Title: Leonardo da Vinci
Author: Walter Isaacson
Genre: Biography & Autobiography
Publisher: Simon & Schuster
Release Date: October 2, 2018
Pages: 624

Largely due to his work, dimensionality became the supreme innovation of Renaissance art.

I embarked on this book because Leonardo da Vinci is the ultimate example of the main theme of my previous biographies: how the ability to make connections across disciplines—arts and sciences, humanities and technology—is a key to innovation, imagination, and genius.

Leonardo had almost no schooling and could barely read Latin or do long division. His genius was of the type we can understand, even take lessons from. It was based on skills we can aspire to improve in ourselves, such as curiosity and intense observation. He had an imagination so excitable that it flirted with the edges of fantasy, which is also something we can try to preserve in ourselves and indulge in our children.

Vision without execution is hallucination. But I also came to believe that his ability to blur the line between reality and fantasy, just like his sfumato techniques for blurring the lines of a painting, was a key to his creativity. Skill without imagination is barren. Leonardo knew how to marry observation and imagination, which made him history’s consummate innovator.

Kenneth Clark called “the most relentlessly curious man in history.”6

Over and over again, year after year, Leonardo lists things he must do and learn.

I did learn from Leonardo how a desire to marvel about the world that we encounter each day can make each moment of our lives richer.

The painter Giorgio Vasari, born in 1511 (eight years before Leonardo died), wrote the first real art history book, Lives of the Most Eminent Painters, Sculptors, and Architects,

Leonardo was not always a giant. He made mistakes. He went off on tangents, literally, pursuing math problems that became time-sucking diversions. Notoriously, he left many of his paintings unfinished, most notably the Adoration of the Magi, Saint Jerome in the Wilderness, and the Battle of Anghiari.

His ability to combine art, science, technology, the humanities, and imagination remains an enduring recipe for creativity. So, too, was his ease at being a bit of a misfit: illegitimate, gay, vegetarian, left-handed, easily distracted, and at times heretical.

Above all, Leonardo’s relentless curiosity and experimentation should remind us of the importance of instilling, in both ourselves and our children, not just received knowledge but a willingness to question it—to be imaginative and, like talented misfits and rebels in any era, to think different.

Other than a little training in commercial math at what was known as an “abacus school,” Leonardo was mainly self-taught.

His lack of reverence for authority and his willingness to challenge received wisdom would lead him to craft an empirical approach for understanding nature that foreshadowed the scientific method developed more than a century later by Bacon and Galileo. His method was rooted in experiment, curiosity, and the ability to marvel at phenomena that the rest of us rarely pause to ponder after we’ve outgrown our wonder years.

In 1452 Johannes Gutenberg had just opened his publishing house, and soon others were using his moveable-type press to print books that would empower unschooled but brilliant people like Leonardo.

The Ottoman Turks were about to capture Constantinople, unleashing on Italy a migration of fleeing scholars with bundles of manuscripts containing the ancient wisdom of Euclid, Ptolemy, Plato, and Aristotle. Born within about a year of Leonardo were Christopher Columbus and Amerigo Vespucci,

The whale fossil triggered a dark vision of what would be, throughout his life, one of his deepest forebodings, that of an apocalyptic deluge.

There was no place then, and few places ever, that offered a more stimulating environment for creativity than Florence in the 1400s. Its economy, once dominated by unskilled wool-spinners, had flourished by becoming one that, like our own time, interwove art, technology, and commerce.

It was also a center of banking; the florin, noted for its gold purity, was the dominant standard currency in all of Europe, and the adoption of double-entry bookkeeping that recorded debits and credits permitted commerce to flourish.

Shops became studios. Merchants became financiers. Artisans became artists.7

Unlike some city-states elsewhere in Italy, Florence was not ruled by hereditary royalty. More than a century before Leonardo arrived, the most prosperous merchants and guild leaders crafted a republic whose elected delegates met at the Palazzo della Signoria, now known as the Palazzo Vecchio.

Exercising power from behind its façade was the Medici family, the phenomenally wealthy bankers who dominated Florentine politics and culture during the fifteenth century without holding office or hereditary title. (In the following century they became hereditary dukes, and lesser family members became popes.)

After Cosimo de’ Medici took over the family bank in the 1430s, it became the largest in Europe. By managing the fortunes of the continent’s wealthy families, the Medici made themselves the wealthiest of them all.

Cosimo supported the rebirth of interest in antiquity that was at the core of Renaissance humanism.

During his twenty-three-year reign, he would sponsor innovative artists, including Botticelli and Michelangelo, as well as patronize the workshops of Andrea del Verrocchio, Domenico Ghirlandaio, and Antonio del Pollaiuolo, which were producing paintings and sculptures to adorn the booming city.

The legacy of two such polymaths had a formative influence on Leonardo. The first was Filippo Brunelleschi (1377–1446), the designer of the cathedral dome.

Vitruvius’s paean to classical proportions, De Architectura.

Brunelleschi also rediscovered and greatly advanced the classical concepts of visual perspective, which had been missing in the art of the Middle Ages.

Brunelleschi showed how parallel lines seemed to converge in the distance toward a vanishing point. His formulation of linear perspective transformed art and also influenced the science of optics, the craft of architecture, and the uses of Euclidean geometry.11

Leon Battista Alberti (1404 –1472), who refined many of Brunelleschi’s experiments and extended his discoveries about perspective.

Alberti wrote his masterpiece analyzing painting and perspective, On Painting, the Italian edition of which was dedicated to Brunelleschi.

Alberti, on the other hand, was dedicated to sharing his work, gathering a community of intellectual colleagues who could build on each other’s discoveries, and promoting open discussion and publication as a way to advance the accumulation of learning.

Alberti’s On Painting expanded on Brunelleschi’s analysis of perspective by using geometry to calculate how perspective lines from distant objects should be captured on a two-dimensional pane.

Leonardo’s only formal learning was at an abacus school, an elementary academy that emphasized the math skills useful in commerce.

A left-hander, Leonardo wrote from right to left on a page,

“They are not to be read save with a mirror,” as Vasari described these pages. Some have speculated that he adopted this script as a code to keep his writings secret, but that is not true; it can be read, with or without a mirror. He wrote that way because when using his left hand he could glide leftward across the page without smudging the ink.

Being left-handed also affected Leonardo’s method of drawing. As with his writing, he drew from right to left so as not to smudge the lines with his hand.16 Most artists draw hatching strokes that slope upward to the right, like this: ////. But Leonardo’s hatching was distinctive because his lines started on the lower right and moved upward to the left, like this: \.

Being left-handed was not a major handicap, but it was considered a bit of an oddity, a trait that conjured up words like sinister and gauche rather than dexterous and adroit, and it was one more way in which Leonardo was regarded, and regarded himself, as distinctive.

Around the time Leonardo was fourteen, his father was able to secure for him an apprenticeship with one of his clients, Andrea del Verrocchio, a versatile artist and engineer who ran one of the best workshops in Florence.

When Leonardo arrived, Verrocchio’s workshop was creating an ornate tomb for the Medici, sculpting a bronze statue of Christ and Saint Thomas, designing banners of white taffeta gilded with flowers of silver and gold for a pageant, curating the Medici’s antiques, and generating Madonna paintings for merchants who wanted to display both their wealth and their piety.

Verrocchio’s bottega, like those of his five or six main competitors in Florence, was more like a commercial shop, similar to the shops of the cobblers and jewelers along the street, than a refined art studio. On the ground floor was a store and workroom, open to the street, where the artisans and apprentices mass-produced products from their easels, workbenches, kilns, pottery wheels, and metal grinders.

The goal was to produce a constant flow of marketable art and artifacts rather than nurture creative geniuses yearning to find outlets for their originality.

Unlike Michelangelo’s iconic marble statue of a muscular David as a man, Verrocchio’s David seems to be a slightly effeminate and strikingly pretty boy of about fourteen.

Nevertheless there are reasons to think that Leonardo posed for Verrocchio’s David.

Verrocchio’s art was sometimes criticized as workmanlike. “The style of his sculpture and painting tended to be hard and crude, since it came from unremitting study rather than any inborn gift,” Vasari wrote. But his statue of David is a beautiful gem that influenced the young Leonardo.

That ability to convey the subtleties of motion in a piece of still art was among Verrocchio’s underappreciated talents, one that Leonardo would adopt and then far surpass in his paintings.

The beauty of geometry.

For Leonardo, the drapery studies helped foster one of the key components of his artistic genius: the ability to deploy light and shade in ways that would better produce the illusion of three-dimensional volume on a two-dimensional surface.

“The first intention of the painter,” Leonardo later wrote, “is to make a flat surface display a body as if modeled and separated from this plane, and he who surpasses others in this skill deserves most praise.

In his Benois Madonna, for example, he painted the Virgin Mary’s blue dress in shades ranging from almost white to almost black.

The term sfumato derives from the Italian word for “smoke,” or more precisely the dissipation and gradual vanishing of smoke into the air. “Your shadows and lights should be blended without lines or borders in the manner of smoke losing itself in the air,” he wrote in a series of maxims for young painters.

The hooked nose and jutting jaw create a profile that became a leitmotif in Leonardo’s drawings, that of a gruff old warrior, noble but faintly farcical.

In Washington, DC’s National Gallery there is a marble relief of a young Alexander the Great, attributed to Verrocchio and his workshop, which features a similar ornate helmet with a winged dragon, a breastplate adorned with a roaring face, and the profusion of curls and fluttering swirls that the master imparted to his apprentice.

The glory of being an artist, he realized, was that reality should inform but not constrain.

With the Baptism of Christ, Verrocchio went from being Leonardo’s teacher to being his collaborator. He had helped Leonardo learn the sculptural elements of painting, especially modeling, and also the way a body twists in motion. But Leonardo, with thin layers of oil both translucent and transcendent, and his ability to observe and imagine, was now taking art to an entirely different level.

There was another reason, one even more fundamental, that Leonardo did not complete the painting: he preferred the conception to the execution. As his father and others knew when they drew up the strict contract for his commission, Leonardo at twenty-nine was more easily distracted by the future than he was focused on the present. He was a genius undisciplined by diligence.

All of Leonardo’s paintings are psychological, and all give vent to his desire to portray emotions, but none more intensely than Saint Jerome. The saint’s entire body, through its twists and uncomfortable kneeling, conveys passion. The painting also represents Leonardo’s first anatomical drawing and—as he fiddled with and revised it over the years—shows the intimate connection between his anatomical and artistic endeavors.

