THIS is the year of Leonardo da Vinci – the 500th anniversary of his death in France. And while such celebrations are normally the occasion for “reassessing” what we supposedly know about a particular artist and how we view them, the many exhibitions on his work from Edinburgh to Milan via Paris are a spur to make the effort to come to terms with the subtlety of da Vinci’s mind, the vastness of his curiosity, the immensity of his skills and the sheer range of his interests.

Maybe it is even an invitation to grapple with what people in other ages would have unashamedly called his soul – the term he used. The nature of his religious beliefs can be open to debate, if only because he rarely mentions God or theology in his private writings, but he operated within a religious framework and most of his artwork deals with subjects taken from Christian history, such as the Last Supper or the Annunciation.

He intended to write several treatises, on anatomy for instance, but never completed any of them. The treatise on painting put together from scattered comments after his death contains the comment that there are two challenges facing any artist in painting a portrait. The first is to capture the physical appearance and the second is to portray his or, more commonly for da Vinci, her soul. The first is easy, he said nonchalantly, but the real problem lies in achieving the second aim, which can only be done “by means of the gestures and movements of the limbs”.

READ MORE: Profile: The once-in-a-lifetime Leonardo da Vinci Louvre exhibition

There has been no shortage of efforts to reach da Vinci’s soul or inner being, most notably by Sigmund Freud, who devoted the book he regarded as his favourite among his own works to attempting to analyse the man, concentrating most strongly on the magnificent canvas, The Virgin and Child with Saint Anne. He applied his theories of narcissism and homosexuality, and in the course of the analytic process managed to identify the form of a vulture formed by the dress of the two women.

This approach and such notions have been rejected by later art critics who accused Freud of mere ignorance of the artistic techniques and conventions of the Renaissance, and who approach the mind and mastery of da Vinci by other means. For the exhibitions in British cities, including Glasgow last May and the larger exhibition just opened in the Queen’s Gallery in Edinburgh, the Royal Library in Windsor has made available sketches and notebooks in its possession.

The Edinburgh exhibition, expertly laid out and enhanced by highly informative audio-commentary, contains stray pages which often seem a jumble of words and sketches but all done with exquisite mastery, as well as others which are preparatory studies for well known canvases.

The trajectory follows his life and broadening interests which often prevented him from completing one project before his restless mind shifted focus. There are some works tiny in size but immense in their implication, like the drawings on anatomical subjects done after he had dissected corpses, or the stunningly lovely, enigmatic allegory in red chalk of the Eagle and the Dog, afloat on some mysterious sea.

The Castello Sforzesco in Milan hosted in spring a multimedia event in the very rooms which da Vinci himself had decorated with an intricate tracery of leaves and branches, demonstrating his love of nature. These motifs were later whitewashed over but recently have been partially recovered and restored. He also planned for the castle courtyard a great bronze sculpture of a horse, an animal whose muscular frame fascinated him and which he frequently sketched, but this scheme too was aborted and the clay model he had completed was used contemptuously as target practice by French archers when they overran Milan.

The fact is that da Vinci was so much more than an artist, and the most complete display of every facet of his work is the exhibition currently running at the Louvre in Paris. The run-up was dominated by a feud stirred up by the Italian populist politician, Matteo Salvini, who accused France of an attempt to make da Vinci, who did spend the last three years of his life in Paris, retrospectively French and to deny his Italian cultural origins.

READ MORE: Edinburgh and Glasgow set for exhibitions on Leonardo da Vinci

The Italian government threatened to refuse to loan the famous sketch of Vitruvian Man, although when Salvini was ousted from government the Ministry in Rome relented. There was also uncertainty over whether the world’s most expensive painting, the Salvator Mundi, would be lent by the work’s new owners. Its whereabouts are uncertain and the attribution to da Vinci questioned, and this may explain why the work did not turn up.

No matter. The scale of the show is overwhelming, but so was the mind and creativity of da Vinci. Only between 15 and 20 paintings can be viewed with varying degrees of confidence as da Vinci’s, a meagre total when put alongside the exuberant productivity of a Michelangelo or Titian.

