In Albrecht Dürer’s print The Sea Monster, a woman lies, quite happy with her lot, on the back of a bizarre beast as he swims away with her. He has a scaly body, bearded human face and antlers. Wearing nothing much but a necklace, she rests her hand on her curvaceous hip as she watches the people screaming from shore, in front of a fairytale castle on a craggy hill. It is weird and it is wonderful. It also captures exactly what the National Gallery’s foray into Dürer’s wanderlust is about – or would be if it worked. When Dürer engraved this, in about 1498, he was eagerly assimilating what he’d seen on his first visit to Italy a few years earlier. Born in Nuremberg in 1471, the son of a goldsmith, Albrecht had barely begun his career when he set off across the Alps for Venice. There, he found a sexualised culture in which courtesans played prominent roles, licensed by pagan mythology. But Dürer doesn’t just bring the Renaissance home to Germany. He wildly transforms it. The Sea Monster takes Ovid’s story of Europa and the Bull, and turns the (literally) horny male creature into a beast straight out of northern forest folklore. In a nearby woodcut, he portrays the Whore of Babylon as an actual Venetian sex worker. Not that Dürer was heteronormative. On his next, better documented, trip to Venice he admired the physique and style of soldiers. His German friends teased him for picking up the ways they attributed to Italian artists (“Florenzer”, Florentine, was a German word for a homosexual) and joked that he grew his beard to impress his apprentice. Unfortunately, not much of this comes through in Dürer’s Journeys. It sounds like a great idea – a micro-history of the Renaissance through the eyes of an artist who loved to travel, first to Italy, later to the bustling Atlantic port of Antwerp where he encountered people and artworks from beyond Europe. But it doesn’t tell that story well or let us feel the force of those piercing eyes. It is not so much a magical mystery tour as a sedate plod. It will impress traditionalists as a no-nonsense dive into art history, free from annoying wall texts that denounce the past – this show only alludes to the grotesque antisemitic caricatures in Dürer’s Christ and the Doctors by explaining that the evil scholars “were often represented as caricatures of Jewish people in this period”. Well, clearly there’s no possible modern resonance to this hatred of Jews in an artist who came from Nuremberg. For all its apparent seriousness this exhibition fails to take you to the heart of Dürer. It even made me doubt my adoration of his art. The old-fashioned fustiness – some of the rooms are painted brown and brick as if to make you feel you are in a dusty library – can’t hide a lack of clear argument. The trouble starts before Dürer even sets out. However far he travelled he always came back to his starting point, Nuremberg. Yet we don’t get much sense of what life was like there: the walled community with its prayers and festivals; the local market where Dürer wasn’t too proud to let his mother flog his woodcuts. That lack of any sense of place pervades a big room about his second trip to Venice. You have to pinch yourself to realise that Giorgione painted his provocative bare-breasted Portrait of a Young Woman (Laura), in Venice when Dürer was there in 1506, and Titian was making his bones as Giorgione’s young rival. To judge from the assortment of drab paintings you can’t tell why Dürer went there or what there was to see. For all its ostentatious scholarly air this exhibition misses the point of Dürer’s journeys to Venice completely. It was this: as well as being thrilled by the freedom and sensuality of Venice, what struck Dürer in Italy was a new idea of the artist. Leonardo da Vinci, Michelangelo and Raphael were hitting the heights as well as Giorgione. With all these geniuses around someone needed to define genius itself – to consciously portray the artist, no longer as a servile artisan like Dürer’s father, but a godlike spirit of mysterious creative powers. It was Dürer, seeing the Italian Renaissance from outside, who worked this out. He’s the first artist who was conscious of living in a Renaissance – and who explicitly advances the idea of the modern artist, the genius. That is nearly lost here. But you can see it in his print Melencolia I, lent from the Fitzwilliam, Cambridge. In this unforgettable image Dürer personifies genius as a woman with her face in shadow, resting her head on her hand as she sits paralysed among mathematical and sculptural tools. It is a deeply insightful interpretation of his Italian contemporaries Leonardo and Michelangelo who took pride in not finishing art, as it proved they were free minds, not craftsmanlike hacks. Dürer celebrates the creative melancholy of the genius awaiting inspiration. Then we’re off to Antwerp and Brussels. But the freshness and immediacy of Dürer’s own journal of his trip to the North Sea is totally drowned out by a pedantic array of drawings. And really, couldn’t the National Gallery have let its hair down to bring this long-ago age to life? I am not calling for a theme park boat trip up the Rhine but couldn’t they at least have brought in some objects to give a sense of the wonder of it all? For it was in the low lands that Dürer saw the golden, turquoise and feathered treasures of Moctezuma, sent as booty by Cortés to the new Emperor Charles V. He was amazed and humbled, writing of his admiration for “the craftsmen of distant lands”. It is the most fulsome tribute a European Renaissance artist ever paid to extra-European art. Some Aztec art from the British Museum would have set this show alight. It’s currently fashionable to attack exhibitions that pull the past uncomfortably into the present, that remind us that 18th-century Britain had a slave trade. But the past can also be killed by conservatism disguised as rigour. At times I lost sight of Dürer here. Travelling along the North Sea coast, he writes in his journal, he got trapped with other passengers on a boat that was suddenly pulled out to sea by a gale. While everyone stood paralysed, he took charge and commanded the vessel until they safely reached shore. With each exhibition that buries the excitement of the Renaissance as this one does, this dazzling age gets further away, as if Dürer had not saved that ship and we saw his strong features fade in the mist, receding not with a cancellation but a respectful whimper. Dürer’s Journeys: Travels of a Renaissance Artist is at the National Gallery, London, from 20 November to 27 February.