The curator of drawings at Windsor, Martin Clayton, came up with the most convincing explanation. He posited that the painting was done in two phases, the first around 1480 and the other following the dissection studies he made in 1510.

The significance of this goes beyond helping us understand the anatomical aspects of the Saint Jerome. It shows that Leonardo’s record of unreliability was not simply because he decided to give up on certain paintings. He wanted to perfect them, so he kept hold of many of them for years, making refinements.

Even some of his commissions that were completed, or almost so—Ginevra de’ Benci and the Mona Lisa, for example—were never delivered to clients.

He did not like to let go. That is why he would die with some of his masterpieces still near his bedside.

He knew that there was always more he might learn, new techniques he might master, and further inspirations that might strike him. And he was right.

“The good painter has to paint two principal things, man and the intention of his mind,” he wrote.

His inability to finish the Adoration of the Magi and Saint Jerome may have been caused by, and in turn contributed to, melancholy or depression. His notebooks from around 1480 are filled with expressions of gloom, even anguish.

“Tell me if anything was ever done . . . Tell me . . . Tell me.”

“There is no perfect gift without great suffering. Our glories and our triumphs pass away.”

Leonardo and Atalante were probably part of a February 1482 diplomatic delegation headed by Bernardo Rucellai, a wealthy banker, arts patron, and philosophy enthusiast who was married to Lorenzo’s older sister and had just been made Florence’s ambassador to Milan.2 In his writings, Rucellai introduced the term balance of power to describe the continuous conflicts and shifting alliances involving Florence, Milan, other Italian city-states, plus a pride of popes, French kings, and Holy Roman emperors. The competition among the various rulers was not only military but cultural, and Leonardo sought to be useful on both fronts.

Milan, with 125,000 citizens, was three times the size of Florence. More important for Leonardo, it had a ruling court. The Medici in Florence were generous supporters of the arts, but they were bankers who operated behind the scenes.

In other words, Milan’s castle provided a perfect environment for Leonardo, who had a fondness for strong leaders, loved the diversity of talent they attracted, and aspired to be on a comfortable retainer.

THE JOB APPLICATION

Most illustrious Lord, Having now sufficiently studied the inventions of all those who proclaim themselves skilled contrivers of instruments of war, and having found that these instruments are no different than those in common use, I shall be bold enough to offer, with all due respect to the others, my own secrets to your Excellency and to demonstrate them at your Convenience.
1) I have designed extremely light and strong bridges, adapted to be easily carried, and with them you may pursue and at any time flee from the enemy; and others, indestructible by fire and battle, easy to lift and place. Also methods of burning and destroying those of the enemy.

2) I know how, during a siege, to take the water out of the trenches, and make an infinite variety of bridges, covered ways, ladders, and other machines suitable to such expeditions.

3) If a place under siege cannot be reduced by bombardment, because of the height of its banks or the strength of its position, I have methods for destroying any fortress even if it is founded upon solid rock.

4) I have kinds of cannons, convenient and easy to carry, that can fling small stones almost resembling a hailstorm; and the smoke of these will cause great terror to the enemy, to his great detriment and confusion.

9) [Leonardo moved up this item in the draft.] And when the fight is at sea, I have many kinds of efficient machines for offense and defense, and vessels that will resist the attack of the largest guns, and powder and fumes.

5) I have ways of making, without noise, underground tunnels and secret winding passages to arrive at a desired point, even if it is necessary to pass underneath trenches or a river.

6) I will make unassailable armored chariots that can penetrate the ranks of the enemy with their artillery, and there is no body of soldiers so great that it could withstand them. And behind these, infantry could follow quite unhurt.

7) In case of need I will make cannons and artillery of beautiful and useful design that are different from those in common use.

8) Where bombardment will not work, I can devise catapults, mangonels, caltrops and other effective machines not in common use.

10) In times of peace I can give perfect satisfaction and be the equal of any other in architecture and the composition of buildings public and private; and in guiding water from one place to another. Also, I can execute sculpture in marble, bronze and clay. Likewise in painting, I can do everything possible, as well as any other man, whosoever he may be. Moreover, work could be undertaken on the bronze horse, which will be to the immortal glory and eternal honor of His Lordship, your father, and of the illustrious house of Sforza. And if any of the above-mentioned things seem impossible or impracticable to anyone, I am most readily disposed to demonstrate them in your park or in whatsoever place shall please Your Excellency.

Leonardo mentioned none of his paintings. Nor did he refer to the talent that ostensibly caused him to be sent to Milan: an ability to design and play musical instruments. What he mainly pitched was a pretense of military engineering expertise.

Leonardo cast himself as an engineer because he was going through one of his regular bouts of being bored or blocked by the prospect of picking up a brush.

After settling into Milan, he would in fact begin to pursue military engineering earnestly and come up with some innovative concepts for machines, even as he continued to dance around the line between ingenuity and fantasy.

Here is our gentle and beloved Leonardo, who became a vegetarian because of his fondness for all creatures, wallowing in horrifying depictions of death. It is, perhaps, yet another glimpse of his inner turmoil. Within his dark cave was a demon imagination.

Leonardo was a pioneer in propounding laws of proportion: how one quantity, such as force, rises in proportion to another, such as the length of a lever.

How serious was Leonardo? Was he merely being clever on paper and trying to impress Ludovico? Was the giant crossbow another example of his ingenuity blurring into fantasy? I believe his proposal was serious. He made more than thirty preparatory drawings, and he detailed with precision the gears, worm screws, shafts, triggers, and other mechanisms.

Leonardo would be known for paintings, monuments, and inventions that he conceived but never brought to fruition. The giant crossbow falls into that category.

That was also true, it turned out, for most of the military devices he conceived and drew during the 1480s. “I will make unassailable armored chariots,” he promised in his letter to Ludovico.

Only one of Leonardo’s military conceptions is known to have made it off the pages of his notebooks and onto the battlefield, and he arguably deserves priority as its inventor. The wheellock, or wheel lock, which he devised in the 1490s, was a way to create a spark for igniting the gunpowder in a musket or similar hand-carried weapon. When the trigger was pulled, a metal wheel was set spinning by a spring. As it scraped against a stone, it sparked enough heat to ignite the gunpowder.

The wheellock came into use in Italy and Germany around that time and proved to be influential in facilitating both warfare and the personal use of guns.

Leonardo would not be involved in military activity until 1502, when he went to work for a more difficult and tyrannical strongman, Cesare Borgia.

The best example was his set of plans for a utopian city, which was a favorite subject for Italian Renaissance artists and architects. Milan had been ravaged in the early 1480s by three years of the bubonic plague, which killed close to one-third of its inhabitants. With his scientific instincts, Leonardo realized that the plague was spread by unsanitary conditions and that the health of the citizens was related to the health of their city.

The population of Milan would be relocated to ten new towns, designed and built from scratch along the river, in order to “disperse its great congregation of people which are packed like goats one behind the other, filling every place with fetid smells and sowing seeds of pestilence and death.”

He applied the classic analogy between the microcosm of the human body and the macrocosm of the earth: cities are organisms that breathe and have fluids that circulate and waste that needs to move.

Leonardo’s idea was to combine the streets and canals into a unified circulation system. The utopian city he envisioned would have two levels: an upper level designed for beauty and pedestrian life, and a level hidden below for canals, commerce, sanitation, and sewage.

Unlike the cramped streets of Milan, which Leonardo realized led to the spread of disease, the boulevards in the new town would be at least as wide as the height of the houses. To keep these boulevards clean, they would be sloped to the middle to allow rainwater to drain through central slits into a sewer circulation system below.

In collecting such a medley of ideas, Leonardo was following a practice that had become popular in Renaissance Italy of keeping a commonplace and sketch book, known as a zibaldone.

On the center-left is a figure Leonardo loved to draw or doodle: a semiheroic, craggy old man with a long nose and jutting chin. Wearing a toga, he looks both noble and slightly comic.

And we will see variations of this craggy character reappearing often in his notebooks.

The result is a seamless connection of geometry to nature and a glimpse into Leonardo’s art of spatial thinking.

A fundamental theme in his art and science: the interconnectedness of nature, the unity of its patterns, and the analogy between the workings of the human body and those of the earth.

Another set of drawings that Leonardo produced for the amusement of the Sforza court were pen-and-ink caricatures of funny-looking people he dubbed “visi mostruosi” (monstrous faces), which are now commonly called his “grotesques.”

As he wrote in his notes for his treatise on painting, “If the painter wishes to see beauties that charm him, it lies within his power to create them; and if he wishes to see monstrosities that are frightful, buffoonish, or ridiculous, or pitiable, he can be lord thereof.”

In notes for his treatise on painting, Leonardo recommended to young artists this practice of walking around town, finding people to use as models, and recording the most interesting ones in a portable notebook: “Take a note of them with slight strokes in a little book which you should always carry with you,” he wrote. “The positions of the people are so infinite that the memory is incapable of retaining them, which is why you should keep these sketches as your guides.”

An early example of a theme that Leonardo would return to repeatedly until the end of his life: cataclysmic scenes of destruction and deluge that consume all earthly

He was not motivated by wealth or material possessions. In his notebooks, he decried “men who desire nothing but material riches and are absolutely devoid of the desire for wisdom, which is the sustenance and truly dependable wealth of the mind.”2

“In narrative paintings you should closely intermingle direct opposites, because they offer a great contrast to each other, especially when they are adjacent. Thus, have the ugly one next to the beautiful, the large next to the small, the old next to the young.”

Sought to harmonize the proportions of a human to that of a church, an effort that would culminate with an iconic drawing by Leonardo that came to symbolize the harmonious relationship between man and the universe.

Leonardo made a philosophical pitch that drew on the analogy, of which he was so fond, between human bodies and buildings. “Medicines, when properly used, restore health to invalids, and a doctor will make the right use of them if he understands the nature of man,” he wrote. “This too is what the sick cathedral needs—it needs a doctor-architect, who understands the nature of the building and the laws on which correct construction is based.”

The greater the weight placed on the arches, the less the arch transmits the weight to the columns:

Marcus Vitruvius Pollio, born around 80 BC, served in the Roman army under Caesar and specialized in the design and construction of artillery machines.

Vitruvius later became an architect and worked on a temple, no longer in existence, in the town of Fano in Italy. His most important work was literary, the only surviving book on architecture from classical antiquity: De Architectura, known today as The Ten Books on Architecture.13 For many dark centuries, Vitruvius’s work had been forgotten, but in the early 1400s it was one of the many pieces of classical writing, including Lucretius’s epic poem On the Nature of Things and Cicero’s orations, that were rediscovered and collected by the pioneering Italian humanist Poggio Bracciolini.