Da Vinci worked slowly and meticulously, to the annoyance of his patrons who one after the other complained of his tardiness and demanded in vain that he respect the timescales stipulated in the contract.

His contemporary and biographer Giorgio Vasari recorded that while painting the Last Supper, he would stand gazing for hours in rapt abstraction at the work in progress, sometimes adding only a couple of faint brush strokes as a complete day’s work. He carried the Mona Lisa with him over many years from Italy to France and never regarded the work as complete.

Da Vinci seems to have been at peace with himself, and to have had nothing of that tormented psyche with which modern critics prefer to endow genius or the artistic cast of mind. ‘‘The spirit of the painter is transmuted into an image of the spirit of God,’’ he wrote and maybe he viewed his work as stretching into eternity.

Already in his own life there were those who offered an alternative suggestion for his failure to deliver on time, that da Vinci became bored with painting as his interests widened and deepened and he undertook exploration of the natural world and indulged more visionary interests in philosophy and science. It seems an unlikely theory, but there may be something to it.

There is another dual dimension to the man which defies facile characterisation. On the one hand, he roamed freely in his mind into transcendental realms of metaphysics or mystery, on the other he was at home with the brutal reality of contemporary politics and power. When he wrote what was basically a job application to the ruler of Milan, Ludovico Sforza, known to history as the Moor, he made scant reference to his artistic prowess but instead boasted of his ability to devise weapons of war, almost of mass destruction, including a giant crossbow, which fortunately only exists in sketch form.

He made the acquaintance of Machiavelli, and the pair did not discuss the abstract questions of ‘‘atmospheric perspective’’ which da Vinci developed in his painting. They did debate a scheme to build a canal to bypass Pisa, then an enemy of Florence, and drain the water from the river Arno as it coursed through the city, to Pisa’s discomfiture. There were schemes and there are sketches but it all came to nothing.

In the Louvre, the organisers have eschewed too abstract a critical approach and have laid his work out systematically and chronologically, from his apprenticeship with in the studio of the artist Verrocchio to his maturity.

They have imaginatively employed all the wizardry of modern science and technology to aid research into his work and his mind. The infrared reflectograph is used to probe under the finished surface of the paintings to reveal rethinking and reworking, and to show his attention to detail as he shifted in, for example, The Annunciation, the angle of the angel’s arm as the heavenly messenger arrives to proclaim to the Madonna her divine pregnancy.

To emphasise the meticulous craftsmanship which preceded the art, his best known works are accompanied by the studies in ink he completed before he picked up a brush. He would draw in detail the folds of the clothing of the Madonna, since he wrote in a manuscript that ‘‘drapery has to be painted according to nature,’’ and would expend visual energy on the twists of the body of St Sebastian as it would react when the arrows, which were the nature of his martyrdom, bit into his flesh.

Da Vinci devoted the same loving care to sketches which were never intended to be carried forward, such as the delicate drawing of the Virgin Mother washing the feet of her infant son, or of the graceful bloom of the Star of Bethlehem surrounded by anemones, which was on show in Glasgow.

In Paris, the Mona Lisa, the most famous of his paintings and perhaps the most famous of all works of art of all time, is subjected to the most striking of modern scientific innovations, virtual reality. The visitor is invited into a small room, seated on a stool, has lenses fitted on the forehead and thus escorted out of the standard dimensions of time and space and initiated into a parallel, virtual world which da Vinci never saw.

The viewer watches as the subject of the portrait, the wife of the merchant Francesco del Giocondo, named La Gioconda as the feminine form of his name, turns in her chair to reveal the veil over her long hair, moves her hands from the clasped position, alters her enigmatic smile and then turns to draw attention to the mountains and the lake behind her which form the backdrop to the portrait. Da Vinci was fascinated by the potential of flight, and indeed by the possibility of underwater travel, so his notebooks shown elsewhere in the exhibition contain sketches, even working forms, of a flying machine, of a solid-material parachute and of a round shaped submarine. This flying machine will take off in imaginary flight over the landscape behind Mona Lisa herself, giving it greater prominence.

