Leonardo Da Vinci

by Walter Isaacson

Troy Shu
Troy Shu
Updated at: March 12, 2024
Leonardo Da Vinci
Leonardo Da Vinci

What are the big ideas? 1. Leonardo's Notebooks as a Source of Interdisciplinary Inspiration: The book emphasizes the importance of studying Leonardo's notebooks fo

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What are the big ideas?

  1. Leonardo's Notebooks as a Source of Interdisciplinary Inspiration: The book emphasizes the importance of studying Leonardo's notebooks for their unique insights into his interdisciplinary explorations in art, science, mathematics, and engineering. Unlike other sources that may focus solely on his completed works, the book draws attention to the value of Leonardo's unfinished ideas and the potential they hold for inspiring new discoveries across various fields.
  2. Genius as a Universal Mindset: The book presents a holistic view of genius, which encompasses creativity, intellect, and curiosity in all areas of human endeavor. By exploring Leonardo's diverse interests and accomplishments, the book demonstrates that genius is not limited to one discipline but rather represents a unique mindset that can be applied universally.
  3. The Role of Imagination in Scientific Discovery: The book highlights Leonardo's innovative use of imagination in his scientific discoveries, such as his theories on fossils and the color of the sky. By emphasizing this aspect of Leonardo's work, the book challenges traditional perceptions of science as being purely fact-based and data-driven, instead showcasing the importance of creativity and intuition in scientific discovery.
  4. The Ambiguity of Spiritual and Sensual: The book explores how Leonardo's late paintings, such as the Mona Lisa and the lost Battle of Anghiari, challenge traditional perceptions by connecting the spiritual to the sensual and highlighting the ambiguity between the two. By examining these works in depth, the book sheds light on Leonardo's mastery of conveying complex emotions and themes through art.
  5. The Value of Persistent Curiosity: The book emphasizes Leonardo's persistent curiosity as a driving force behind his many accomplishments. It explores how his willingness to pursue various interests, from anatomy to engineering to painting, ultimately contributed to his groundbreaking discoveries and enduring influence on art and science. By highlighting the importance of maintaining a sense of wonder and curiosity throughout one's life, the book encourages readers to continue exploring new ideas and fields.


Introduction I Can Also Paint


  • Leonardo da Vinci (1452-1519) was a polymath, an artist, scientist, engineer, and inventor who is widely regarded as a pioneer of the Renaissance.
  • He was born out of wedlock in the Tuscan village of Vinci and grew up in a household headed by his grandfather. His mother married a Florentine notary when Leonardo was about fifteen.
  • Leonardo's early education was in the studio of painter Andrea del Verrocchio, but he also studied mathematics, geometry, botany, anatomy, music, and optics.
  • He spent much of his adult life as a freelance artist and scientist, working for various patrons, including Ludovico Sforza of Milan and Francis I of France. He traveled extensively throughout Italy and Europe.
  • Leonardo's notebooks contain a vast range of observations, ideas, and sketches on subjects such as art, science, engineering, and mathematics. They reveal his insatiable curiosity and his innovative approaches to problem-solving.
  • Leonardo is best known for his paintings, including the Mona Lisa, The Last Supper, and the Vitruvian Man. However, he also made important contributions to fields such as anatomy, optics, hydraulics, and military engineering.
  • Leonardo was a man of many talents and contradictions. He was renowned for his beauty and grace, but he was also moody and troubled. He left many of his paintings unfinished, but he was meticulous in his studies of nature and the human form. He was a vegetarian and a heretic, but he was also a consummate professional who worked tirelessly to perfect his craft.
  • Leonardo's legacy lies not only in his art and scientific discoveries, but also in his enduring influence on subsequent generations of artists, scientists, and thinkers. His curiosity, his creativity, and his willingness to explore new ideas continue to inspire us today.


“when he was engaged in blue-sky thinking, his science was not a separate endeavor from his art. Together they served his driving passion, which was nothing less than knowing everything there was to know about the world, including how we fit into it. He had a reverence for the wholeness of nature and a feel for the harmony of its patterns, which he saw replicated in phenomena large and small. In his notebooks he would record curls of hair, eddies of water, and whirls of air, along with some stabs at the math that might underlie such spirals. While at Windsor Castle looking at the swirling power of the “Deluge drawings” that he made near the end of his life, I asked the curator, Martin Clayton, whether he thought Leonardo had done them as works of art or of science. Even as I spoke, I realized it was a dumb question. “I do not think that Leonardo would have made that distinction,” he replied.”