More broadly, Vitruvius’s belief that the proportions of man are analogous to those of a well-conceived temple—and to the macrocosm of the world—became central to Leonardo’s worldview.

When Leonardo drew his Vitruvian Man, he had a lot of interrelated ideas dancing in his imagination. These included the mathematical challenge of squaring the circle, the analogy between the microcosm of man and the macrocosm of earth, the human proportions to be found through anatomical studies, the geometry of squares and circles in church architecture, the transformation of geometric shapes, and a concept combining math and art that was known as “the golden ratio” or “divine proportion.”

“Though I have no power to quote from authors as they have,” he proclaimed almost proudly, “I shall rely on a far more worthy thing—on experience.”1 Throughout his life, he would repeat this claim to prefer experience over received scholarship. “He who has access to the fountain does not go to the water-jar,” he wrote.2 This made him different from the archetypal Renaissance Man, who embraced the rebirth of wisdom that came from rediscovered works of classical antiquity.

We can see a turning point in the early 1490s, when he undertook to teach himself Latin, the language not only of the ancients but also of serious scholars of his era.

In that regard, Leonardo was born at a fortunate moment. In 1452 Johannes Gutenberg began selling Bibles from his new printing press, just when the development of rag processing was making paper more readily available.

Leonardo thus was able to become the first major European thinker to acquire a serious knowledge of science without being formally schooled in Latin or Greek.

In the late 1480s he itemized five books he owned: the Pliny, a Latin grammar book, a text on minerals and precious stones, an arithmetic text, and a humorous epic poem, Luigi Pulci’s Morgante, about the adventures of a knight and the giant he converted to Christianity, which was often performed at the Medici court.

Thus Leonardo became a disciple of both experience and received wisdom. More important, he came to see that the progress of science came from a dialogue between the two. That in turn helped him realize that knowledge also came from a related dialogue: that between experiment and theory.

A natural observer and experimenter, he was neither wired nor trained to wrestle with abstract concepts. He preferred to induce from experiments rather than deduce from theoretical principles.

He would try to look at facts and from them figure out the patterns and natural forces that caused those things to happen.

Scholastic theologians of the Middle Ages had fused Aristotle’s science with Christianity to create an authorized creed that left little room for skeptical inquiry or experimentation. Even the humanists of the early Renaissance preferred to repeat the wisdom of classical texts rather than test it.

When he began absorbing knowledge from books in the 1490s, it helped him realize the importance of being guided not only by experiential evidence but also by theoretical frameworks. More important, he came to understand that the two approaches were complementary, working hand in hand.

He even came to be dismissive of experimenters who relied on practice without any knowledge of the underlying theories. “Those who are in love with practice without theoretical knowledge are like the sailor who goes onto a ship without rudder or compass and who never can be certain whither he is going,” he wrote in 1510. “Practice must always be founded on sound theory.”

As a result, Leonardo became one of the major Western thinkers, more than a century before Galileo, to pursue in a persistent hands-on fashion the dialogue between experiment and theory that would lead to the modern Scientific Revolution. Aristotle had laid the foundations, in ancient Greece, for the method of partnering inductions and deductions: using observations to formulate general principles, then using these principles to predict outcomes.

Any person who puts “Describe the tongue of the woodpecker” on his to-do list is overendowed with the combination of curiosity and acuity.

His curiosity, like that of Einstein, often was about phenomena that most people over the age of ten no longer puzzle about: Why is the sky blue? How are clouds formed? Why can our eyes see only in a straight line? What is yawning?

We can, if we wish, not just marvel at him but try to learn from him by pushing ourselves to look at things more curiously and intensely.

Look carefully and separately at each detail.

Deep observation must be done in steps: “If you wish to have a sound knowledge of the forms of objects, begin with the details of them, and do not go on to the second step until you have the first well fixed in memory.”

Leonardo had a strategy he used to refine his observational skills. He would write down marching orders to himself, determining how he would sequence his observations in a methodical step-by-step way. “First define the motion of the wind and then describe how the birds steer through it with only the simple balancing of the wings and tail,” he wrote in one example. “Do this after the description of their anatomy.”

Leonardo thus realized, before other scientists, that a bird stays aloft not merely because the wings beat downward against the air but also because the wings propel the bird forward and the air lessens in pressure as it rushes over the wing’s curved top surface.

He used drawing as a tool for thinking.

A major enterprise of the late Renaissance was finding a way to equalize the power of an unwinding spring.

His mechanical ingenuity is combined with his artistic passion for spirals and curls.

Leonardo understood the concept of what he called impetus, which is what happens when a force pushes an object and gives it momentum. “A body in motion desires to maintain its course in the line from which it started,” he wrote. “Every movement tends to maintain itself; or, rather, every body in motion continues to move so long as the influence of the force that set it in motion is maintained in it.”9 Leonardo’s insights were a precursor to what Newton, two hundred years later, would make his first law of motion: that a body in motion will stay in the same motion unless acted upon by another force.

What prevents perpetual motion, Leonardo realized, is the inevitable loss of momentum in a system when it rubs against reality. Friction causes energy to be lost and prevents motion from being perpetual.

Through his work on machinery, Leonardo developed a mechanistic view of the world foreshadowing that of Newton. All movements in the universe—of human limbs and of cogs in machines, of blood in our veins and of water in rivers—operate according to the same laws, he concluded. These laws are analogous; the motions in one realm can be compared to those in another realm, and patterns emerge. “Man is a machine, a bird is a machine, the whole universe is a machine,” wrote Marco Cianchi in an analysis of Leonardo’s devices.

Leonardo increasingly came to realize that mathematics was the key to turning observations into theories. It was the language that nature used to write her laws. “There is no certainty in sciences where mathematics cannot be applied,” he declared.

One of Leonardo’s close friends at Milan’s court was Luca Pacioli, a mathematician who developed the first widely published system for double-entry bookkeeping.

His sixty illustrations for Pacioli were the only drawings he published during his lifetime.

Leonardo’s mastery of perspective added to the three-dimensional look. He could envision the shapes in his head as real objects, then convey them on the page.

Leonardo became the first person to discover the center of gravity of a triangular pyramid (one-quarter of the way up a line from the base to the peak).

Pacioli’s book focused on the golden ratio, or divine proportion, an irrational number that expresses a ratio that pops up often in number series, geometry, and art. It is approximately 1.61803398, but (being irrational) has decimals that stretch on randomly forever. The golden ratio occurs when you divide a line into two parts in such a way that the ratio between the whole length and the longer part is equal to the ratio between the longer part and the shorter part. For example, take a line that’s 100 inches long and divide it into two parts of 61.8 inches and 38.2 inches. That comes close to the golden ratio, because 100 divided by 61.8 is about the same as 61.8 divided by 38.2; in both cases, it’s approximately 1.618.

Euclid wrote about this ratio in around 300 BC, and it has fascinated mathematicians ever since. Pacioli was the first to popularize the name divine proportion for it. In his book by that title, he described the way it turns up in studies of geometric solids such as cubes and prisms and polyhedrons. In popular lore, including in Dan Brown’s The Da Vinci Code, the golden ratio is found throughout Leonardo’s art.11 If so, it is doubtful it was intentional.

As an artist, Leonardo was particularly interested in how the shapes of objects transformed when they moved. From his observations on the flow of water, he developed an appreciation for the idea of the conservation of volume: as a quantity of water flows, its shape changes, but its volume remains exactly the same.

An example would be if you took a square and transformed it into a circle with the exact same area. A three-dimensional example would be showing how a sphere could be transformed into a cube with the same volume.

By grappling with these transformations and persistently recording his insights, Leonardo helped to pioneer the field of topology, which looks at how shapes and objects can undergo transformations while keeping some of the same properties.

We now know that a mathematical process for squaring a circle requires use of a transcendental number, in this case π, which cannot be expressed as a fraction and is not the root of any polynomial with rational coefficients.

Leonardo wanted to know how psychological emotions led to physical motions. As a result, he would also become interested in the way the nervous system works and how optical impressions are processed.

When he moved to Milan, he discovered that the study of anatomy there was pursued primarily by medical scholars rather than by artists.

If there were not so much else to remember him for, Leonardo could have been celebrated as a pioneer of dentistry.

Beginning with the drapery studies done in Verrocchio’s studio, Leonardo mastered the art of rendering light hitting rounded and curved objects. Now he was deploying that art to transform, and make beautiful, the study of anatomy.

More important, his fascination with the connection between the mind and the body became a key component of his artistic genius: showing how inner emotions are manifest in outward gestures. “In painting, the actions of the figures are, in all cases, expressive of the purpose of their minds,” he wrote.14 As he was finishing his first round of anatomical studies, he was beginning work on what would be the greatest expression in the history of art of that maxim, The Last Supper.

“When the arm is bent, the fleshy part shrinks to two-thirds of its length,” he recorded. “When a man kneels down he will diminish by the fourth part of his height. . . . When a heel is raised, the tendon and ankle get closer to each other by a finger’s breadth. . . . When a man sits down, the distance from his seat to the top part of his head will be half of his height plus the thickness and length of the testicles.”

Plus the thickness and length of the testicles? Once again it is useful to pause and marvel. Why the obsessiveness? Why the need for reams of data? Partly, at least initially, it was to help him paint humans, or horses, in various poses and movements. But there was something grander involved. Leonardo had set for himself the most magnificent of all tasks for the mind of mankind: nothing less than knowing fully the measure of man and how he fits into the cosmos. In his notebook, he proclaimed his intention to fathom what he called “universale misura del huomo,” the universal measure of man.17 It was the quest that defined Leonardo’s life, the one that tied together his art and his science.

Leonardo was a master at storytelling and conveying a sense of dramatic motion, and like many of his paintings, beginning with the Adoration of the Magi, the Virgin of the Rocks is a narrative. In his first version of the painting, the androgynous curly-haired angel begins the narrative by looking out directly from the scene, catching our eye, smiling enigmatically, and pointing to make us look at the baby Saint John. John in turn is dropping to his knees and clasping his hands in reverence toward the baby Jesus, who returns the gesture with a sign of blessing. The Madonna, her body twisted in motion, glances down at John and grasps his shoulder protectively while hovering her other hand over Jesus. And as our eyes finish a clockwise rotation of the scene, we notice the left hand of the angel holding Jesus as he leans on the rocky precipice over a pond, his hand touching the ledge. Taken in as a whole, it becomes a sequential medley of hand gestures presaging The Last Supper.