This supposedly coarse experiment has enraged fastidious aesthetes who have taken to the press to denounce such out rages , but it is tempting, if futile, to wonder what da Vinci himself would have made of such attempts. He was not afraid of novelty, and is perhaps the supreme genius of the Western tradition, perhaps the greatest mind and creative imagination Europe has ever produced. This is the man who embodies the Renaissance ideal, now reduced to a tawdry cliche, of the Universal Man.

He seems to chafe at the limitations of thought and belief, even when it has a Biblical base. Would he have baulked at steps in virtual reality? If this exercise does nothing to clarify the soul of Mona Lisa or indeed of da Vinci, it does help reveal technique and illustrate detail. He began the portrait in Florence towards the end of the 16th century, worked on it for four years and then took it with him wherever he went, meaning that the unfortunate woman never saw the final work. He also, it was reported at the time, employed clowns and musicians to ensure that the famous smile stayed in place. The exhibition’s directors stated that one of their objectives was to heighten da Vinci’s image as artist as against his growing reputation as restless intellect or pioneer engineer, and they succeed superbly with the Mona Lisa.

This painting has suffered from over familiarity. It as been ridiculed or caricatured, for example by the surrealist Marcel Duchamp when he gave La Gioconda herself a moustache and goatee beard, or by advertisers out to sell their products by shock effect. In the context of the exhibition, the portrait is reinstated as not only the most tantalising but, with all due respect to Michelangelo or Titian, as one of the most beautiful works of human art. Visitors can leave the confines of the exhibition for the main gallery upstairs where they can, in competition with the crowds made worse by that modern pest, the selfie-taker, jostle for a glimpse of the lady herself as she stares back at them. As universal man, da Vinci took an interest in every sphere of human endeavour.

There are seemingly some 8000 pages of notebook scattered in archives, libraries and private and public collections in several European cities, and only around half of these have been translated and published, although the rate has picked up in recent years. Da Vinci did not make the task of deciphering his words easy since while his handwriting is neat and precise, the letters are tiny and he employed mirror writing from right to left of the page. The large room where some manuscripts are displayed in Paris is dominated by a garishly coloured copy of the Last Supper by his near contemporary, Marco D’Oggiono, perhaps to keep da Vinci the artist in mind.

However, there is no possibility of separating da Vinci the artist from da Vinci the investigator since in words and sketches the two went together. The subjects which seized his interest include hydraulics, astronomy and the order of the cosmos, botany, optics, geometry, anatomy, flight, inventive if cruel military machines and many more. His manuscripts contain the results of his dissection of corpses for the furtherance of his anatomical research, and the depiction of his observations demonstrates that union. There is, for instance, a delicate study of a foetus in the womb on show in Edinburgh, as well as of arteries and of the heart.

He drew a miniature, nasty, highly realistic representation of the hanging of Bernardo di Bandino Baroncelli for taking part in a rebellion against the Medici rulers of Florence, with a caption above his left shoulder explaining the victim’s crime. Da Vinci was engrossed by the gruesomeness as much as by tenderness or gentleness, as witnessed by the bizarre heads and expressions of the face, made sharper by infrared exposure, which gather round the Virgin and Child in The Adoration of the Magi. Perhaps he aimed for perfection of ugliness as well as beauty. The overall synthetic vision and composition are portrayed in the tantalising Vitruvian Man, a small, reddish-chalk coloured sketch normally displayed in Venice’s Accademia and kept in semidarkness in a glass case. The name is taken from the Latin author of a treatise on architecture, and for all its tiny dimensions, the image has become as omnipresent as the Mona Lisa.

It demonstrates da Vinci’s obsession with proportion in architecture, with the added dimension of expressing a quintessentially Renaissance philosophy of man as the measure of all things. The subject, totally naked, forward facing, with a fine head of tousled hair, stands in a circle inside a square, and is given four arms which touch the square and four legs which rest on the circle. This human being is perfect in his proportions, while the human being as such is central in earthly reality and not marginal in the natural world around him. The image offers an enigma which defies full, coherent understanding, but which is challenging and enriching, as is all da Vinci. He exhausts the superlatives, drains all feeling of awe before the magnificence and multiplicity of his achievements in so many fields. The fullness of life was his subject, and 500 years after his death he still embodies the mystery and enchantment of genius.