“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. .. Skill without imagination is barren. Leonardo [da Vinci] knew how to marry observation and imagination, which made him history’s consummate innovator.”

“But 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.”

“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.”

Chapter 1 Childhood


  • Leonardo da Vinci was born out of wedlock in 1452 in the Tuscan town of Vinci, the illegitimate son of a notary and a peasant woman.
  • His unconventional upbringing, with his father living primarily elsewhere and his mother having many children, allowed him to develop a love for nature and creativity that was not stifled by formal education or societal expectations.
  • He grew up in the household of his paternal grandfather Antonio, who lived a leisurely lifestyle, along with his uncle Francesco, who became an important influence on Leonardo's life.
  • The Renaissance period (14th to 17th centuries) was an era of creativity and intellectual growth in Europe, marked by the revival of classical learning, humanism, and scientific inquiry.
  • Leonardo was a self-taught artist and scientist who valued experience over book learning. He was known for his curiosity, empirical approach, and innovative techniques.
  • A vivid childhood memory that Leonardo recorded later in life involved encountering a dark cave and deciding to enter it despite feeling fear and desire. Inside, he discovered a fossilized whale bone.
  • This experience sparked both scientific curiosity and philosophical contemplation, as well as an awareness of the destructive power of nature.
  • Leonardo's later artworks, such as Saint Jerome in the Wilderness, reflect his fascination with caves and natural wonders, as well as his preoccupations with mortality and the destructive forces of nature.


“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.”

“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.”

Chapter 2 Apprentice


  • Leonardo's early works show his experimentation with light, perspective, and narratives involving human reactions.
  • The Annunciation shows Leonardo's use of chiaroscuro, subtle coloring, and his depiction of the angel Gabriel.
  • Madonnas with a focus on realistic depictions of baby Jesus were common in Verrocchio's workshop, and Leonardo painted at least two such works.
  • Ginevra de’ Benci is Leonardo's first non-religious painting, which presages the Mona Lisa.
  • The portrait shows Ginevra looking pale and melancholic, with a dreamlike landscape in the background.
  • Leonardo's use of thin layers of oil and his attention to detail, such as the luster on Ginevra's eyes and curls, were signature marks.
  • Ginevra de’ Benci set Leonardo on a trajectory towards painting the Mona Lisa, which would become the greatest psychological portrait in history.


“Its leading thinkers embraced a Renaissance humanism that put its faith in the dignity of the individual and in the aspiration to find happiness on this earth through knowledge.”

“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. They were innovators in bookkeeping, including the use of debit-and-credit accounting that became one of the great spurs to progress during the Renaissance. By means of payoffs and plotting, Cosimo became the de facto ruler of Florence, and his patronage made it the cradle of Renaissance art and humanism.”

“One must apply the greatest artistry in three things,” Alberti wrote, “walking in the city, riding a horse, and speaking, for in each of these one must try to please everyone.”12 Leonardo mastered all three.”

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

Chapter 3 On His Own


  • Leonardo's early years in Florence were marked by a strong desire to learn and explore various artistic techniques under Verrocchio's guidance, as well as an intense curiosity about the natural world.
  • He made detailed studies of anatomy, light, water, and other phenomena, often using his notes as references for later paintings and drawings.
  • Leonardo was passionate about pageants, theater, and court amusements, which influenced his approach to narrative painting and portraiture by helping him capture the attitudes and motions of characters.
  • He aimed to portray not only the physical movements (moti corporali) but also the mental states (atti e moti mentali) of his subjects.
  • Leonardo's notebooks from around 1480 reveal expressions of sadness, despair, and anguish, possibly due to his inability to finish major works and the success of his rivals.
  • He was not selected for important commissions, such as the decoration of the Sistine Chapel, and eventually left Florence to seek patronage elsewhere.


“If there is no love, what then?”

“he never finished any of the works he began because, so sublime was his idea of art, he saw faults even in the things that to others seemed miracles.”

“Leonardo at twenty-nine was more easily distracted by the future than he was focused on the present.”

“The good painter has to paint two principal things, man and the intention of his mind,” he wrote. “The first is easy and the second is difficult, because the latter has to be represented through gestures and movements of the limbs.”44 He expanded on this concept in a long passage in his notes for his planned treatise on painting: “The movement which is depicted must be appropriate to the mental state of the figure. The motions and postures of figures should display the true mental state of the originator of these motions, in such a way they can mean nothing else. Movements should announce the motions of the mind.”45 Leonardo’s dedication to portraying the outward manifestations of inner emotions would end up driving not only his art but some of his anatomical studies. He needed to know which nerves emanated from the brain and which from the spinal cord, which muscles they activated, and which facial movements were connected to others. He would even try, when dissecting the brain, to figure out the precise location where the connections were made between sensory perceptions, emotions, and motions. By the end of his career, his pursuit of how the brain and nerves turned emotions into motions became almost obsessive. It was enough to make the Mona Lisa smile.”