Leonardo’s apprentices and students did not merely copy his designs. A show at the Louvre in 2012 featured paintings that students and assistants in his workshop did of his masterpieces. Many were variations that were produced alongside his original, indicating that he and his colleagues were together exploring various alternative approaches to the planned painting. While Leonardo worked on the master version, other versions were being painted under his supervision.20

The angel, like the one he painted for Verrocchio’s Baptism of Christ, is an example of Leonardo’s proclivity for gender fluidity.

The drawing is fascinating because it is one of the best displays of Leonardo’s genius as a draftsman. With a few simple lines and brilliant strokes, concise and precise, he is able to create a sketch of unsurpassed beauty. At first glance it captivates you, then its deceptive simplicity draws you into a prolonged and profound engagement.

The drawing is an exquisite example of Leonardo’s use of hatching to create shadows and texture. These parallel strokes are delicate and tight in some places (the shadow on her left cheek) and bold and spacious in others (her back shoulder). The variations in the hatching allow, with just simple strokes, wondrous gradations of shadow and subtle blurring of contours.

Like the angel in the Louvre’s Virgin of the Rocks, she stares out at us even as her left eye drifts. As you walk back and forth, her eyes follow you. She drinks you in.

Portrait of a Musician (fig. 67), painted in the mid-1480s. His only known portrait of a man, there are no surviving records or contemporary mentions of it.

And unlike Leonardo’s other works, his body faces in the same direction as his gaze, with no sense of movement.

Cecilia Gallerani’s alluring beauty would be captured for the ages. At the height of their relationship, around 1489, when she was fifteen, Ludovico commissioned Leonardo to paint her portrait

The result is a stunning and innovative masterpiece, in many ways the most delightful and charming of Leonardo’s paintings. Other than the Mona Lisa, it is my favorite of his works.

Painted in oil on a walnut panel, the portrait of Cecilia, now known as Lady with an Ermine, was so innovative, so emotionally charged and alive, that it helped to transform the art of portraiture. The twentieth-century art historian John Pope-Hennessy called it the “first modern portrait” and “the first painting in European art to introduce the idea that a portrait may express the sitter’s thoughts through posture and gestures.”6 Instead of being shown in profile, as was traditional, she is in three-quarters view.

The twisting head and body, a form of contrapposto, had become one of Leonardo’s lively signatures, such as in the angel of Virgin of the Rocks.

He gave a rigorous scientific and aesthetic defense of painting, which was then considered a mechanical art, arguing that it should instead be regarded as the highest of the liberal arts, transcending poetry and music and sculpture.

This type of staged debate on the comparative value of various intellectual endeavors, ranging from math to philosophy to art, was a staple of evenings at the Sforza Castle. Known as a paragone, from the Italian word for “comparison,” such a discourse was a way for artists and scholars to attract patrons and elevate their social status during the Italian Renaissance.

in 1489 by Francesco Puteolano, who argued that poetry and historical writing were most important. The reputations and memories of the great rulers, including Caesar and Alexander the Great, came from historians rather than sculptors or painters, he said.

The goal of Leonardo’s argument was to elevate the work of painters—and their social status—by linking their art to the science of optics and the mathematics of perspective. By exalting the interplay between art and science, Leonardo wove an argument that was integral to understanding his genius: that true creativity involves the ability to combine observation with imagination, thereby blurring the border between reality and fantasy. A great painter depicts both, he said.

He had first tackled the complexities of shadows when drawing draperies as an exercise in Verrocchio’s studio. He came to understand that the use of shadows, not lines, was the secret to modeling three-dimensional objects on a two-dimensional surface. The primary goal of a painter, Leonardo declared, “is to make a flat surface display a body as if modeled and separated from this plane.” This crowning achievement of painting “arises from light and shade.”

Reading his studies on reflected light provides us with a deeper appreciation for the subtleties of the light-dappled shadow on the edge of Cecilia’s hand in Lady with an Ermine or the Madonna’s hand in Virgin of the Rocks, and it reminds us why these are innovative masterpieces. Studying the paintings, in turn, leads to a more profound understanding of Leonardo’s scientific inquiry into rebounding and reflected light. This iterative process was true for him as well: his analysis of nature informed his art, which informed his analysis of nature.

He realized that nature itself, independent of how our eyes perceive it, does not have precise lines.

In his mathematical studies, he made a distinction between numerical quantities, which involve discrete and indivisible units, and continuous quantities of the sort found in geometry, which involve measurements and gradations that are infinitely divisible. Shadows are in the latter category; they come in continuous, seamless gradations rather than in discrete units that can be delineated. “Between light and darkness there is infinite variation, because their quantity is continuous,” he wrote.

That was not a radical proposition. But Leonardo then took a further step. Nothing in nature, he realized, has precise mathematical lines or boundaries or borders. “Lines are not part of any quantity of an object’s surface, nor are they part of the air which surrounds this surface,” he wrote. He realized that points and lines are mathematical constructs.

Instead an artist needs to represent the shape and volume of objects by relying on light and shadow.

Leonardo’s insistence that all boundaries, both in nature and in art, are blurred led him to become the pioneer of sfumato, the technique of using hazy and smoky outlines such as those so notable in the Mona Lisa.

Sfumato is not merely a technique for modeling reality more accurately in a painting. It is an analogy for the blurry distinction between the known and the mysterious, one of the core themes of Leonardo’s life.

Like much of his science, his optics research was begun to help inform his art, but by the 1490s he was pursuing it with a relentless, seemingly insatiable and pure curiosity.

In a small notebook sketch done late in his life, which historian James Ackerman called “a token of one of the most consequential changes in the history of Western art,” Leonardo shows a receding row of trees. Each one loses a little detail, until the ones near the horizon are just a simple shape devoid of individual branches. Even in his botanical drawings and the depiction of plants in some of his paintings, leaves in the foreground are more distinct than those in the background.

Acuity perspective is related to what Leonardo called aerial perspective: things become blurrier in the distance not only because their details disappear as they become smaller but also because the air and mists soften distant objects.

When Leonardo was painting The Last Supper (fig. 74), spectators would visit and sit quietly just so they could watch him work. The creation of art, like the discussion of science, had become at times a public event.

Ludovico Sforza. Upon the death of his nephew, he had become the official Duke of Milan in early 1494, and he set about enhancing his stature in a time-honored way, through art patronage and public commissions.

When Leonardo was summoned by the duke, they ended up having a discussion of how creativity occurs. Sometimes it requires going slowly, pausing, even procrastinating. That allows ideas to marinate, Leonardo explained. Intuition needs nurturing. “Men of lofty genius sometimes accomplish the most when they work least,” he told the duke, “for their minds are occupied with their ideas and the perfection of their conceptions, to which they afterwards give form.”

By conveying ripples of motions and emotions, Leonardo was able not merely to capture a moment but to stage a drama, as if he were choreographing a theatrical performance.

The twelve apostles are clustered into groups of three. Starting on our left, we can sense the flow of time, as if the narrative moves from left to right. On the far left is the cluster of Bartholomew, James the Minor, and Andrew, all still showing the immediate reaction of surprise at Jesus’ announcement. Bartholomew, alert and tough, is in the process of leaping to his feet, “about to rise, his head forward,” as Leonardo wrote.

The second trio from the left is Judas, Peter, and John. Dark and ugly and hook-nosed, Judas clutches in his right hand the bag of silver he has been given for promising to betray Jesus, whose words he knows are directed at him. He rears back, knocking over a salt cellar (which is clearly visible in early copies but not the current painting) in a gesture that becomes notorious. He leans away from Jesus and is painted in shadow. Even as his body recoils and twists, his left hand reaches for the incriminating bread that he and Jesus will share. “He that dippeth his hand with me in the dish shall betray me,” Jesus says, according to Matthew. Or as in the gospel according to Mark, “Behold, the hand of him that betrayeth me is with me on the table.

Peter is pugnacious and agitated, elbowing forward in indignation. “Who is it of whom he speaks?” he asks. He seems ready to take action. In his right hand is a long knife; he would, later that evening, slice off the ear of a servant of the high priest while trying to protect Jesus from the mob that came to arrest him.

By contrast, John is quiet, knowing that he is not suspect; he seems saddened by yet resigned to what he knows cannot be prevented. Traditionally, John is shown asleep or lying on Jesus’ breast. Leonardo shows him a few seconds later, after Jesus’ pronouncement, wilting sadly.

Dan Brown in his novel The Da Vinci Code, which draws on The Templar Revelation by Lynn Picknett and Clive Prince, wove a conspiracy theory that has as one piece of evidence the assertion that the effeminate-looking John is actually secretly meant to be Mary Magdalene, the faithful follower of Jesus.

Ross King points out in a book on The Last Supper, “On the contrary: Leonardo was skilled at blurring the differences between the sexes.”

Jesus, sitting alone in the center of The Last Supper, his mouth still slightly open, has finished making his pronouncement. The expressions of the other figures are intense, almost exaggerated, as if they are players in a pageant. But Jesus’ expression is serene and resigned. He looks calm, not agitated. He is slightly larger than the apostles, although Leonardo cleverly disguised the fact that he has used this trick. The open window with the bright landscape beyond forms a natural halo. His blue cloak is painted with ultramarine, the most expensive of pigments. In his studies of optics, Leonardo had discovered that objects against a light background look larger than when against a dark background.

The trio to the right of Jesus includes Thomas, James the Greater, and Philip. Thomas raises his index finger with his hand turned inward in a pointing gesture closely associated with Leonardo.

Later he will be known as doubting Thomas because he demanded proof of Jesus’ resurrection, which Jesus provided by letting Thomas place a finger in his wounds.

The final trio on the right comprises Matthew, Thaddeus, and Simon. They are already in a heated discussion about what Jesus may have meant. Look at the cupped right hand of Thaddeus.

Is he slapping his hand down as if to say, I knew it? Is he jerking his thumb toward Judas? Now look at Matthew. Are his two upturned palms gesturing toward Jesus or Judas? The viewer need not feel bad about being confused; in their own ways Matthew and Thaddeus are also confused about what has just occurred, and they are trying to sort it out and turning to Simon for answers.

Jesus’ right hand is reaching out to a stemless glass one-third filled with red wine. In a dazzling detail, his little finger is seen through the glass itself. Just beyond the glass are a dish and a piece of bread. His left hand is palm up, gesturing at another piece of bread, which he gazes at with downcast eyes.

