In 1906, the French savant Pierre Duhem published a three-volume work on Leonardo as scientist under the innocuous title Études sur Leonard de Vinci. It was the work’s subtitle that struck a note of novelty: Ceux qu’il a lus et ceux qui l’ont lu (“Those he read and those who read him”). Leonardo, then as now, was celebrated as an artist, an inventor, an engineer, a universal wizard and, to appropriate the title of the current exhibition at the Metropolitan Museum of Art (until March 30), a master draftsman. One would take it for granted that he was literate, but how interesting could it be to know what his reading list was, or on whose list of required reading his writings appeared? Duhem’s book, however, was really a profound contribution to the history of science. It analyzed Leonardo’s debts to medieval scientists like John Buridan, Albert of Saxony and Nicolas Oresme, and then went on to the scientific impact of Leonardo’s writings on subsequent investigators. It was no part of Duhem’s intention to diminish Leonardo’s originality as a scientist but rather to redeem the Middle Ages as a chapter in the history of scientific thought. It had been a historical commonplace to view the long interval between Archimedes and Galileo as a period of unrelieved ignorance and superstition. Duhem, a distinguished physicist and a great philosopher of science, was also a believing Catholic, and it was his aim to prove that Catholicism had played an importantly supportive role in the development of knowledge. He showed that Leonardo was carrying forward programs of research in mathematics, mechanics and biological science that had a long and remarkable medieval development. And he demonstrated that Leonardo, far from jotting down his observations on whatever came along, had a systematic scientific agenda that bears comparison with that of such later thinkers as Descartes, and that his various treatises contributed to research carried on well after his death.

The rebirth implied by the concept of the Renaissance had reference to classical learning. It was more or less self-promotion that demanded an interval of darkness between the fall of Rome and the rebirth of its culture in Tuscany. What Duhem established was that Leonardo mediated between the great investigators of the medieval period and those that were to come after him. And to a very large extent, one can construct a Duhemian picture of Leonardo’s place in the history of art–a parallel narrative which shows that even where Leonardo was most original, he was also in effect in conversation with his predecessors, and his successors in conversation with him. Like Duhem’s, this would not have the aim of diminishing his achievement as an artist but, since art comes from art as much as science comes from science, explaining it historically. Indeed, the Met’s exhibition has exactly this format. One could almost paraphrase Duhem’s subtitle: Ceux qu’il a vus, et ceux qui l’ont vu. The show begins with those whom Leonardo learned from, and ends with those who learned from him.

There is little doubt that it is valuable to situate Leonardo in the history of art in this way. Consider the article on Leonardo in the celebrated eleventh edition of the Encyclopedia Britannica, by then-Slade Professor of Fine Arts at Cambridge, Sidney Colvin. “By his own instincts he was an exclusive student of nature…. He was the first painter to recognize the play of light and shade as among the most significant and attractive of the world’s appearances.” But just as many of Leonardo’s observations were intended to confirm ideas he acquired from Albert of Saxony and others, the “play of light and shade” that he made his own was taught him by Andrea del Verrocchio, to whom he was apprenticed. So it is entirely appropriate that the exhibition begin with a drawing of Verrocchio’s, which shows that sfumato–a technique for depicting the way light and dark softly and almost indiscernibly grade into each other, convey the roundedness of a form–was already a matter of studio practice when Leonardo was in his teens. It was thus not something he learned by studying nature but that he acquired from his master. It could be true that the way it was used by Leonardo stamped him as a pupil of Verrocchio. But sfumato was not a workshop mannerism–it was a discovery, like perspective. It was a way of showing the shape in three dimensions of volumes through light and shadow, just as perspective is a way of showing how objects recede in space. The decision to present things in these terms was one of the marks of the Renaissance. To show things the way the eye sees them defined the artistic culture in which Leonardo worked. But it is not a matter of culture that the eye sees the world the way it does. That, as we say, is hard-wired. Because it was a cultural agenda to “conquer appearance,” the history of art in the Renaissance is like the history of science when viewed as a progress. “In early modern Europe,” the philosophical historian of science Thomas Kuhn wrote, “painting was regarded as the cumulative discipline.” That medieval art did not conform to this agenda was counted by Renaissance writers like Vasari as palpable evidence that it belonged to the Dark Ages.