Chapter 4 Milan


  • Leonardo da Vinci's application letter to Ludovico Sforza, Duke of Milan, in 1482 included a promise to create military innovations and architectural designs.
  • In Milan, he drew plans for a giant crossbow that could launch a 100-pound projectile, but it was never built. He also proposed an armored tank, a steam cannon, and a machine gun design, though none were constructed during his lifetime.
  • Leonardo's most practical military invention was the wheellock, or wheel lock, which used a spinning wheel to create a spark for igniting gunpowder in muskets or similar hand-held weapons.
  • In 1487, Leonardo proposed plans for an ideal city to address public health concerns and improve living conditions, including wide streets for pedestrian use, a hidden lower level for commerce and sanitation, and a unified circulation system for rainwater and waste management.

Chapter 5 Leonardo’s Notebooks


  • Leonardo da Vinci kept notebooks throughout his life, recording observations, ideas, sketches, and lists.
  • He used various sizes of notebooks for different purposes, including field notes and studio work.
  • His notebooks contained a medley of ideas from his many passions and obsessions, including engineering, art, and science.
  • Leonardo's notebooks are an invaluable documentary record of applied creativity and contain over 7,200 pages now extant.
  • The order and dates of the pages have been lost, making it difficult for modern scholars to determine their sequence.
  • Leonardo primarily recorded ideas useful to his art and engineering in the early notebooks, but later he pursued curiosity for its own sake.
  • He tried to use every edge and corner of each page and would go back to add new thoughts years later.
  • The juxtapositions of seemingly random items from diverse fields allow us to sense connections in our cosmos and extract patterns that underlie disconnected things.
  • Leonardo's notebooks are an example of the universal mind wandering freely over arts and sciences.


“One purpose of these notebooks was to record interesting scenes, especially those involving people and emotions. “As you go about town,” he wrote in one of them, “constantly observe, note, and consider the circumstances and behavior of men as they talk and quarrel, or laugh, or come to blows.”1 For that purpose, he kept a small notebook hanging from his belt.”

Chapter 6 Court Entertainer


  • Leonardo spent seventeen years at the Sforza court in Milan, where he was a prolific painter, sculptor, engineer, and inventor.
  • He created numerous works for the ducal family during this period, including portraits of Ludovico Sforza and his wife Beatrice d'Este, as well as the Last Supper fresco in the Convent of Santa Maria delle Grazie.
  • Leonardo also worked on various engineering projects for the duke, such as designing a huge bridge across the Po River and an enormous water-powered bell foundry.
  • The Milan court was known for its intellectual and artistic prowess, attracting figures like Leonardo, Bramante, and Machiavelli. This atmosphere fueled Leonardo's creativity and allowed him to explore various fields.
  • During his time in Milan, Leonardo kept extensive notebooks filled with sketches, ideas, and notes on a wide range of topics, from mathematics and anatomy to literature and music.
  • He also contributed to life at the Sforza court by creating literary amusements such as fables, prophecies, riddles, pranks, and performances. These were designed for oral delivery and entertainment during social gatherings.
  • Leonardo's literary amusements showcased his cleverness, wit, and versatility, further cementing his status among the intellectual elite at the Milan court.
  • His notebooks also contain drafts of fantasy novellas and letters describing mysterious lands and adventures, some of which may have been performed for the court. These tales often involve cataclysmic scenes of destruction and deluge that consume all earthly life.


“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.”22”

“Closely related are the entries in his bestiary, a compendium of short tales of animals and moral lessons based on their traits. Bestiaries were popular among the ancients and in the Middle Ages, and the spread of printing presses meant that many were reprinted in Italy beginning in the 1470s. Leonardo had a copy of the bestiary written by Pliny the Elder and three others by medieval compilers.”

“Occasionally Leonardo appended a moral lesson to the entry, such as this: “The oyster, when the moon is full, opens itself wide, and when the crab looks in he throws in a stone or seaweed and the oyster cannot close again, whereby it serves for food to that crab. This is what happens to him who opens his mouth to tell his secret. He becomes the prey of the treacherous hearer.”