That gesture and glance create the second moment that shimmers in the narrative of the painting: that of the institution of the Eucharist. In the gospel of Matthew, it occurs in the moment after the announcement of the betrayal: “Jesus took bread, and blessed it, and broke it, and gave it to the disciples, and said, ‘Take, eat; this is my body.’ And he took the cup, and gave thanks, and gave it to them, saying, ‘Drink ye all of it, for this is my blood of the new testament, which is shed for many for the remission of sins.’ This part of the narrative reverberates outward from Jesus, encompassing both the reaction to his revelation that Judas will betray him and the institution of the holy sacrament.

with a painting as large as The Last Supper, the viewer might see it from the front or the side or while walking past. That required what Leonardo called “complex perspective,” which is a mix of natural and artificial perspective. The artificial part was needed to adjust for the fact that a person looking at a very large painting would be closer to some parts of it than to other parts. “No surface can be seen exactly as it is,” Leonardo wrote, “because the eye that sees it is not equally remote from all its edges.”

In The Last Supper, the painted room diminishes in size so quickly that the back wall is just large enough to have three windows showing the landscape outside. The tapestries are not proportional. The table is too narrow for a comfortable supper, and the apostles are all on one side of it, where there are not enough places for them to sit. The floor is raked forward, like a stage, and the table is slanted a bit toward us as well. The characters are all at the forefront, as if in a play, and even their gestures are theatrical.

All told, The Last Supper is a mix of scientific perspective and theatrical license, of intellect and fantasy, worthy of Leonardo. His study of perspective science had not made him rigid or academic as a painter. Instead, it was complemented by the cleverness and ingenuity he had picked up as a stage impresario. Once he knew the rules, he became a master at fudging and distorting them, as if creating perspectival sfumato.

As a result, The Last Supper, both in its creation and in its current state, becomes not just an example of Leonardo’s genius but also a metaphor for it. It was innovative in its art and too innovative in its methods. The conception was brilliant but the execution flawed. The emotional narrative is profound but slightly mysterious, and the current state of the painting adds another thin veil of mystery to the ones that so often shroud Leonardo’s life and work.

But his life became unsettled in the late 1490s, after Caterina’s death and the completion of The Last Supper. The bronze for his horse monument had been redirected in 1494 to make cannon to defend against a possible French invasion, and it soon became clear that Ludovico was not going to replace it.

Larger forces intervened to rescue Leonardo from his employment concerns. In the summer of 1499, an invasion force sent by the new French king, Louis XII, was bearing down on Milan. Leonardo added up the money in his cash box, 1,280 lire, distributed some to Salai (20 lire) and others, and then proceeded to hide the rest in paper packets around his studio to keep it safe from invaders and looters.

The French were, it turned out, protective of Leonardo. The day after his arrival, the king went to see The Last Supper, and he even asked whether it might be possible to cart it back to France. Fortunately, his engineers told him it was impossible. Instead of fleeing, Leonardo spent the next few months working with the French.

In fact, he had forged a secret deal with the new French governor of Milan, the Count of Ligny, to meet him in Naples and act as a military engineer inspecting fortifications.

When Leonardo reached Florence in late March 1500, he found a city that had just lived through a reactionary spasm that threatened to destroy its role in the vanguard of Renaissance culture. In 1494 a radical friar named Girolamo Savonarola had led a religious rebellion against the ruling Medici and instituted a fundamentalist regime that imposed strict new laws against homosexuality, sodomy, and adultery.

On Mardi Gras of 1497 Savonarola led what became known as the “Bonfire of the Vanities,” in which books, art, clothing, and cosmetics were set aflame. The following year, popular opinion turned on him, and he was hanged and burned in the central square of Florence.

Friar Pietro, in one of his letters to the persistent Isabella, described a painting that Leonardo was doing at the request of Louis XII’s secretary, Florimond Robertet. “The little picture he is working on is of a Madonna who is seated as if she were about to spin yarn,” he wrote, “and the child has placed his foot in the basket of yarns and has grasped the yarnwinder, and stares attentively at the four spokes, which are in the form of a cross, and he smiles and grips it tightly, as if he were longing for this cross, not wishing to yield it to his mother, who appears to want to take it away from him.”

When he returned to Florence in 1500, Leonardo set up a collaborative workshop, and production of some pictures, especially small devotional ones, became a team effort, just as it had been in Verrocchio’s studio.

But the Yarnwinder paintings are energized by what had become Leonardo’s special ability to convey a psychological narrative.

There is a flow of physical motions as Jesus reaches toward the cross-like object, his finger pointed heavenward, the gesture that Leonardo loved. His moist eyes are shiny with a tiny sparkle of luster, and they have their own narrative: he is just the age when a baby can discern objects and focus on them, and he is doing so with a concerted effort that combines his sight with his sense of touch. We sense that his ability to focus on the cross causes a premonition of his fate. He looks innocent and at first playful, but if you look at his mouth and eyes you sense a resigned and even loving comfort with what will be his destiny. By comparing Madonna of the Yarnwinder to the Benois Madonna (fig. 13), we can see the historic leap Leonardo made by turning static scenes into emotion-laden narratives.

Our eyes swirl counterclockwise as the narrative continues with Mary’s motions and emotions. Her face and her hand indicate anxiety, a desire to intervene, but also an understanding and an acceptance of what shall be. In the Virgin of the Rocks paintings (figs. 64 and 65), Mary’s hovering hand offers a serene benediction; in the Yarnwinders, her gesture is more conflicted, as if coiled to grasp her child while also recoiling from the temptation to intervene. She reaches out nervously, as if trying to decide whether to restrain him from his fate.

Leonardo’s studio was like a shop in which he devised a painting and his assistants worked with him to make multiple copies. This is similar to the way it had been in Verrocchio’s bottega.

How did the collaboration occur? What was the nature of the team and the teamwork? As with so many examples in history where creativity was turned into products, Leonardo’s Florence studio involved individual genius combined with teamwork. Both vision and execution were required.

one of Leonardo’s greatest masterpieces, the Virgin and Child with Saint Anne (fig. 79), featuring Mary sitting on the lap of her mother. The final painting combines many elements of Leonardo’s artistic genius: a moment transformed into a narrative, physical motions that match mental emotions, brilliant depictions of the dance of light, delicate sfumato, and a landscape informed by geology and color perspective. It was proclaimed to be “Leonardo da Vinci’s ultimate masterpiece” (l’ultime chef d’oeuvre) in the title of the catalogue published by the Louvre for a 2012 exhibition celebrating its restoration—this from the museum that also owns the Mona Lisa.

It is important, Leonardo wrote, to “have a movement of a person’s limbs appropriate to that person’s mental movements.” His painting of the Virgin and Child with Saint Anne shows what he meant. Mary’s right arm is stretched as she tries to restrain the Christ child, showing a protective but gentle love. But he is intent on wrestling with the lamb, his leg over its neck and his hands grappling with its head. The lamb, as Friar Pietro told us, represents the Passion, Jesus’ fate, and he will not be restrained from it.

The image of a squirming boy with what looks like two mothers conjures up Leonardo’s own childhood being raised by both his birth mother, Caterina, and his slightly younger stepmother.

Leonardo had also been wrestling with the question of why the sky appears blue, and around that time he had correctly concluded that it had to do with the water vapor in the air.

Most significant, the painting conveys the paramount theme in Leonardo’s art: the spiritual connection and analogy between the earth and humans. Echoing so many of his paintings—Ginevra de’ Benci, Virgin of the Rocks, Madonna of the Yarnwinder, and of course the Mona Lisa—a river curls from the distant horizon of the macrocosm of the earth and seems to flow into the veins of the Holy Family, ending with the lamb that foreshadows the Passion. The curving flow of the river connects to the flowing composition of the characters.

The Saint Anne is the most complex and layered of Leonardo’s panel paintings, and many see it as a masterpiece on a par with the Mona Lisa, perhaps even surpassing it because it is more complex in its composition and motion.

The myth of Leda and the swan tells how the Greek god Zeus assumed the form of a swan and seduced the beautiful mortal princess Leda. She produced two eggs, from which hatched two sets of twins Helen (later known as Helen of Troy) and Clytemnestra, and Castor and Pollux. Leonardo’s depiction focuses more on fertility than sex; instead of painting the seduction scene, as others had done, he chose to portray the moment of the births, showing Leda caressing the swan as the four children squirm from their shells. One of the most vivid copies is by his pupil Francesco Melzi (fig. 81).

When Leonardo was working on this painting during his second period in Florence in the early 1500s, he was doing his most intense studies on the flight of birds and also planning a test flight of one of his flying machines, which he hoped to launch from the top of nearby Swan Mountain (Monte Ceceri). His note about his childhood memory of a bird flying into his crib and flapping its tail in his mouth is also from this period.

The painting conveys a domestic and familial harmony, a pleasant portrayal of a couple at home by their lake, cuddling as they admire their newborns. It also goes beyond the erotic to focus on the tale’s procreative aspects. From the lushness of the seeding plants, to the fecundity of the soil and the hatching of the eggs, the painting is a celebration of the fertility of nature. Unlike the usual depictions of the Leda myth, Leonardo’s is not about sex but birth.2

Ludovico Sforza, Leonardo’s patron in Milan, had a reputation for ruthlessness that included, among other alleged acts, poisoning his nephew in order to seize the ducal crown. But Ludovico was a choir boy compared to Leonardo’s next patron, Cesare Borgia.

Machiavelli used him as a model of cunning in The Prince and taught that his ruthlessness was a tool for power.1

Cesare Borgia was the son of the Spanish-Italian cardinal Rodrigo Borgia, soon to become Pope Alexander VI, who vies for the hotly contested title of most libertine Renaissance pope.

he forged an alliance with the French, and he was with King Louis XII marching into Milan in 1499. The day after their arrival, they went to see The Last Supper, and there Borgia first met Leonardo. Knowing Leonardo, it is likely that during the next few weeks he showed Borgia his military engineering designs.

in June 1502 Borgia was back. As his army sacked more surrounding towns, he commanded the leaders in Florence to send a delegation to hear his latest demands. Two people were selected to try to deal with him.

Accompanying him was the son of a bankrupt lawyer, well-educated but poor, whose writing skills and savvy understanding of power games had established him as Florence’s cleverest young diplomat: Niccolò Machiavelli.

He shared with Leonardo the trait of being a sharp observer.

Leonardo may have gone to work with Borgia at the behest of Machiavelli and Florence’s leaders as a gesture of goodwill, similar to the way he had been dispatched twenty years earlier to Milan as a diplomatic gesture to Ludovico Sforza. Or he may have been sent as a way for Florence to have an agent embedded with Borgia’s forces.

Borgia, it turned out, had disguised himself as a Knight Hospitaller and snuck away with three trusted guards to ride north at a furious pace to reinstate himself in the good graces of Louis, which he did.

