The portrait of the artist as pure genius

"What immortal hand or eye could form thy fearful symmetry?"

William Blake had a tiger in his mind's eye. Interpreting fearful as awesome, his words are an apt description of Leonardo da Vinci (1452-1519). He was beautiful and physically strong. The portrait of the artist as an old man in the V&A exhibition Experience, Experiment, Design: Leonardo da Vinci has a youthful and penetrating gaze.

Giorgio Vasari, describing him in 1550, said he surpassed all other musicians in Milan, playing the lyre. He was the best declaimer of improvised verse. He sang like an angel. The world playing court to his Mona Lisa today senses artistic perfection. Wouldn't you think that would be sufficient genius for one man?

His prodigious intellect and ability didn't appear to incite animosity or jealousy, possibly because, according to Vasari, he "was so pleasing in conversation that he won everyone's heart". That heart was warm: he bought caged birds from market stalls only to set them free. Though maybe he just wanted to observe them in flight.

The exhibition aims to explore the workings of the mind behind this multitude of talents. The curator, Martin Kemp, is Professor of the History of Art in Oxford. I suspect he approached his task with a combination of trepidation and pleasure.

The sophisticated computer animations designed by Paul Williams illuminate Martin's insightful vision. Prof Kemp's book, Leonardo da Vinci: Experience, Experiment and Design, published this autumn to accompany this landmark exhibition, is beautifully produced.

Sight is what it is all about. For Leonardo it was the noblest and most certain sense. He regarded any knowledge that could not be certified by the eye as unreliable. Enlightenment ideas of observation and experiment were practised more than 200 years earlier in Leonardo's tiny notebooks. He drew his thoughts on precious paper and the exhibition consists of 60 of his, mostly annotated, drawings.

Even if you understand 15th-century Italian, you will still have difficulty reading the notes. He was left-handed and wrote from right to left. So, if your Italian is good enough, take a mirror.

He investigated the relationship of the eye to the brain. In his drawings, the brain is layered like an onion and the blood vessels from the heart are spreading roots. In the exhibition, it is described as the "seed heart". but Leonardo's word is 'nocciolo', a wonderful nutty expression.

He spoke of "the body of the world", "veins of water" and the "tree" of blood vessels. Number 21 is called Irrigation Systems and maybe the inside of Mona Lisa. It is a drawing of the physiology of the female body, respiratory, vascular and genital.

His studies of anatomy we would call science and the expression of them art. His drawings of horses as well as humans reveal his knowledge of their inner workings as well as the outer vision. Modern science has confirmed his detailed study of the heart's structure and the vortex motion of the blood.

He studied the movement of water and the action of light on it. His image of water in spiral motion is like tresses of curling hair.

His thoughts on paper include inventions from tanks to periscopes, parachutes and flying machines. Despite describing war as "beastly madness", he was fascinated by military engineering. Large-scale models of his designs, including a flying machine, tank and bridge are displayed around the museum and outside.

In 21st-century Britain, children at 14 years of age choose to study either arts or science and from then on they inhabit different worlds.

Prof Kemp said: "In Leonardo's mind, they (his art and inventions) weren't very separate. If you were painting the Mona Lisa or making a flying machine, they're both great creations of nature." Leonardo himself is an incredible force of nature determined to understand intimately how all life works and express it on paper.

This creature from Mount Olympus was, however, all too human. Time curbed his dreams of perfection. The exhibition ends with a question he asked: "Tell me if anything ever was done." It rather explains why he left so many works of art unfinished.

During his 67 years on earth, his imagination delved far into our world of flight and space. He inhabited the mathematics of combinatorics but without the computer that generates the fine images in this exhibition. The quest for knowledge is possibly the most inspiring quality in this mathematician, artist and scientist.

This review can only hint at the mathematics and geometry of proportion that informed his thinking and his art. In his brilliant mind, art and science are one. Perhaps we should try to emulate it. The idea of conceptual art interests me but the concepts of some 21st-century artists seem lacking in ambition when viewed beside the thoughts of Leonardo.

The exhibition is at the V&A, South Kensington, London, until January 7. For advance tickets, call 0870 906 3883; joint tickets are available for this exhibition and At Home in the Renaissance. Experience, Experiment and Design is part of a Europe-wide celebration of Leonardo, including exhibitions at the Ashmolean Museum and the Museum of the History of Science. Visit www.universalleonardo.org