Chapter 7 Personal Life


  • Leonardo's drawings of old and young men in profile, often juxtaposing a craggy, jut-jawed man with a youthful, curly-haired boy, were a recurring motif in his sketchbooks.
  • The older man is typically depicted as having a long pointed nose, a sunken upper lip, and an exaggerated jutting chin.
  • The younger man is often soft and sensuous, with bountiful curls pouring from his head and cascading down his neck.
  • These drawings likely reflect Leonardo's own thoughts on aging and his fascination with the contrast between virility and effeminacy.
  • One of the younger men depicted in these sketches is believed to be Salai, Leonardo's male servant and possible lover.
  • The pairing of an old man and a young man also appeared in Leonardo's allegorical drawings, such as one depicting Pleasure and Pain as twins.


“Leonardo became known in Milan not only for his talents but also for his good looks, muscular build, and gentle personal style. “He was a man of outstanding beauty and infinite grace,” Vasari said of him. “He was striking and handsome, and his great presence brought comfort to the most troubled soul.”

“Most notably, he was known for his willingness to share his blessings. “He was so generous that he sheltered and fed all his friends, rich or poor,” according to Vasari. 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 As a result, he spent more time pursuing wisdom than working on jobs that would make him money beyond what he needed to support his growing household retinue. “He possessed nothing and worked little, but he always kept servants and horses,” Vasari wrote. The horses brought him “much delight,” Vasari wrote, as did all animals.”

Chapter 8 Vitruvian Man


  • Leonardo and his friend Francesco di Giorgio independently drew illustrations of Vitruvius's description of a man inscribed within a square and circle based on human proportions.
  • Giacomo Andrea, another friend of Leonardo, also made a drawing of Vitruvian Man around the same time.
  • Leonardo's version is the most famous and precise one, with meticulous lines and careful shading to create a beautiful image. It reflects his scientific interest in human proportion and Vitruvius's descriptions, but Leonardo also made adjustments based on his own studies.
  • Collaboration and the sharing of ideas played a significant role in the creation of Vitruvian Man and the design process for the tiburio of Milan's cathedral. Leonardo engaged in intellectual conversations with friends and colleagues, which contributed to his ongoing education and inspiration.


“Leonardo’s Vitruvian Man embodies a moment when art and science combined to allow mortal minds to probe timeless questions about who we are and how we fit into the grand order of the universe. It also symbolizes an ideal of humanism that celebrates the dignity, value, and rational agency of humans as individuals. Inside the square and the circle we can see the essence of Leonardo da Vinci, and the essence of ourselves, standing naked at the intersection of the earthly and the cosmic.”

Chapter 9 The Horse Monument


  • Leonardo got a commission from Ludovico Sforza in 1489 to design a mammoth equestrian statue, which finally earned him an official appointment at court
  • The horse was cast all in one mold instead of in pieces like traditional methods
  • Leonardo planned to use a casting hood and inner core made of clay and rubble
  • Molten bronze would be poured into the mold through many holes for even distribution
  • Four furnaces were used for the casting process, with ingredients tested for best results
  • The project ended when defense expenditures took precedence over artistic ones, leading to the destruction of the clay model by French archers.

Chapter 10 Scientist


  • Leonardo was an early proponent of the scientific method, combining theory, experiment, and handed-down knowledge
  • He observed patterns in nature and made analogies between different phenomena
  • His curiosity and acute observational skills were essential to his scientific pursuits
  • He recommended looking at details separately and observing motion carefully to deepen one's understanding of the natural world.


“Leonardo da Vinci liked to boast that, because he was not formally educated, he had to learn from his own experiences instead”

“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.”11”

“While Europe was mired in its dark years of medieval superstition, the work of combining theory and experiment was advanced primarily in the Islamic world. Muslim scientists often also worked as scientific instrument makers, which made them experts at measurements and applying theories. The Arab physicist Ibn al-Haytham, known as Alhazen, wrote a seminal text on optics in 1021 that combined observations and experiments to develop a theory of how human vision works, then devised further experiments to test the theory.”

“That goes a step too far, I think. Leonardo did not invent the scientific method, nor did Aristotle or Alhazen or Galileo or any Bacon. But his uncanny abilities to engage in the dialogue between experience and theory made him a prime example of how acute observations, fanatic curiosity, experimental testing, a willingness to question dogma, and the ability to discern patterns across disciplines can lead to great leaps in human understanding.”

“We saw an example of this pattern-based analysis on the “theme sheet,” where he made the analogy between a branching tree and the arteries in a human, one that he applied also to rivers and their tributaries. “All the branches of a tree at every stage of its height when put together are equal in thickness to the trunk below them,” he wrote elsewhere. “All the branches of a river at every stage of its course, if they are of equal rapidity, are equal to the body of the main stream.”15 This conclusion is still known as “da Vinci’s rule,” and it has proven true in situations where the branches are not very large: the sum of the cross-sectional area of all branches above a branching point is equal to the cross-sectional area of the trunk or the branch immediately below the branching point.”