“Be sure that the escape tunnel does not lead to the inner fortress, lest the fortress be captured by treachery or betrayal of the lord.”

While he was in Imola with Machiavelli and Borgia, Leonardo made what may be his greatest contribution to the art of war. It is a map of Imola, but not any ordinary map (fig. 87).18 It is a work of beauty, innovative style, and military utility. It combines, in his inimitable manner, art and science.

Drawn in ink with colored washes and black chalk, the Imola map was an innovative step in cartography. The moat around the fortified town is tinted a subtle blue, the walls are silvery, and the roofs of the houses brick red. The aerial view is from directly overhead, unlike most maps of the time. On the edges he has specified the distances to nearby towns, useful information for military campaigns, but written in his elegant mirror script, indicating that the version that survives is a copy he made for himself rather than Borgia.

Around this time, he perfected the odometer he had been developing to measure long distances (fig. 88).19 On a cart he mounted a vertical cog wheel, which looks like the front wheel of a wheelbarrow, that intersects with a horizontal cog wheel. Every time the vertical wheel completed a revolution, it would move the horizontal wheel a notch, and that would cast a stone into a container.

Acting as an artist-engineer, Leonardo had devised a new military weapon: accurate, detailed, and easily read maps.

In a larger sense, Leonardo’s maps are another example of one of his greatest, though underappreciated, innovations: devising new methods for the visual display of information.

In a land where the Medici, Sforzas, and Borgias jostled for power, Leonardo was able to time his patronage affiliations well and know when to move on. But there is more. Even as he remained aloof from most current events, he seemed to be attracted to power.

Just before Pisa broke away, a major world event made Florence even more eager to control a sea outlet. In March 1493 Christopher Columbus returned safely from his first voyage across the Atlantic Ocean, and the report of his discoveries quickly spread throughout Europe. This was soon followed by a flurry of other accounts of amazing explorations. Amerigo Vespucci, whose cousin Agostino worked with Machiavelli in the Florentine chancery, helped supply Columbus’s third voyage in 1498, and the following year he made his own voyage across the Atlantic, landing in what is now Brazil. Unlike Columbus, who thought he was finding a route to India, Vespucci correctly reported to his Florentine patrons that he had “arrived at a new land which for many reasons . . . we observed to be a continent.” His correct surmise led to its being named America, after him.

An entry for an account book in Florence that month lists a set of expenses and then adds, “This money has been spent to provide six horse coaches and to pay the board expenses for the expedition with Leonardo in the territory of Pisa to divert the Arno from its course and take it away from Pisa.”

Diverting the Arno River from its course and taking it away from Pisa? It was an audacious way to reconquer the city without storming the wall or wielding any weapons. If the river could be channeled somewhere else, Pisa would be cut off from the sea and lose its source of supply. The primary advocates of the idea included the two clever friends who had been holed up together that past winter in Imola, Leonardo da Vinci and Niccolò Machiavelli.

Even though it failed, the project to divert the Arno rekindled Leonardo’s interest in a larger scheme: creating a navigable waterway between Florence and the Mediterranean Sea.

But as with so many of his projects, Leonardo ended up not finishing the Battle of Anghiari, and what he painted is now lost. We can envision it mainly through copies. The best, which shows only the central part of what would have been a much larger mural, is by Peter Paul Rubens (fig. 91), which was made from other copies in 1603, after Leonardo’s unfinished work was covered up.

Heightening the significance of the commission was the fact that Leonardo would end up pitted against his personal and professional young rival, Michelangelo, who was chosen in early 1504 to paint the other large mural in the hall.

During the seventeen years that Leonardo was away in Milan, Michelangelo became Florence’s hot new artist. He was apprenticed to the thriving Florence workshop of the painter Domenico Ghirlandaio, won the patronage of the Medici, and traveled to Rome in 1496, where he carved his Pietà, showing Mary grieving over the body of Jesus.

By 1500 the two artists were back in Florence. Michelangelo, then twenty-five, was a celebrated but petulant sculptor, and Leonardo, forty-eight, was a genial and generous painter who had a following of friends and young students. It is enticing to think of what might have occurred if Michelangelo had treated him as a mentor. But that did not happen. As Vasari reported, he displayed instead “a very great disdain” toward Leonardo.

Michelangelo’s painting has the sharp, delineated outlines that Leonardo, with his love of sfumato and blurred borders, scorned as a matter of philosophy, optics, mathematics, and aesthetics. To define objects, Michelangelo used lines rather than following Leonardo’s practice of using shadows, which is why Michelangelo’s look flat rather than three-dimensional.

But Leonardo was obsessed by the optics, mathematics, and art of perspective.

For The Last Supper he had come up with tricks and illusions and artifices to make his work appear realistic from different vantages. He was able to make a preferred vantage point that was far away from the painting; he calculated it would ideally be located ten to twenty times as far away as the painting was wide. But the area that he was supposed to paint in Florence’s council hall was fifty-five feet long, twice that of The Last Supper, and his mural would be viewed from at most seventy feet away, far less than twice its width.

He was a perfectionist faced with challenges other artists would have disregarded but that he could not. So he put down his brushes. That behavior meant he would never again receive a public commission. But it is also what allowed him to go down in history as an obsessed genius rather than merely a reliable master painter.

“These battle cartoons of Leonardo and Michelangelo are the turning point of the Renaissance,” according to Kenneth Clark.

To understand Leonardo, it is necessary to understand why he moved away from Florence, this time for good. One reason is simple: he liked Milan better. It had no Michelangelo, no cadre of half-brothers suing him, no ghost of his father hovering. It had royalty rather than republicans, with jubilant pageants rather than the after-stench of bonfires of the vanities. It had doting patrons rather than oversight committees. And the foremost patron there was the one who loved Leonardo the most, Charles d’Amboise, the French royal governor who had written a flowery letter reminding the Florentines how brilliant their native son was.

Florence was the artistic center of the Italian Renaissance, but Milan and its nearby university town of Pavia had become more intellectually diverse.

He dissected the corpse of a man who claimed to be a hundred, planned a test of one of his flying machines, began a treatise on geology and water, devised a glass tank to examine the way flowing water deposits sediment, and swam underwater to compare the propulsion of a fish tail to a bird’s wing, jotting his conclusions on the same notebook page where he drafted his angry letter to his half-brothers.

We should pause to imagine the dandy-dressing Leonardo, now in his mid-fifties and at the height of his fame as a painter, spending his night hours at an old hospital in his neighborhood talking to patients and dissecting bodies. It is another example of his relentless curiosity that would astonish us if we had not become so used to it.

In his quest to figure out how the centenarian died, Leonardo made a significant scientific discovery: he documented the process that leads to arteriosclerosis, in which the walls of arteries are thickened and stiffened by the accumulation of plaque-like substances.

“The network of vessels behaves in man as in oranges, in which the peel becomes tougher and the pulp diminishes the older they become.”

Leonardo, who was not strongly religious, pushed back on the fundamentalists who considered dissection heretical. He believed it was a way to appreciate God’s handiwork. “You should not be distressed that your discoveries come through another’s death; rather you should rejoice that our Creator has provided an instrument of such excellence,” he wrote on a tinted blue notebook page on which he drew the muscles and bones of the neck.

“I have dissected more than ten human bodies,” he wrote, and after making that statement he would dissect even more, working on each as long as possible, until they decomposed so badly he was forced to move on. “As one body did not last so long, it was necessary to proceed by stages with as many bodies as would render my knowledge complete.” He then performed even more dissections so that he could ascertain the variances between humans.

Then comes my favorite item on any Leonardo list: “Describe the tongue of the woodpecker.” This is not just a random entry. He mentioned the woodpecker’s tongue again on a later page, where he described and drew the human tongue. “Make the motions of the woodpecker,” he wrote.

There is an echo in this passage of Leonardo’s memory of coming across the mouth of a cave as a young man. As in that tale, he had to overcome his fear to go into a dark and fearful space. Although at times he was irresolute and willing to abandon tasks, his powerful curiosity tended to overcome any hesitations when it came to exploring nature’s wonders.

In most of his studies of nature, Leonardo theorized by making analogies. His quest for knowledge across all the disciplines of arts and sciences helped him see patterns. Occasionally this mode of thinking misled him, and it sometimes substituted for reaching more profound scientific theories. But this cross-disciplinary thinking and pattern-seeking was his hallmark as the quintessential Renaissance Man, and it made him a pioneer of scientific humanism.

So here is another secret to Leonardo’s unique ability to paint a facial expression: he is probably the only artist in history ever to dissect with his own hands the face of a human and that of a horse to see if the muscles that move human lips are the same ones that can raise the nostrils of the nose.

Leonardo’s studies of the human heart, conducted as part of his overall anatomical and dissection work, were the most sustained and successful of his scientific endeavors.26 Informed by his love of hydraulic engineering and his fascination with the flow of liquids, he made discoveries that were not fully appreciated for centuries.

In the early 1500s the European understanding of the heart was not all that different from that described in the second century AD by Galen, whose work was revived during the Renaissance. Galen believed that the heart was not merely a muscle but was made of a special substance that gave it a vital force. Blood was made in the liver, he taught, and distributed through the veins. Vital spirits were produced by the heart and distributed through arteries, which Galen and his successors considered a separate system. Neither the blood nor vital spirits circulated, he thought; instead, they pulsed back and forth in the veins and arteries.

Leonardo was also able to show, contrary to Galen, that the heart is simply a muscle rather than some form of special vital tissue. Like all muscles, the heart has its own blood supply and nerves. “It is nourished by an artery and veins, as are other muscles,” he found.

Leonardo’s greatest achievement in his heart studies, and indeed in all of his anatomical work, was his discovery of the way the aortic valve works, a triumph that was confirmed only in modern times. It was birthed by his understanding, indeed love, of spiral flows. For his entire career, Leonardo was fascinated by the swirls of water eddies, wind currents, and hair curls cascading down a neck.

Leonardo dedicated himself to his anatomy studies with a persistence and diligence that were often lacking in his other endeavors.

He was mainly motivated by his own curiosity.

He was more interested in pursuing knowledge than in publishing it. And even though he was collegial in his life and work, he made little effort to share his findings.

This is true for all of his studies, not just his work on anatomy. The trove of treatises that he left unpublished testifies to the unusual nature of what motivated him. He wanted to accumulate knowledge for its own sake, and for his own personal joy, rather than out of a desire to make a public name for himself as a scholar or to be part of the progress of history. Some have even said that he wrote in mirror script partly to guard his discoveries from prying eyes; I do not think that is true, but it is indisputable that his passion for gathering knowledge was not matched by one for sharing it widely. As the Leonardo scholar Charles Hope has pointed out, “He had no real understanding of the way in which the growth of knowledge was a cumulative and collaborative process.”