Instructive as it is to weaken the myth that Leonardo was the first artist to see nature as it looks, a certain price is paid. It is, we might say, unfair at once to Verrocchio and to us to see his magnificent drawing as a paradigm from which Leonardo learned the art of chiaroscuro. Verrocchio’s drawing is of a young woman, shown at bust length, facing to the left. It is, to use an unfashionable word, a beautiful drawing of a beautiful woman, so much so that it is hard to tear one’s eyes away from it and from her. The drawing is done in charcoal or in black chalk, and with a tenderness that matches the tenderness that it shows. The term sfumato derives from the word for smoke, and the areas of gray look as if they were breathed onto the woman’s cheek and neck. There is a firmness in the drawing of the underlip, and in tracing the curve of the chin until it fades into shadow. There is a delicacy and certitude in forming the curls that define the ornamental hairdo and the diaphanousness of the woman’s garment. It would be worth dwelling on Verrocchio’s famous drawing, even had the Met borrowed it from Christ Church, Oxford, and displayed it in a gallery by itself, just to provide pleasure to its viewers, without using it to teach anything whatever.

But it could also be used to teach a stronger and more difficult lesson by displaying it alongside what the catalogue describes as Leonardo’s “hauntingly beautiful” drawing of the head of the Virgin, which is also in the present show. Next to Leonardo’s drawing, Verrocchio’s looks almost abstract and schematic. Still, there is nothing that belongs to the progressive history of Renaissance drawing that Leonardo did not find in Verrocchio, though one might say that in it he has perfected the art of sfumato. On the other hand, there is something magical in the way in which Leonardo evoked the Virgin’s head out of marks and smudges. And beyond that, Leonardo has imbued her with an expression of love and meditation. She is looking at something and is feeling something powerful about what she sees. Her smile is gentle. My sense is that those who look at her for very long will insensibly reproduce her expression on their own faces. Verrocchio’s work could be used to teach the meaning of what great drawing is. Leonardo’s could teach the meaning of great art. How he does it defies analysis, but it goes beyond being a master draftsman.

As it happens, we know a great deal about what the Virgin is looking at, since the head is a preparatory study for one of Leonardo’s most mysterious paintings–the Virgin and Child with Saint Anne, in the Louvre. The Virgin is sitting on Saint Anne’s knee, and the Child, holding a lamb, looks back over his shoulder at her from between her knees. Saint Anne looks at the Virgin looking at the Child; the Virgin holds the Child as the Child holds the lamb. The scene is set in a strange rocky landscape. The arrangement of the figures is like a mystical knot. I can appreciate that the Louvre would be unwilling to lend the painting under any circumstances, but it would be worth having a reproduction of it near the drawing, so that we could see what the object and meaning of the Virgin’s look is. In another of the sketches for the Virgin and Child with Saint Anne, on loan from the British Museum, the figures are clotted together in a tangle of lines and washes. Saint Anne is an older woman, and the Virgin looks at her. They are given a sort of frame, to give Leonardo a sense of how they might fill a panel later on. It is a dense, vigorous drawing, but it is also a path not taken–something we would not know from the drawing seen on its own.

Many of the drawings in the show refer to known works, and viewers might achieve a deeper understanding of Leonardo’s creative processes by seeing the drawings as stages in a process, and not simply in their own terms. There is, for example, an exceedingly energetic study for the Uffizi’s Adoration of the Magi, a work so strange that it could be the transcription of a dream. The painting, in yellow ochre and brown ink, is so close to a drawing in its own right that scholars have wondered whether it is finished or not. In it, the Virgin and Child are in space of their own, surrounded by a crowd of adorers, astounded by the wonder of the event. The Child reaches out to accept a gift from a kneeling magus with one hand, while his other hand is raised as if he were making a Talmudic point. In the piazza behind the company, horsemen rear wildly in front of a visionary ruin with a double staircase. Things are a great deal more confused in the drawing we are shown at the Met, where adorers invade the Virgin’s space. In the painting, the architecture has been clarified. One still has to interpret what connection there is between the horsemen and the holy pair. No one in the history of art drew horses with the truth and passion of Leonardo. They gallop through the entire show, and one cannot help but wonder what Eadweard Muybridge thought he could discover by his battery of cameras set up to photograph a horse at gallop that he could not better learn from Leonardo’s drawings. Horses do not pause in mid-charge to pose for an artist. In some way Leonardo had stored a complete knowledge of how horses look from every angle and in every gait, with or without riders, and could transcribe that knowledge as easily as we write our names.

Horses figure centrally in two works we cannot, alas, compare with their preparatory drawings in the show, since they were never completed: Leonardo’s career was punctuated with aborted masterpieces. One was the great equestrian monument to Francesco Sforza, commissioned by his son Ludovico. Leonardo worked on this colossal sculpture on and off for about sixteen years. A contemporary writer described it as “the most gigantic, stupendous and glorious work ever made by the hands of man.” By contrast with Verrocchio’s famous equestrian statue of Colleoni in Venice, Leonardo was to have depicted Francesco on a rearing horse. It was to have stood, even without its rider, over thirty-one feet from the ground. Something like seventy tons of bronze was set aside for casting it, but it was never cast. The bronze was melted down for cannons, and the clay model for the “Sforza Horse” was used for target practice by Gascon bowmen after the French stormed the city of Milan, and Ludovico was forced to flee. We have only the drawings left, and some uncertainty whether they were done for the Sforza monument, The Adoration of the Magi or The Battle of Anghiari.

