about the snowman. All that is known for certain is that it happened; it was very beautiful; and it melted.

There are other lost or unknown works by Michelangelo. Some he never started, like his plan to carve an entire mountain into a human figure. Others we have to guess at their final effect, left incomplete or abandoned at an early stage, like the Battle of Cascina fresco. But surely the snowman is the perfect, archetypal lost work of art. We can just respond to it with pure enthusiasm, undisturbed by knowing anything about it.

We can test our reactions, since this week a pair of long-lost paintings surfaced from unusual seclusion. In 1970, two works by Paul Gauguin and Pierre Bonnard were stolen from a house in Regent's Park. Subsequently they seem to have been abandoned on a train travelling to Italy. In 1975, an art-loving employee of Fiat paid 45,000 lira, (about £19), for them in a lost property auction. They remained in his kitchen, first in Turin and then, when he retired, in Sicily, when his son recognised similarities with other Gauguins.

There are quite a few other still lives by Gauguin, some of which have never been stolen or lost. For the moment, it seems hard to raise any interest in them. Works of art, after all, are often complicated and puzzling, even if they've hung on the walls of the National Gallery for decades. They don't quite mean what we want them to mean. When they do, they are not art but kitsch.

But lost works of art are much more convenient, and the less known about them the better. You could, if you chose, rhapsodise about the lost Boston Vermeer, stolen in 1990, but it is very well known from modern photographs and memories. Rather better are the Gustav Klimt allegories for the University of Vienna that were lost as Schloss Immendorf was set on fire by retreating German troops in 1945. We know they must have been major statements, and we have some photographs of them. But here's the thing – the photographs are monochrome and few in number. Other Klimts that survive can be tiresome, surprising, even embarrassing, like the monsters in the Beethoven Frieze in the Secession building in Vienna. Our feeble imaginations are set to work on the suggestive, inadequate images of the university allegories and construct something much more pleasing.

When long-lost works of art surface when nothing whatsoever is known about them, the result can be confusing. Sometimes this is because the work of art was never very good, compared to our wishes. Vladimir Nabokov's sketches for his final novel, The Original of Laura, were finally published in 2009. The result turned out to be even worse than Nabokov's other last novels, currently selling in very small numbers. In the minds of his fans, reality was worse than the kitsch reconstruction.

If a great work of art ever surfaced in this way, would we recognise it as such? Perhaps the most feverishly examined lost work of art is Leonardo da Vinci's Battle of Anghiari. We know it was in part executed for the Palazzo Vecchio in Florence and was painted over in the late 16th century. In 2012 a team of Italian scholars claimed that they had evidence that it still existed, behind a false wall. Work has been suspended because of ferocious arguments about propriety, but can we really think that the Leonardo we would love to see would be an immensely involved battle scene? There are plenty of those, by the greatest Renaissance painters, and 21st-century taste walks right by them.

Works of art, literature, and music have their own ideas of what to do with us, and a resistance to our necessarily more ordinary ideas. When a Gauguin that was always unfamiliar returns from a Sicilian kitchen, we ought to be thankful that it was in the possession for the last 40 years of someone who innocently loved it and took care of it.

But then we look at the painting itself. It is cut off in strange places, the fruit is grouped oddly in three ensembles and there is a sleeping animal on the floor at the top. It is not very obviously in the good taste that the words "still life" often imply. It has a particular quality of great art: it is interesting. So it surfaces, and goes back into the realm of the confounding that great art inhabits when it can be seen and not just comfortingly imagined.