“In addition to his instinct for discerning patterns across disciplines, Leonardo honed two other traits that aided his scientific pursuits: an omnivorous curiosity, which bordered on the fanatical, and an acute power of observation, which was eerily intense. Like much with Leonardo, these were interconnected. 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? Einstein said he marveled about questions others found mundane because he was slow in learning to talk as a child. For Leonardo, this talent may have been connected to growing up with a love of nature while not being overly schooled in received wisdom.”

“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.1 There is no reason you actually need to know any of this. It is information that has no real utility for your life, just as it had none for Leonardo. But I thought maybe, after reading this book, that you, like Leonardo, who one day put “Describe the tongue of the woodpecker” on one of his eclectic and oddly inspiring to-do lists, would want to know. Just out of curiosity. Pure curiosity.”

“Kenneth Clark referred to Leonardo’s “inhumanly sharp eye.” It’s a nice phrase, but misleading. Leonardo was human. The acuteness of his observational skill was not some superpower he possessed. Instead, it was a product of his own effort. That’s important, because it means that 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. In his notebook, he described his method—almost like a trick—for closely observing a scene or object: look carefully and separately at each detail. He compared it to looking at the page of a book, which is meaningless when taken in as a whole and instead needs to be looked at word by word. 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.”

Chapter 11 Birds and Flight


  • Leonardo da Vinci's studies on flight began with his observations during theatrical productions, where he saw devices that allowed actors to appear as if they were flying.
  • His first drawings of flight mechanisms were meant for theater rather than actual human flight. He made careful observations of birds and their movements to inform his designs.
  • Leonardo discovered that some bird species lower their wings faster than they raise them, while others do the opposite. This observation helped him understand the physics of how birds stay aloft.
  • Leonardo realized that the pressure a bird puts on the air is met by an equal and opposite reaction from the air on the bird. He also recognized that water cannot be compressed like air, which allows birds to support themselves while flying.
  • Leonardo believed that it was possible for humans to build a machine that would allow them to fly based on his observations of birds and physics principles. He designed several human-powered flying machines throughout his career.
  • Leonardo experimented with wing designs for both gliders and machines with flapping wings. He also considered using skin flaps in the wings to minimize air resistance.
  • Leonardo envisioned testing some of his flying machine designs on the roofs of buildings or over water, taking safety precautions such as wearing a life preserver.
  • Despite his advances in understanding the physics and mechanics of flight, Leonardo was never able to create a self-propelled human flying machine during his lifetime.


“When birds are descending near the ground and the head is below the tail, they lower the tail, which is spread wide open, and take short strokes with the wings; consequently, the head is raised above the tail, and the speed is checked so that the bird can alight on the ground without a shock.”9 Ever notice all that?”

Chapter 12 The Mechanical Arts


  • Leonardo's approach to machine design was unique in that he analyzed each component and its role in transferring motion.
  • He drew machines disassembled, using exploded and layered views, to understand the engineering principles behind their functions.
  • Leonardo pioneered the use of gears to equalize the power of an unwinding spring and transmit constant power.
  • The purpose of machinery is to harness energy and turn it into useful movements.
  • Leonardo studied human muscles to determine their power and apply that knowledge to mechanical design.
  • He explored various practical applications for harnessing energy from rivers, such as regulating flow with piles or using waterwheels.
  • Leonardo designed a needle-grinding machine and estimated it could generate significant revenue but never executed the plan.
  • Leonardo's understanding of impetus laid the groundwork for Newton's first law of motion.
  • He believed that perpetual motion was possible but realized through visual thought experiments that none of the proposed mechanisms would work.
  • Friction causes energy loss and prevents perpetual motion, so Leonardo studied it methodically to reduce its effects in machines.
  • Leonardo discovered laws of friction, including the independence of contact surface area from friction, but did not publish them.
  • He was among the first to use ball bearings and roller bearings and calculated the coefficient of friction for various materials.
  • Leonardo's screw jack design included ball bearings to reduce friction.
  • He created the first recorded formula for an anti-friction alloy, consisting of three parts copper and seven parts tin.

