Gallery going is usually a sedate affair – hushed and reverential – and that’s what I expected in the southern Netherlands when I went to ’s-Hertogenbosch, or Den Bosch, as it is colloquially known, for the extraordinary exhibition there of the city’s best-known son. Straight off the train, however, I walked into a scene of kermesse, or festival, that could have been painted by Hieronymus Bosch’s most talented follower, Pieter Bruegel. The Den Bosch carnival was in full flow, a riotous Lenten release that often featured in 16th-century paintings and continues today, pulling in revellers from the province of Brabant and beyond.

In Bosch’s day the festival was marked with games of goose pulling and rooster smashing, cat burning, wolf hunting and herring biting (exactly as they sound). Today’s burghers are more RSPCA-friendly, and carouse in circus-ringmaster costumes decorated in badges while wearing scarves and long socks in white, yellow and red, colours that originally signified the city’s allegiance to the Catholic Church and Brabant. The entertainment comes not in the form of animal cruelty, but tuba bands and drum groups that belt out folk and drinking songs as well as Beach Boys medleys. Beer plays a leading role.

As it works its way around the city’s streets the parade passes, appropriately, in front of the doors of the Noordbrabants Museum. The subject on display there, Hieronymus Bosch (c.1450-1516), was one of the great chroniclers of human folly and an unparalleled inventor of the types of hybrid creatures that these carnivalers – men dressed as bananas on bicycles, women with elephant tea-cosy headdresses, giant fish and superheroes – distantly ape. Carnival is a celebration of inversion where the natural order is turned on its head and today’s celebrations are an inversion, too, of the world on display in Bosch’s paintings.

Bosch did not celebrate human folly, he painted it as an affront, innate perhaps, to God’s order. Mankind, for him, found it so much easier to disobey God’s strictures than to obey them, and humanity was one long parade. The people in his pictures – the misers, the licentious, the drunken, as well as, far less often, the devout – are always on their way to one of only two destinations: heaven or hell.

The new Bosch show is far more than a remarkable, once-in-several-generations exhibition: it is also a remarkable piece of exhibition-making. It marks the 500th anniversary of the painter’s death and includes 17 of just 24 paintings fully accredited to him and 19 of his 20 existing drawings. Certainly never before – not even in his own studio – and almost certainly never again, have so many of his pictures been gathered in one place. About 20 institutions from ten countries have lent works to a provincial gallery that has nothing to offer them by way of return loans, the usual bartering currency between museums.

The Prado, the Accademia in Venice, the Louvre, the Met et al were persuaded to lend their infinitely precious pictures in part through altruism and because other major institutions were lending (it doesn’t do to look parsimonious), and partly because of the Bosch Research and Conservation Project. The BRCP is the definitive adjudicator on what is and isn’t a Bosch and, on the back of the exhibition, it is compiling a two-volume monograph comprising a full catalogue and a report of technical analysis of all his works. At the same time as knocking back attributions, it has unearthed two new pictures – a Temptation of St Anthony from Kansas and a drawing, Infernal Landscape, from a Belgian private collection, both of which are included in the show. The exhibition has also reunited dispersed panels from the same works for the first time since they left the churches for which they were painted and the organisers have arranged (and funded) the restoration of nine of the paintings. This show, in other words, is only part of a much wider project.

So what is it about Bosch that is worth the fuss? His dates almost exactly coincide with those of Leonardo da Vinci (1452-1519) but they painted worlds that could not be less alike. Leonardo was a humanist who saw and tried to depict man as the centre of the universe, as fully fledged, sentient, an agent of free will and made of the same materials as nature – veins branching like the tributaries of rivers, hair flowing like torrents. He wanted, too, to show what painting could do, that it could represent internal thought and indeed internal biology as well as outward appearances.

About 800 miles to the north, across the Alps, Bosch felt hardly a flutter of the Renaissance. He was, for all the later claims of his psychological modernity, a painter of the Middle Ages: an orthodox Catholic who painted orthodox subjects – praying saints in the wilderness and Christ en route to Golgotha and crucifixion – with a miniaturist detail that had its roots in Gothic manuscript illumination and the inventive marginalia of monks left to their own devices in the scriptorium.

Bosch, unlike Leonardo, was no Renaissance man: he hardly travelled outside Den Bosch, where he was a figure of civic importance, nor did he experiment with science or engineering or the proportions of the human figure, or even the media in which he worked. He was not taken up by a royal or princely court (although the Spanish overlords of Brabant collected his pictures), but painted largely for religious patrons and even joined a religious confraternity (there is barely a secular picture in all his work) while running an efficient and profitable studio in Den Bosch’s market square. The world depicted by some Renaissance artists seems familiar – it is ours, wearing different clothes – but not Bosch’s.

Bosch was very much a painter of his time and place, his art being marked by the northern emphasis on tradition and minute observation of nature; where he was unique was in his imagination. He was sometimes known as “the Devil’s painter” and he conjured up a monstrous world of damnation that is unequalled in art. If he examined with the utmost attention to detail such mundane items as fish, rabbits, birds, knives and wine jugs it was so that he could, like some painterly Dr Moreau, graft them into monsters – humanoids with avian heads, sword-wielding sprites with a kitchen funnel for a helmet, huge spiked insects, heads attached to feet without an intervening body, creeping scaled or feathered creatures.