Modern anatomy instead began twenty-five years after Leonardo’s death, when Andreas Vesalius published his epochal and beautifully produced On the Fabric of the Human Body. That was the book that Leonardo—perhaps in conjunction with Marcantonio della Torre, had he not died young from the plague—could have preceded and surpassed.

He was skillful at discerning how patterns resonate in nature, and the grandest and most encompassing of these analogies, in both his art and his science, was the comparison between the body of man and the body of the earth. “Man is the image of the world,” he wrote.

Known as the microcosm-macrocosm relationship, it harkened back to the ancients.

As a painter who marveled at nature’s patterns, Leonardo embraced the microcosm-macrocosm connection as more than merely an analogy. He viewed it as having a spiritual component, which he expressed in his drawing of Vitruvian Man. As we have seen, this mystical connection between humans and the earth is reflected in many of his masterpieces, from Ginevra de’ Benci to Saint Anne to Madonna of the Yarnwinder and eventually the Mona Lisa. It also became an organizing principle for his scientific inquiries. When he was immersed in his anatomical research on the human digestive system, he instructed himself, “First give the comparison with the water of the rivers; then with that of the bile which goes to the stomach against the course of the food.”

Codex Leicester.I More focused than most of his other notebooks, it contains seventy-two pages jammed with long written passages and 360 drawings on geology, astronomy, and the dynamics of flowing water.

Among the questions it addresses: What causes springs of water to emerge from mountains? Why do valleys exist? What makes the moon shine? How did fossils get on mountains? What causes water and air to swirl in a vortex? And, most emblematically, why is the sky blue?

As he embarked on the Codex Leicester, Leonardo reached back to the microcosm-macrocosm analogy as his framework. “The body of the earth, like the bodies of animals, is interwoven with ramifications of veins, which are all joined together and are formed for the nutrition and vivification of this earth and of its creatures,” he wrote, echoing his words from almost two decades earlier.5 And on the following page he added, “Its flesh is the soil, its bones are the arrangements of the connections of the rocks of which the mountains are composed, its cartilage is the porous rock, its blood is the veins of waters; the lake of the blood, which is throughout the heart, is the ocean; its breathing and the increase and decrease of the blood through the pulses in the earth is thus: it is the flow and ebb of the sea.”6

By the time he finished the Codex Leicester, he would discover that the comparison between the earth and the human body was not always useful. Instead, he came to fathom how nature had two traits that sometimes appeared to be in conflict: there was a unity to nature that resonated in its patterns and analogies, but there was also a wondrously infinite variety.

The primary focus of the Codex Leicester is the topic that Leonardo regarded as the most fundamental force in the life of the planet and in our bodies: the role and movements of fluids and, in particular, water.

Water provided the perfect manifestation of Leonardo’s fascination with how shapes are transformed when in motion. How can something change its shape—a square becoming a circle, a torso narrowing as it twists—and keep the exact same area or volume? Water provides an answer. Leonardo learned early on that it cannot be compressed; a given quantity always has the exact same volume, whatever the shape of the river or container. So flowing water is constantly going through perfect geometric transformations. No wonder he loved it.

“When you put together the science of the motions of water, remember to include under each proposition its application, in order that this science may not be useless.”15

Leonardo had a keen interest in what happens when a flow of water is obstructed. The dynamics of water, he realized, are connected to the two proto-Newtonian ideas about motion that he embraced: impetus and percussion.

Impetus, a concept developed in the Middle Ages and adopted by Leonardo, describes how a body set in motion tends to keep moving in the same direction. It is a rudimentary precursor to the concepts of inertia, momentum, and Newton’s first law. Percussion involves what happens when a body in motion hits another object; it will be reflected or deflected at an angle and with a force that can be calculated. Leonardo’s understanding of fluid dynamics was also informed by his studies of transformations; when water is deflected, it changes path and shape, but it always remains the exact same volume.

One mark of a great mind is the willingness to change it. We can see that in Leonardo. As he wrestled with his earth and water studies during the early 1500s, he ran into evidence that caused him to revise his belief in the microcosm-macrocosm analogy. It was Leonardo at his best, and we have the great fortune of being able to watch that evolution as he wrote the Codex Leicester.

The evolution of Leonardo’s thinking about the microcosm-macrocosm analogy began with his curiosity about why water, which should in theory tend to settle on the earth’s surface, emerges from springs and flows into rivers at the top of mountains. The veins of the earth, he wrote, carry “the blood that keeps the mountains alive.”

Only after pitting various theories against experience did Leonardo eventually get to the correct answer: the existence of springs and mountain rivers, indeed the entire circulation of water on the earth, results from the evaporation of surface water, the formation of clouds, and the subsequent rains.

Leonardo’s willingness to question and then abandon the enticing analogy between the circulation of water on the earth and the circulation of blood in the human body shows his curiosity and ability to be open-minded. Throughout his life, he was brilliant at discerning patterns and abstracting from them a framework that could be applied across disciplines. His geology studies show an even greater talent: not letting these patterns blind him. He came to appreciate not only nature’s similarities but also its infinite variety. Yet even as he abandoned the simplistic version of the microcosm-macrocosm analogy, he retained the aesthetic and spiritual concept underlying it: the harmonies of the cosmos are reflected in the beauty of living creatures.

Il sole nó si muóve. The sun does not move.

Is this statement a brilliant leap decades ahead of Copernicus, Galileo, and the realization that the sun does not revolve around the earth? Or is it merely a random thought, perhaps a note for a pageant or play?

More impressive was his realization that the moon does not emit light but reflects the light of the sun, and that a person standing on the moon would see that the earth reflects light in the same way.

Leonardo was always on the lookout for powerful patrons, and in 1513, with Milan still controlled by his former patrons the Sforzas, a new one appeared in Rome. In March of that year, Giovanni de’ Medici was elected to become Pope Leo X. The son of Lorenzo “the Magnificent” de’ Medici, the Florentine ruler who was a halfhearted patron to Leonardo and sent him off to Milan as a young man, Giovanni was the last non-priest to maneuver himself into the papacy. Much of his time was spent tending to the Vatican’s uncertain alliance with France, which was again aiming to retake Milan and was making pacts with various other Italian cities. The new pope would also later face the threat of Martin Luther and his Reformation.

Over the years, Leonardo became increasingly interested in the mathematics involved in focusing a mirror, drawing scores of diagrams of light rays from different directions hitting a curved surface and showing the angles at which they would be reflected. He tackled the problem identified by Ptolemy in AD 150 and studied by the eleventh-century Arab mathematician Alhazen of finding the point on a concave mirror where light coming from a certain source will be reflected to a designated spot (akin to finding the spot on the edge of a circular billiard table where you have to hit a cue ball so that it will bounce and hit your target). Leonardo failed to solve this using pure math. So in a series of drawings, he made a device that could solve the problem mechanically. He was better at using visualizations than equations.

“The pope has found out that I have skinned three corpses,” he wrote, and he blamed it on the jealous Giovanni. “This person has hindered me in anatomy, denouncing it before the Pope and also at the hospital.”

And as Kenneth Clark noted, “Mystery to Leonardo was a shadow, a smile and a finger pointing into darkness.”

So it makes sense to consider the Mona Lisa near the end of his career, exploring it as the culmination of a life spent perfecting an ability to stand at the intersection of art and nature. The poplar panel with multiple layers of light oil glazes, applied over the course of many years, exemplifies the multiple layers of Leonardo’s genius. What began as a portrait of a silk merchant’s young wife became a quest to portray the complexities of human emotion, made memorable through the mysteries of a hinted smile, and to connect our nature to that of our universe. The landscape of her soul and of nature’s soul are intertwined.

Ginevra de’ Benci was made by a young artist with astonishing skills of observation. The Mona Lisa is the work of a man who had used those skills to immerse himself in a lifetime of intellectual passions. The inquiries chronicled on his thousands of notebook pages—of light rays striking curved objects, dissections of human faces, geometrical volumes being transformed into new shapes, flows of turbulent water, the analogies between the earth and human bodies—had helped him fathom the subtleties of depicting motion and emotion. “His insatiable curiosity, his restless leaps from one subject to another, have been harmonized in a single work,” Kenneth Clark wrote of the Mona Lisa. “The science, the pictorial skill, the obsession with nature, the psychological insight are all there, and so perfectly balanced that at first we are hardly aware of them.”

At the time when he was perfecting Lisa’s smile, Leonardo was spending his nights in the depths of the morgue under the hospital of Santa Maria Nuova, peeling the flesh off cadavers and exposing the muscles and nerves underneath. He became fascinated about how a smile begins to form and instructed himself to analyze every possible movement of each part of the face and determine the origin of every nerve that controls each facial muscle. Tracing which of those nerves are cranial and which are spinal may not have been necessary for painting a smile, but Leonardo needed to know.

Perhaps the most interesting derivatives of the Mona Lisa made by Leonardo’s followers are the seminude variations often called Monna Vanna, of which there remain at least eight, one of them attributed to Salai

Much of Leonardo’s career was consumed by his quest for patrons who would be unconditionally paternalistic, supportive, and indulgent in ways that his own father had only occasionally been. Although Piero da Vinci got his son a good apprenticeship and helped him get commissions, his behavior was variable from beginning to end: he declined to legitimate his son and excluded him from his will. His primary bequest to his son was to give him an insatiable drive for an unconditional patron.

“The Medici made me and destroyed me,” he wrote cryptically in his notebook at the time of Giuliano’s death.

Along the way, he and his traveling party stopped in Milan. Salai decided to stay there, at least temporarily. He was then thirty-six, solidly middle-aged and no longer playing the role of Leonardo’s pretty-boy companion or competing for attention with the aristocratic Melzi, who was still only twenty-five and remained at Leonardo’s side. Salai would settle down at the vineyard and house on the edge of Milan that had been given to Leonardo by Ludovico Sforza.

Perhaps another reason Salai stayed behind was that Leonardo had a new manservant, Battista de Vilanis, who traveled with him from Rome to France. He would soon replace Salai in Leonardo’s affections. Salai would end up inheriting only half of the Milan vineyard and its rights; Battista would get the other half.

