Leonardo da Vinci, Painter at the Court of Milan, National Gallery, London

Unexpectedly, the subtitle to the National Gallery's Leonardo show – Painter at the Court of Milan – is more about its first word than it is the other five.

This is not the narrow reappraisal of a period in Leonardo's career so much as a reminder that he was a painter at all: a necessary nudge, given that Da Vinci the artist has recently been hidden by so many other Da Vincis. There has been Leonardo the inventor of submarines (as seen at the V&A in 2006); Leonardo the anatomist and cartographer (ditto); Leonardo the tortured homosexual; Leonardo the Renaissance genius; and, last and most wearisomely, Leonardo the occult anti-hero of The Da Vinci Code. Buried beneath these and easy to lose sight of is the man who merely created the two most famous images in the history of art, Mona Lisa and The Last Supper.

If the first is the best known of Leonardo's works, the second is his masterpiece, the culmination of the 17 years he spent as court painter to Ludovico Sforza, the Duke of Milan. The bastard son of a Tuscan notary, the 30-year-old Da Vinci was already known as a gifted maker – of war machines, water screws, silver lyres – when Lorenzo de' Medici sent him to the Milanese ruler as a living objet de luxe in 1482. It was in this time away from Florence that Leonardo came into his own as a painter, as something more than the talented student of his master, Verrocchio.

There were certain things he did not leave behind in Florence, however, among them a woeful inability to finish projects. Commissioned to make a vast equestrian statue in bronze of Ludovico's father, Francesco, Leonardo never got further than a full-scale clay model. Catastrophic in one sense, this did at least mean that he spent his time in Milan thinking about sculpture, and – being Leonardo – about sculpture vis-à-vis painting.

Dan Brown's apart, the various Da Vincis listed above are all contained in his paintings, Leonardo's particular genius consisting in his ability to see the bigger picture. In, say, the Krakow Portrait of Cecilia Gallerani – more famous as The Lady with an Ermine – are his studies of the anatomy of bears and dogs, his ideas on the relation between art and poetry, and, pre-eminently, his understanding of sculpture. Compare it with Ambrogio de Predis's static Portrait of Bianca Maria Sforza across the way and you sense Leonardo's sculptural underpinnings – not just the convincing way in which his subject is modelled but the sense that, though still, she is capable of movement; indeed, that she is just about to move. That subverting of the medium – paint is static, after all – lends Cecilia her faintly subversive air, a naughtiness that would find its apogee 20 or so years later, back in Florence, with Mona Lisa.

More than all of this, though, Leonardo's meditations on sculpture taught him about the power of the void. Painting had traditionally concentrated on solids, on what was there. In Milan, he came to see that what wasn't there is at least as potent, a realisation which so beguiled him that, for a time, it led to a kind of Leonardesque Mannerism. In the middle of this period sits that astonishing work, the National Gallery's Virgin of the Rocks.

Newly arrived in Milan, the Florentine prodigy was commissioned by the Franciscans to paint an altarpiece for their main church, San Francesco Grande. As ever with Leonardo, things weren't quite that simple. It would be 25 years before he was paid for the work, this apparently due to his incessant changes of mind. In the meantime, Leonardo had painted not one but two Virgins of the Rocks, the other being in the Louvre. Reunited after centuries, the pair now face each other across a space of 50 feet or so, a gap as charged as the one between the forefingers of God and Adam on Michelangelo's Sistine Chapel ceiling.

To the left is the Paris Virgin, seemingly painted between 1483 and 1485 and then put aside, her surface damaged by rough handling. To the right is her London sister, younger – this Virgin was painted in two stints, in the 1490s and 1500s – and is altogether glossier, perhaps too much so. There are numerous differences between the pair, the most obvious being the London painting's more vertical composition. In the Paris picture, the angel points across the Virgin to the infant John the Baptist while the Virgin's left hand hovers over the gesturing finger. In the London version, the angel no longer points, and Mary's hand is higher and more open.

As a result, our eye is drawn not to any of the characters in the drama but to the pyramidal void they describe and, beyond that, to the void-like landscapes on either side of the Madonna's head. The perspective of these is yawning, vertiginous; the gaps through which we see them are like the eye-sockets of a skull. Paintings of Christ's childhood customarily included symbols of the Passion, but Leonardo's sculptural vision is Nazareth and Golgotha in one. His spaces become the two-edged story of Christianity, of loss and gain and loss.

What can you do with a Leonardo show but praise it? Yet the National Gallery's exhibition isn't just good because of the works it contains but of how it treats them. Like its subject, Leonardo tells you as much as you need to know and no more. For what it's worth, I really don't think the much-debated Salvator Mundi is by Leonardo: it is too two-dimensional, the symbolism of the crystal ball too blatant. But this wonderful exhibition will equip you to make up your own mind, and I can say no better than that.

To 5 Feb (020-7747 2885)

Next Week:

Jenny Gilbert seeks enlightenment in illuminated manuscripts at the British Library

Art Choice

Visit the V&A’s newest gallery, dedicated to photography, to explore the world’s oldest museum collection of snaps chronicling a photographic journey from experiments in 1839 to the 1960s. Place your bets now for who will win the Turner Prize: work by the four shortlisted artists is on display at the Baltic in Gateshead (till 8 Jan).