When the French occupied Milan, Leonardo slipped back to Florence by way of Venice, where he paused to advise the Venetians on fortifications. His counsel to artists was to “flee before the storm.” In Florence he was given an extraordinary commission, to paint a colossal fresco in the Great Council Hall of the Palazzo della Signoria. The subject selected was a battle scene, showing a victory of Florence over Milan. Michelangelo was commissioned to do a facing mural. Neither work was completed, but Leonardo’s was a spectacular failure: Because of his impetuosity, the plaster did not dry and the pigment ran to form an incoherent muddle–something, one imagines, like the painting Balzac describes in his Chef d’oeuvre inconnu. It is a sad truth that Leonardo’s genius outran his patience: He was not a perfectionist, as the material history of the Last Supper, already a preservationist’s nightmare in his lifetime, shows. But the drawings for The Battle of Anghiari are among his great achievements, and for me they are the glory of the show.

Here is Leonardo’s description of what he aimed at in the great fresco:

First you will have the smoke of the artillery, mixed in the air with the dust raised by the movements of horses and troops…. This mixture of air, smoke, and dust will be lighter on the opposite side; and as the combatants advance into this vortex, they will become less and less visible, and there will be less difference between their lit and shaded parts…. The musketeers, as well as their neighbors, will be reddish. And this redness will diminish in proportion to the distance from its cause…. You will have different sorts of weapons between the feet of the combatants, such as splintered shields, spears, broken swords, etc. You will have dead bodies, some half covered with dust….

From this account, the work sounds like a monumental drawing in red and black chalk, which lends itself, through smudging, to the atmospheric effects of mingled battle smoke and dust, and visual correlatives of clashing bodies, of shouts and screams, swords clanging against swords, the cries of horses and exploding ordnance. The actual cartoon–the full-scale working drawing Leonardo was to have found means to transfer to the wall–was lost or destroyed in his lifetime (the same is true of Michelangelo’s cartoon for his companion fresco, The Battle of Cascina). It is one of the insoluble puzzles of art history to reconstruct what the work would have looked like as a whole.

Leonardo is said to have painted a central episode of The Battle of Anghiari, of which a copy was made, and this is exhibited in the present show. The copy has a certain interest in that Rubens is associated with it. This is a matter for experts in connoisseurship to determine. It is entirely credible that Rubens, in his own depictions of battles and hunting scenes, was inspired by Leonardo’s example–that Rubens should be included in a Duhemian narrative of those whose work owes something to Leonardo’s example. But there is not the slightest chance, based on Leonardo’s words and the preparatory drawings in the show, that The Battle of Anghiari would have looked like this. It almost looks like a “cartoon”–not in the sense of a working drawing but of lampoon–by Leonardo of a group of grimacing warriors, engaged in mounted combat. But the small preparatory drawings themselves are just astonishing. They represent, as the titles given them in the catalogue state, a “skirmish between horsemen and foot soldiers,” “foot soldiers wielding long weapons” and a “fight for the standard at the bridge.” These are in brown ink and black chalk and are about six inches long and between four and six inches high. Men and horses hurl themselves at one another under clouds of dust. Weapons fly through the air. Bodies and heads emerge out of urgent tangles of ink. A man’s arm holds some sort of hammer, a horse rears, a figure lies on the ground. It is inconceivable that in the final result, every contour would be carefully traced as in the almost hateful copy. There is not a single other case in which drawing and work are so incommensurable. The sole value of the copy lies in the way it makes this incommensurability palpable.

That is the one dissonance in an exhibition the like of which has never been attempted. This is the largest collection of Leonardo’s drawings ever to have been shown together. I spoke briefly with designer Milton Glaser at the press opening, standing in awe in front of a depiction of mortar fire. Milton told me that he had never expected to see a show like this in his lifetime. We are all in debt to the audacity of its organizers and sponsors. However much or little any of us knows about Leonardo, we cannot but be overwhelmed by the unfurling from sheet to sheet of his graphic imagination, whether he is studying the fall of draperies or registering the grotesqueness or beauty of the human face, or simply the way the body is twisted in the show of love or anger. Reviewers have suggested that by contrast with Verrocchio, there is something cold and indifferent in Leonardo’s personality. But that assessment is impossible to sustain the moment one sees the drawings in which the Virgin holds the Child, who hugs a cat, or in which the Child awkwardly attempts to feed his mother with something he has taken out of a bowl with his pudgy fist. There is a drawing by Verrocchio of a horse literally made out of numbers, which show the proportions from point to point. Leonardo did not need diagrams to help him draw horses with truth and passion. When he drew a horse, he was a horse, drawing its form from what it felt like to be one.