Chapter 13 Math


  • Leonardo was deeply interested in mathematics, particularly geometry, and applied his knowledge to art and science throughout his career.
  • He studied the works of Euclid, Pacioli, and other mathematicians, but had difficulty mastering advanced mathematical concepts and techniques.
  • Leonardo's notebooks contain numerous studies on geometric transformations, such as how shapes change when they move or are transformed from one shape to another while maintaining the same volume.
  • He was fascinated by the concept of equivalent areas and spent years trying to find ways to calculate the area of curved shapes using straight-sided shapes with the same area.
  • Leonardo attempted to solve ancient mathematical puzzles, such as squaring the circle and doubling the cube, which required advanced mathematical concepts beyond his grasp.
  • Despite these challenges, Leonardo's geometric studies significantly influenced his art and scientific discoveries, particularly in depicting motion and anatomy.

Chapter 14 The Nature of Man


  • Leonardo's fascination with anatomy began when he was studying for the Sforza monument in Milan.
  • He made detailed studies of the human skeleton, muscles, and nerves using freshly exhumed bodies.
  • He drew the first accurate depiction of the human dental elements, including a depiction of the roots that is almost perfect.
  • Leonardo used his artistic skills to make anatomical drawings beautiful, which influenced the development of scientific illustration.
  • He studied the relationship between the brain and the nervous system, and was the first person to describe the concept of a senso comune or common sense.
  • In the mid-1490s, Leonardo put aside his work on anatomy and began measuring and drawing the proportions of the human body.
  • He made over forty drawings and six thousand words describing the measurements and proportional relationships between different parts of the body.
  • He was inspired by Vitruvius' detailed studies of human proportions, but went much deeper in his own observations.
  • Leonardo's obsession with measuring every aspect of the human body was driven by his desire to understand the universal measure of man and his place in the cosmos.

Chapter 15 Virgin of the Rocks


  • Leonardo's drawing of a young woman, also known as "Head of a Young Woman," is a masterpiece of draftsmanship and considered one of the most beautiful drawings in the world.
  • The drawing was created using silverpoint on paper coated with a pale pigment, with highlights added using white gouache.
  • Leonardo's use of hatching to create shadows and texture is evident in the drawing, with delicate and tight hatching in some areas and bold and spacious hatching in others.
  • The young woman's eyes are rendered with incredible detail, with one eye staring directly at the viewer and the other eyelid heavy and drooping, giving the impression of a dreamy gaze.
  • Leonardo's use of lines to suggest movement and his exploratory approach to drawing are also evident in the drawing.
  • Some art critics have suggested that the angel in Leonardo's painting "Virgin of the Rocks" is gender fluid or even feminine, due to its androgynous features and seductive gaze.
  • The relationship between the "Head of a Young Woman" drawing and the angel in "Virgin of the Rocks" has been noted, with some suggesting that the angel was inspired by the drawing or that they represent the same figure.
  • Leonardo's studio was characterized by collaboration and teamwork, with him working closely with established painters as well as training his own apprentices.
  • The creation of paintings in Leonardo's studio often involved a combination of his designs and the work of his assistants, resulting in variations on a theme or different styles within a single painting.

Chapter 16 The Milan Portraits


  • The attribution of artworks to specific artists can be a complex and subjective process that involves a combination of historical, artistic, and scientific analysis.
  • Leonardo da Vinci's drawing "La Bella Principessa" was long believed to be the work of an unknown German artist until new evidence suggested otherwise.
  • Scientific analysis using multispectral imaging revealed that the portrait was drawn on vellum, which was used for books in the late 15th century.
  • Further research revealed that the portrait was once part of a book dedicated to Bianca Sforza, and the holes and cuts on the edges of the drawing match those in the original binding.
  • The discovery of this connection provided strong evidence for the authenticity of the drawing as a Leonardo work, although some art experts remain skeptical.
  • Fingerprint analysis by forensic expert Peter Paul Biro was initially seen as supportive evidence for Leonardo's authorship, but later criticisms raised doubts about its reliability and validity.


“An object will display the greatest difference of light and shade when it is seen in the strongest light. . . . But this should not be much used in painting, because the works would be crude and ungraceful. An object seen in a moderate light displays little difference in its light and shade, and this is the case towards evening or when the day is cloudy; works painted then are tender, and every kind of face becomes graceful. Thus, in everything extremes are to be avoided: Too much light gives crudeness; too little prevents our seeing.”

“By noting that she seems to listen but not speak, Bellincioni conveyed what makes the portrait so momentous: it captures the sense of an inner mind at work. Her emotions seem to be revealed, or at least hinted at, by the look in her eyes, the enigma of her smile, and the erotic way she clutches and caresses the ermine.”

