Why the sudden interest in Lucas Cranach? Having successfully avoided most people’s attention for half a millennium, he seems to be popping up all over the shop. Switch on the television drama Desperate Housewives, for instance, and the first image in the opening credits is an animated version of his Adam and Eve, successfully setting the slyly sexy tone for the suburban shenanigans ahead. Then there was that amusing squall in a teapot recently about a Cranach Venus that Transport for London refused to display on Underground platforms because the poster was deemed inappropriate. This cretinous decision, now reversed, was prompted by a shoddy piece of printing that made it appear as if Venus was showing off her pubic hair and a sexy cleft. She wasn’t. Her see-through veil had merely cast a suggestive shadow. You need to wait until the middle of the 19th century, and Courbet, before art dared to confront you with realistically painted pudenda.

It isn’t only into cheap media spotlights that Cranach has been thrust. The serious art institutions are also fascinated by him. Last year, the Courtauld Institute organised a wonderful little display devoted to his naughty Adam and Eve. Now a full career overview at the Royal Academy seeks to correct the two misconceptions that continue to circulate about our man: that slyly sexy Venuses were his main subject; and that he was a greedy churner-out of popular formats.

Max Friedländer, a regularly impressive German art historian who was rarely wrong about anything, supplied the most withering assessment of Cranach as far back as the 1930s, when he concluded, in his definitive tome on the artist: “Had Cranach died in 1505, he would have lived in our memory as an artist charged with dynamite. But he did not die until 1553, and instead of watching his powers explode, we see them fizzle out.” Ever since Friedländer wrote that, the rest of us have believed it.

The Academy, in a terrific display of art-historical chutzpah, begs to differ. And, because its show is arranged more or less chronologically, yet arrives at Cranach’s Venuses only in its final room, the first misconception, that sly nudes were his speciality, is easily corrected. The next accusation, that he spent two-thirds of his career phoning it in, is so deeply embedded that challenging it takes the length of the show.

Although Cranach was born in 1472, the earliest works we know by him were not painted until he was about 30 years old. So, the first decade of his output is still out there waiting to be discovered. Which means the opening sighting we have of him here, a gory Crucifixion attended by a band of voyeuristic Franconian nobles who’ve ridden in from the castle at the back, is already the work of a thoroughly accomplished artist. No build-up. No foreplay. And, just five years later, in 1505, he painted what many consider his masterpiece: an action-packed imagining of The Martyrdom of St Catherine.

Because we live in godless times, I cannot assume you know the story. If you don’t, this fireworks display of a painting may strike you as confusing. There’s so much going on in it. Catherine was a beautiful princess from Alexandria whose crime was to persuade 50 heathen philosophers to convert to Christianity. She was sentenced to torture on a wheel studded with spikes, but God destroyed this murderous wheel with a lightning bolt. There it is in the background of Cranach’s frantic crowd scene, being blown apart by a celestial bomb attack. The emperor Maxentius then ordered that Catherine be beheaded instead. And that is the moment we are witnessing: her imminent decapitation.

But look how inventively, and in how many happy directions, Cranach’s exciting painting strays off its narrative path. What is that executioner wearing? One of his legs sports a thigh-length boot, but the other does not. Half his outfit is white, while the other half is covered in multicoloured stripes. Look, too, at the mass of heaving bodies being blown up by the lightning. What impossible positions they adopt. With a colour scheme unlike any other of its times, and a cast of contortionists taking the bit parts, this great and mysterious painting makes instantly clear that we are in the presence of a Renaissance master with a spectacularly unique vision.

Cranach was from Kronach, in Franconia - a loaded stretch of Germany with Nuremburg in it, and Bayreuth, that nowadays constitutes northern Bavaria. This was also where his friend Martin Luther started Christianity’s big civil war, and the region has never since been able to decide if it is Catholic or Protestant. So it has zigzagged between the two positions, as, indeed, did the art of Cranach.

The fantastical religious paintings that surround The Martyrdom of St Catherine in the first outburst of his career confirm the impression that a momentous and unruly talent has been unleashed. Familiar subjects - the Crucifixion, the stigmatisation of St Francis - are reinvented outrageously by an artist determined not to do anything the way others did it. If the religious convolutions in the foregrounds are too complex for you, there are always the backgrounds to enjoy. Cranach was a superb landscapist who always set his biblical duels in recognisable stretches of Upper Franconia, where tottering Harry Potter castles wobble atop mysterious riverside crags.

Because his imagination darted about so much, there wasn’t much he didn’t try. There are portraits, altarpieces, bits of contemporary genre pictures that tug your heartstrings and ones that make you laugh. His woodcuts throb and squirm with events, like an angler’s worm tin. And a gorgeous nocturnal Nativity sets him the tough task of painting candlelit reflections at night. Nowhere does his art settle on a standard look.

I enjoyed, too, his sudden lurch into grotesqueness with a set of cruel paintings mocking the union first of toothless old men with young girls, then of toothless old women with young boys. Just when you think too many tankards of sarcasm are being emptied into Cranach’s art, he switches tack again with a series of noble portrait heads, produced in the unusual medium of oil on paper, that prove what an astute recorder of character he was. The young Luther, for one, stops being a famous name in a textbook and becomes a strange-looking fellow with high cheekbones, tiny eyes and a fierce Oriental cast to his features that promises lots of belligerence. Cranach never gives you what you think you are going to get. Even as mundane a subject as a twin portrayal of the apostles Peter and Paul turns into a battle of hairy eccentrics, won easily by an unlikely St Peter, whose combed-over receding hairline and scruffily twisted moustache give him the air of a recently widowed pudding salesman.

Lots of Cranach’s art has a smile on its face. But it’s never a kind smile, always a sarcastic and bitter one. The final room, where the Venuses are gathered, and around which I urge the officials of Transport for London to skulk with their magnifying glasses aloft, searching for clefts and pubic hair - because they won’t find any - is as full of weird surprises as any room that precedes it. By this time, Cranach is the head of a large and successful studio. In worldly terms, he was among the most successful of all Renaissance artists. Yet, even when his art appears to be mass-producing sexy Venuses, it never actually repeats itself. Every Venus is different. True, the surfaces are harder and slicker - Friedländer complained that the late paintings made him think of chestnuts at conker time - but the unexpected leaps of imagination continue to bring joy.

Look at the extraordinary figure of Mercury presiding over The Judgment of Paris. Gnarled, grey-haired, bearded: he must be 70 if he’s a day. Where else in art is Mercury a creaky 70-year-old?

Thus, a successfully revisionist show proves Cranach’s fizzling-out was actually a redirection of his efforts. And that a giant has been mistaken for a tiddler.

Cranach, Royal Academy, W1, until June 8

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