The whole nightmarish, genetically modified bestiary marauds its way through burning landscapes (as a young boy he had watched a huge fire consume 4,000 houses in Den Bosch), flaying, boiling and impaling as it goes. There is a tradition of pictures of the Last Judgement known as “doom” paintings and Bosch was its greatest practitioner: he painted paradise, too, most notably in the Prado’s Garden of Earthly Delights (too fragile to travel to Den Bosch), but doom was his default and the devil is in his detail.

Whatever their ostensible subject, and in many cases it remains unclear exactly what that is, his paintings are about incident. An old and now discredited theory suggested that Bosch’s pictures related to the occult and that they were carefully coded works for fellow initiates; an alternative reading, one of many, is that they were meant not for a sophisticated but for an unsophisticated audience. The paintings act as a diabolical Where’s Wally?, inviting the layman to comb every inch; diverting, terrifying and fascinating the eye; and, through their accretion of detail, imparting a message of ­human sin.

The monsters, in this reading, are fallen men and women who, because they have forfeited the grace of God, have undergone a process of reverse evolution and lost their human form to become the agents of evil. And Bosch didn’t absolve himself. We know next to nothing about his life outside sparse mentions in civic documents and the account books of the Illustrious Brotherhood of Our Blessed Lady, or about his thoughts. What evidence there is suggests a solid and industrious citizen. Look though at his painting of Saint John on Patmos (c.1490-95) and there next to the saint is Bosch himself, in a tiny self-portrait as a monster. He has carefully depicted his distinctive face, with a long spectacles-bearing nose, but placed it on a body with feathered wings, a bulbous insect torso and reptilian legs.

To make the identification clear he stands directly above his own signature – this painting was the first he signed with his brand name, Hieronymus Bosch, rather than his birth name, Jheronimus van Aken. John of Patmos was the author of the Book of Revelation, which contains his vision of the apocalypse. “My kind of saint,” Bosch is saying. A companion painting for the same altarpiece, showing John the Baptist, is unsigned.

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Almost the only insight Bosch gave to his thinking are the words he wrote at the top of a drawing illustrating the proverb “The wood has ears, the field has eyes” (which can be interpreted as either “be vigilant” or “keep shtum”). “Poor is the mind,” wrote Bosch, “that always uses the inventions of others and invents nothing itself.” It is a telling admonition to himself and became his motto.

Being profligate with his invention didn’t mean he didn’t have to work at it. His drawings are littered with ideas for the sorts of creatures that appeared in his paintings but are perfected with the draughtsmanship of a naturalist. A tiny sheet from Berlin, for instance, has two scuttling furry and feathered, lice-like animals that are to all intents and purposes life drawings, albeit of imaginary beasts. And what would it look like, he asked himself, to come across a man who has crawled into a basket with his breeches pulled down and birds emerging from between his buttocks? So he drew it to see, and added for good measure a man using a lute to hammer the birds back in, an old woman with tongs gasping in astonishment and a crowd of children catching the excreted birds. Why have only one caprice when you can have four?

Small wonder that the surrealists adopted him as a forefather or that he has been a favourite topic for psychoanalytical interpretation (Jung called him “the discoverer of the unconscious”). The man crawling into the basket is just one example of immersion among many; scour the pictures and there are figures burying themselves in giant eggs, jars, grottoes, bells, helmets, mouths, peony buds and cooking pots, as well as, of course, disappearing into the gullets of innumerable voracious beasts. Bosch’s paintings are a Freudian field day.

They are also more than an accumulation of detail. One of his great triptychs, The Haywain (1510-16), from the Prado (the first time it has left Spain in 450 years), offers the viewer an interpretation of the porous membrane between the divine and the human. The left wing shows the story of Adam and Eve and their expulsion from the Garden of Eden; the results of the Fall continue in the central panel showing a huge hay wain being pulled by monsters with people fighting each other to grab handfuls of straw – illustrating the Flemish proverb “The world is a hay cart and every­one takes what they want from it”. Heedless selfishness reaches its endgame in the right-hand wing, a scene of hellish despoliation and slaughter. The picture is meant to be read left to right like a book. Human sin has its origins and its consequences.

Some early commentators regarded Bosch not as a moralist at all but merely as a painter of titillating images. In 1560 the Spanish writer Felipe de Guevara dismissed him as “the inventor of monsters and chimeras” and 50 years later the Dutch art writer Karel van Mander described the paintings as “wondrous and strange fantasies” that were “often less pleasant than gruesome to look at”. No mention of religion.

No mention either of his detachment. There is a matter-of-factness to Bosch’s art: here is religion and here is humanity, he says, they don’t always interact as they should and that’s just the way things are. He doesn’t blame human beings for their wrong choices because the nature of life is to be a passenger on the ship of fools, a reveller at Vanity Fair, and to caper in the dance of death.

“Hieronymus Bosch: Visions of Genius” runs until 8 May. Details: hnbm.nl