Chapter 17 The Science of Art


  • Leonardo's scientific studies influenced his art and vice versa, leading to innovative techniques such as sfumato and mastery of perspective.
  • He realized that there are no precise boundary lines in nature and challenged artists to represent shapes using light and shadow instead of outlines.
  • His study of optics led him to understand that visual perception occurs along the entire area of the retina, which explained why sharp lines are not visible in nature.
  • Leonardo's investigations into perspective expanded beyond linear perspective to include acuity perspective (objects become less distinct as they recede) and aerial perspective (air softens distant objects).
  • His pursuit of scientific knowledge went beyond its utility for painting, leading to discoveries that would not be rediscovered for another century.

Chapter 18 The Last Supper


  • Leonardo's Last Supper was painted on a dry plaster wall using oil and tempera, which led to the paint flaking and deteriorating over time.
  • The painting is an example of Leonardo's mastery of perspective, both natural and artificial, as well as his use of optical tricks to accommodate the fact that it would be viewed from different parts of the room.
  • The Last Supper demonstrates Leonardo's ability to blend scientific knowledge with creativity and theatrical license.
  • The painting has undergone numerous restorations over the centuries, with the latest restoration revealing what is believed to be original work while also speculatively filling in missing areas.
  • The Last Supper is a complex work that raises questions about authenticity and interpretation, and it continues to be a source of fascination and debate among art historians and enthusiasts.


“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. According to the account of a priest, Leonardo would “come here in the early hours of the morning and mount the scaffolding,” and then “remain there brush in hand from sunrise to sunset, forgetting to eat or drink, painting continually.” On other days, however, nothing would be painted. “He would remain in front of it for one or two hours and contemplate it in solitude, examining and criticizing to himself the figures he had created.” Then there were dramatic days that combined his obsessiveness and his penchant for procrastination. As if caught by whim or passion, he would arrive suddenly in the middle of the day, “climb the scaffolding, seize a brush, apply a brush stroke or two to one of the figures, and suddenly depart.”1 Leonardo’s quirky work habits may have fascinated the public, but they eventually began to worry 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. He also wanted to create a holy mausoleum for himself and his family, choosing a small but elegant church and monastery in the heart of Milan, Santa Maria delle Grazie, which he had Leonardo’s friend Donato Bramante reconstruct. For the north wall of the new dining hall, or refectory, he had commissioned Leonardo to paint a Last Supper, one of the most popular scenes in religious art. At first Leonardo’s procrastination led to amusing tales, such as the time the church prior became frustrated and complained to Ludovico. “He wanted him never to lay down his brush, as if he were a laborer hoeing the Prior’s garden,” Vasari wrote. 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.”

“Look longer at the picture. It vibrates with Leonardo’s understanding that no moment is discrete, self-contained, frozen, delineated, just as no boundary in nature is sharply delineated. As with the river that Leonardo described, each moment is part of what just passed and what is about to come. This is one of the essences of Leonardo’s art: from the Adoration of the Magi to Lady with an Ermine to The Last Supper and the Mona Lisa, each moment is not distinct but instead contains connections to a narrative.”

Chapter 19 Personal Turmoil


  • Caterina, Leonardo's mother, came to live with him in Milan around 1493 after her husband's death and their son's killing. She died later that year of malaria.
  • Leonardo recorded her arrival and expenses related to her funeral, which included costs for candles, a bier, priests, gravediggers, and the dean. The expenses were appropriate for his mother's funeral.
  • Leonardo's career reached a high point around 1495 with his official appointment as artist and engineer of the Sforza court in Milan.
  • However, after Caterina's death and the completion of The Last Supper, Leonardo faced unsettled circumstances with disputes over pay and performance on projects like decorating the Sala delle Asse.
  • Leonardo used a tempera-oil mixture on dry plaster for the Sala delle Asse instead of traditional fresco method, resulting in deterioration similar to that suffered by The Last Supper.
  • In 1499, French troops invaded Milan, and Leonardo hid his cash and prepared for a long journey back to Florence while also making arrangements to meet with the new French governor in Naples as a military engineer.
  • Leonardo's plan to meet the French governor never came to fruition, and he eventually left Milan for good and returned to Florence in late 1499 after receiving news of Ludovico's comeback plot.

Chapter 20 Florence Again


  • Leonardo painted multiple versions of Madonna and Child scenes throughout his career.
  • The Yarnwinder paintings show a psychological narrative, with the baby Jesus contemplating and grasping the yarnwinder in the shape of a cross.
  • Mary's expression shows anxiety and understanding of her child's fate.
  • Leonardo likely collaborated with his workshop to produce multiple versions of the painting.
  • The Lansdowne and Buccleuch versions are similar, but have underdrawings that suggest they were painted in the studio at the same time.
  • The Yarnwinder paintings influenced other artists, such as Raphael and Bernardino Luini, to create more emotionally charged Madonna-and-child scenes.