Francis proved to be the perfect patron for Leonardo. He would admire Leonardo unconditionally, never pester him about finishing paintings, indulge his love of engineering and architecture, encourage him to stage pageants and fantasias, give him a comfortable home, and pay him a regular stipend. Leonardo was given the title “First Painter, Engineer, and Architect to the King,” but his value to Francis was his intellect and not his output. Francis had an unquenchable thirst for learning, and Leonardo was the world’s best source of experiential knowledge. He could teach the king about almost any subject there was to know, from how the eye works to why the moon shines. In turn, Leonardo could learn from the erudite and graceful young king. As Leonardo once wrote in his notebooks, referring to Alexander the Great and his tutor, “Alexander and Aristotle were teachers of one another.”

Francis gave Leonardo something he had continually sought: a comfortable stipend that was not dependent on producing any paintings. In addition, he was given the use of a small red-brick manor house, with sandstone trimming and playful spires, next to Francis’s castle in the Loire Valley village of Amboise. Known as the Château de Cloux, and now called Clos Lucé, Leonardo’s house (fig. 138) was set amid almost three acres of gardens and vineyards and connected by an underground tunnel to the king’s Château d’Amboise, about five hundred yards away.

Leonardo’s interest in the art and science of movement, and in particular the flow and swirl of water and wind, climaxed in a series of turbulent drawings that he made during his final years in France.

Deeply personal yet coolly analytic in parts, they provide a powerful and dark expression of many of the themes of his life: the melding of art and science, the blurred line between experience and fantasy, and the frightful power of nature.

The drawings also convey, I believe, his own emotional turmoil as he faced his final days, partly hobbled by a stroke. They became an outlet for his feelings and fears. “They are an outpouring of something really personal,” according to Windsor curator Martin Clayton

Throughout his life he had been obsessed with water and its movements. One of his first drawings, the landscape of the Arno done when he was twenty-one, shows a placid river, calm and life-giving as it meanders gently past fertile land and tranquil villages. It displays no signs of turbulence, just a few gentle ripples. Like a vein, it nourishes life. In his notebooks, there are dozens of references to water as the life-giving fluid that forms the vein that nourishes the earth. “Water is the vital humor [vitale umore] of the arid earth,” he wrote. “Flowing with unceasing vehemence through the ramifying veins, it replenishes all the parts.”17 In the Codex Leicester he described, by his own count, “657 cases of water and its depths.”18 His mechanical engineering work included close to a hundred devices for moving and diverting water.

Now, near the end of his life, he depicted water and its swirls not as calm or tamed but as filled with fury.

for those who love curls and swirls, as Leonardo did, the drawings are an artistic expression of great aesthetic power. They remind us of the curls cascading down the back of the angel in his Annunciation, the painting he made some forty years earlier. Indeed, the underdrawing of the angel’s curls, as revealed by a spectrographic analysis, is strikingly similar to the spirals of the deluge drawings.

His deluge drawings are based on storms he had witnessed and described in his notebooks, but they are also the product of a fevered and frenzied imagination. He was a master at blurring lines, and in his deluge drawings he did so between reality and fantasia.

The deluge drawings conjure up the story of the Flood in Genesis, a topic treated by Michelangelo and many other artists over the years, but Leonardo makes no mention of Noah. He was conveying more than a biblical tale. At one point he adds Greek and Roman classical gods to the fray: “Neptune will be seen in the midst of the water with his trident, and let Aeolus with his winds be shown entangling the trees floating uprooted and whirling in the huge waves.”22 He drew on Virgil’s Aeneid, Ovid’s Metamorphoses, and the thunderous natural phenomena in book 6 of Lucretius’s On the Nature of Things. The drawings and text also conjure up the tale he wrote in Milan in the 1490s, ostensibly addressed to “the Devatdar of Syria.”

Leonardo did not focus on, or for that matter even hint at, the wrath of God in his deluge writings and drawings. He conveyed instead his belief that chaos and destruction are inherent in the raw power of nature. The psychological effect is more harrowing than if he were merely depicting a tale of punishment from an angry God. He was imparting his own emotions and thereby tapping into ours. Hallucinatory and hypnotic, the deluge drawings are the unnerving bookend to a life of nature drawing that began with a sketch of the placid Arno flowing near his native village.

Then abruptly, almost at the end of the page, he breaks off his writing with an “et cetera.” That is followed by a line, written in the same meticulous mirror script as the previous lines of his analysis, explaining why he is putting down his pen. “Perché la minestra si fredda,” he writes. Because the soup is getting cold.

It is the final piece of writing we have by Leonardo’s hand, our last scene of him working. Picture him in the upstairs study of his manor house, with its beamed ceiling and fireplace and the view of his royal patron’s Château d’Amboise. Mathurine, his cook, is down in the kitchen. Perhaps Melzi and others of the household are already at the table. After all these years, he is still stabbing away at geometry problems that have not yielded the world very much but have given him a profound appreciation of the patterns of nature. Now, however, the soup is getting cold.

His science led him to adopt many heretical beliefs, including that the fetus in the womb does not have a soul of its own and that the biblical Flood did not happen. Unlike Michelangelo, a man consumed at times with religious fervor, Leonardo made a point of not expounding much on religion during his lifetime. He said that he would not endeavor “to write or give information of those things of which the human mind is incapable and which cannot be proved by an instance of nature,” and he left such matters “to the minds of friars, fathers of the people, who by inspiration possess the secrets.”

There had apparently been an estrangement, one that had grown with the ascent of Melzi and the arrival of Battista. Salai was no longer at Leonardo’s side when he made the will. Nevertheless, he lived up to his reputation as a sticky-fingered little devil, one who was somehow able to get his hands on things. When he was killed five years later by a crossbow, the inventory of his estate showed that, perhaps during a visit to France, he had been given or had taken many copies of Leonardo’s paintings and possibly some of the originals, perhaps including the Mona Lisa and Leda and the Swan. Always the con artist, it is unclear whether the prices listed in his estate are true values, thus making it hard to know which were copies.

even in his death, there is a veil of mystery. We cannot portray him with crisp sharp lines, nor should we want to, just as he would not have wanted to portray Mona Lisa that way. There is something nice about leaving a little to our imagination. As he knew, the outlines of reality are inherently blurry, leaving a hint of uncertainty that we should embrace. The best way to approach his life is the way he approached the world: filled with a sense of curiosity and an appreciation for its infinite wonders.

“Tell me if anything was ever done,” he repeatedly scribbled in notebook after notebook. “Tell me. Tell me. Tell me if ever I did a thing. . . . Tell me if anything was ever made.”

And by refusing to churn out works that he had not perfected, he sealed his reputation as a genius rather than a master craftsman. He enjoyed the challenge of conception more than the chore of completion.

Similarly, he looked upon his art and engineering and his treatises as a part of a dynamic process, always receptive to a refinement by the application of a new insight.

Relinquishing a work, declaring it finished, froze its evolution. Leonardo did not like to do that. There was always something more to be learned, another stroke to be gleaned from nature that would make a picture closer to perfect.

His facility for combining observation with fantasy allowed him, like other creative geniuses, to make unexpected leaps that related things seen to things unseen. “Talent hits a target that no one else can hit,” wrote the German philosopher Arthur Schopenhauer. “Genius hits a target no one else can see.”

LEARNING FROM LEONARDO

Be curious, relentlessly curious. “I have no special talents,” Einstein once wrote to a friend. “I am just passionately curious.”

Seek knowledge for its own sake. Not all knowledge needs to be useful. Sometimes it should be pursued for pure pleasure.

Retain a childlike sense of wonder. At a certain point in life, most of us quit puzzling over everyday phenomena. We might savor the beauty of a blue sky, but we no longer bother to wonder why it is that color. Leonardo did.

Observe. Leonardo’s greatest skill was his acute ability to observe things. It was the talent that empowered his curiosity, and vice versa.

Start with the details. In his notebook, Leonardo shared a trick for observing something carefully: Do it in steps, starting with each detail. A page of a book, he noted, cannot be absorbed in one stare; you need to go word by word. “If you wish to have a sound knowledge of the forms of objects, begin with the details of them, and do not go on to the second step until you have the first well fixed in memory.”

See things unseen.

He mixed theatrical ingenuity with fantasy. This gave him a combinatory creativity. He could see birds in flight and also angels, lions roaring and also dragons.

Go down rabbit holes. He filled the opening pages of one of his notebooks with 169 attempts to square a circle. In eight pages of his Codex Leicester, he recorded 730 findings about the flow of water; in another notebook, he listed sixty-seven words that describe different types of moving water.

Get distracted.

Respect facts. Leonardo was a forerunner of the age of observational experiments and critical thinking. When he came up with an idea, he devised an experiment to test it. And when his experience showed that a theory was flawed—such as his belief that the springs within the earth are replenished the same way as blood vessels in humans—he abandoned his theory and sought a new one.

Procrastinate.

creativity requires time for ideas to marinate and intuitions to gel. “Men of lofty genius sometimes accomplish the most when they work least,” he explained,

Let the perfect be the enemy of the good.

He carried around masterpieces such as his Saint Anne and the Mona Lisa to the end, knowing there would always be a new stroke he could add.

Think visually. Leonardo was not blessed with the ability to formulate math equations or abstractions. So he had to visualize them, which he did with his studies of proportions, his rules of perspective, his method for calculating reflections from concave mirrors, and his ways of changing one shape into another of the same size.

Avoid silos.

He knew that art was a science and that science was an art.

Let your reach exceed your grasp.

Indulge fantasy.

Just as Leonardo blurred the lines between science and art, he did so between reality and fantasy. It may not have produced flying machines, but it allowed his imagination to soar.

Create for yourself, not just for patrons.

Collaborate. Genius is often considered the purview of loners who retreat to their garrets and are struck by creative lightning. Like many myths, that of the lone genius has some truth to it.

Vitruvian Man was produced after sharing ideas and sketches with friends. Leonardo’s best anatomy studies came when he was working in partnership with Marcantonio della Torre.

Genius starts with individual brilliance. It requires singular vision. But executing it often entails working with others. Innovation is a team sport. Creativity is a collaborative endeavor.

Make lists. And be sure to put odd things on them. Leonardo’s to-do lists may have been the greatest testaments to pure curiosity the world has ever seen.

Take notes, on paper.

Be open to mystery. Not everything needs sharp lines.

Describe the tongue of the woodpecker

The tongue of a woodpecker can extend more than three times the length of its bill. When not in use, it retracts into the skull and its cartilage-like structure continues past the jaw to wrap around the bird’s head and then curve down to its nostril. In addition to digging out grubs from a tree, the long tongue protects the woodpecker’s brain. When the bird smashes its beak repeatedly into tree bark, the force exerted on its head is ten times what would kill a human. But its bizarre tongue and supporting structure act as a cushion, shielding the brain from shock.