Da Vinci showed the great beauties of life that surround us with fresh eyes and an open mind, writes Aidan Dunne, Art Critic

Leonardo da Vinci fits any definition of the word genius. A Renaissance polymath, the breadth of his achievements is astonishing, and art was but one aspect of a crowded portfolio. But even if his activities had been strictly confined to the sphere of fine art, his accomplishments would have been more than enough to secure his reputation. He had an unparalleled ability to turn out works, each of them distinct and exceptional, that engaged the imagination in a deep and persistent way.

The Mona Lisa, The Last Supper, his drawings of The Virgin and Child with St Anneand Vitruvian Manare all absolutely iconic images. You could add many more to that list, including his self- portrait, and drawings of plants and natural phenomena, as well as his engineering sketches. And The Battle of Anghiariand his monumental equestrian bronze are among the most famous lost works in the history of Western art, the source of much speculation. He believed painting to be the pre-eminent art, and after his death his thoughts on it were assembled and published in a text that is still relative and perceptive.

The surviving pages of his famous sketchbooks are crammed with beautifully made drawings, spontaneous and informal, comprising a kind of visual diary or autobiography, reflecting the observations, thoughts and activities of every level of his life (including a few dirty jokes, and shopping lists).

He regarded every aspect of the world with fascinated, analytical attention, and his vision is organised and articulated in his drawings. The key to his mind is his assumption of the role of independent observer.

His own perceptions superseded received opinions on any subject, from philosophy to anatomy. Rather than being satisfied with surfaces, he continually delved into the underlying reality, in everything from the human body to flowing water, leading to startling insights in several areas of exploration.

He was an obsessive perfectionist and when he set about making a commissioned painting you could guarantee that it would generate a huge amount of supplementary material. Before something found its way into a painting, he wanted to know it inside-out. Hence masses of studies - of draperies, figures and animals, for example - inform eventual, single images, often very indirectly. A wealth of immediate, anecdotal observation is digested in the cause of devising an authoritative, idealised account of a subject. The result is the extraordinarily definitive feeling imparted by, say, his figure compositions.

Practically everything he did provided succeeding generations of artists with archetypal models that provided that basis for myriad variations. It is hard to think of more quoted works of art than the Mona Lisa or The Last Supper. They are so universally recognisable that they can be used as references in practically any context. As Dan Browne realised, an element of mystery is close to the heart of Leonardo's appeal. People are drawn to puzzles. The idea that a work of art harbours a secret makes it all the more interesting. Just what is the Mona Lisa smiling about?

Darian Leader's fascinating book Stealing the Mona Lisa recounts the story of the painting's theft from the Louvre in 1911. He points out that the picture's disappearance sealed its fame. Remarkably, more people turned up to look at the empty space where it had been than had come to see it when it was there. It is generally agreed that the most obvious mystery of the Mona Lisa, the identity of the sitter, has been solved. Yet the sitter's identity is not particularly interesting, it doesn't really explain the picture or dispel its underlying mystique.

One could point to another conundrum evident in the painting, one that has also generated much debate: the apparent visual disparity in the fragments of landscape we see beyond the sitter. Left and right don't seem to match up. But even if this issue were definitively resolved, the picture would still exert a curious fascination, still draw hordes of visitors to a room in the Louvre.

HE LEFT MANY projects unfinished, and his completed works are relatively few. But then, he embarked on so many ventures in so many areas that it was never likely that they could all be completed. His numerous beginnings, his expressions of intent to return to particular works and subjects for extended attention, and his apparent reluctance to conclude any particular endeavour, led to an intriguing psychoanalytical diagnosis, the idea that he evidenced signs of a closure complex, linked to his sexuality.

There may well be some truth to the idea, though more orthodox art historians reasonably shy away from it. However, a single human being could hardly hope to see through the sheer volume of work he initiated. Late in his life he became depressed when he realised that even the task of organising his collections of notes and papers was so vast that he could not hope to complete it. He couldn't have done so even if he'd had another lifetime to devote to all this unfinished business.

Across the range of his endeavours, he was driven by curiosity and a sense of possibility. These were defining trait of his genius.

The idea that his work harbours an arcane secret, the basis of Dan Browne's bestseller, is surely a legitimate expression of what engages us about it, but doesn't reflect a literal truth. That is, it's not something hidden and arcane that makes Leonardo interesting, but the fact that he shows us how to look at the world around us, how to address its profound mysteries and possibilities with fresh eyes and an open mind.