“Rather than try to conform, he made a point of being different, dressing and carrying himself as a dandy.”

Chapter 21 Saint Anne


  • Leonardo's painting of the Virgin and Child with Saint Anne shows Mary trying to restrain Jesus from the lamb, representing the Passion
  • The only surviving cartoon related to this project is the Burlington House cartoon, which features Saint Anne, the Virgin Mary, and baby Jesus, but with a young Saint John and no lamb
  • Scholars used to believe Leonardo created the Friar Pietro described cartoon first, then changed his mind and drew the Burlington House cartoon, and finally painted the Louvre version based on the 1501 cartoon
  • However, recent analysis revealed that the figures in the painting are reversed from the original cartoon, with the lamb and young Jesus on the right side
  • Leonardo's studies of geology influenced his paintings, as seen in the accurately depicted stratified rock formations beneath Saint Anne's feet
  • Leonardo had also been studying why the sky appears blue and portrayed it accurately in the painting
  • The painting conveys the spiritual connection between humans and the earth through the curving flow of a river from the macrocosm to the Holy Family
  • Leonardo carried the painting with him for over a decade, making improvements and allowing his assistants to create copies based on his sketches.
  • The painting is complex and layered, often seen as a masterpiece on par with the Mona Lisa or even surpassing it in composition and motion.
  • Some elements of the painting, such as the poses, are less satisfying to some viewers, who may find greater depth of emotion in the unfinished Burlington House cartoon.
  • Leonardo was the master of the unfinished and left some works intentionally incomplete, creating an "unfinished perfection."


“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. In the Saint Anne painting, he portrays the sky’s luminous and misty gradations of blue as no other painter had done. The recent cleaning of the painting fully reveals the magical realism, veiled in vapors, of his distant mountains and skyline.”

Chapter 22 Paintings Lost and Found


  • Leonardo's paintings, including Leda and the Swan and Salvator Mundi, have questionable authenticity due to lack of documentation and signatures.
  • Copies made by Leonardo's followers can provide insight into lost works.
  • Leda and the Swan is a tantalizing lost painting that may have been finished by Leonardo himself, depicting the birth scene rather than the seduction scene from the myth.
  • During his second period in Florence, Leonardo studied birds' flight and planned a flying machine while creating preparatory drawings for Leda and the Swan.
  • Salvator Mundi, a recently rediscovered painting, shows Jesus with a crystal orb and was likely inspired by the popular Salvator Mundi motif of the time.
  • Leonardo's version of Salvator Mundi has distinctive features like mysterious stare, elusive smile, cascading curls, and sfumato softness.
  • The painting underwent a careful authentication process involving experts and historical evidence.
  • Leonardo studied optics around the time he painted Salvator Mundi, using techniques like sharp delineation in foreground objects to create an illusion of depth.
  • A puzzling anomaly in Salvator Mundi is Leonardo's failure to depict the distortion that occurs when looking through a solid clear orb at nearby objects.

Chapter 23 Cesare Borgia


  • In the fall of 1502, Leonardo joined Cesare Borgia's army as a military engineer and advisor.
  • Leonardo's engineering ideas included designing fortifications that could not be breached from within, curved walls to reduce cannonball impact, and self-supporting bridges made of wood.
  • During his time with Borgia, Leonardo also produced a beautiful map of Imola using a magnetic compass and accurate measurements.
  • Leonardo left Borgia's service in March 1503, likely due to his growing disillusionment with the violence and brutality he witnessed.
  • Leonardo's attraction to powerful men may have stemmed from a desire for masculine role models in his own life, as well as his longstanding interest in military engineering.

Chapter 24 Hydraulic Engineer


  • Leonardo's interest in hydraulic engineering began during his time in Milan, where he studied the city's canal system.
  • In Florence, where there were no major hydraulic works at the time, Leonardo aimed to change that and diverted his attention to designing ways for Florence to copy Milan's waterworks.
  • The desire to control a sea outlet became more urgent for Florence due to the excitement over new age of exploration, particularly after Amerigo Vespucci's discovery of America.
  • Leonardo proposed diverting the Arno River from its course and taking it away from Pisa as a way to reconquer the city without storming the walls or wielding any weapons.
  • He calculated that it would take approximately 1.3 million man-hours, or 540 men working 100 days, to dig the Arno diversion ditch.
  • Leonardo designed a machine for digging canals and also considered using wheeled carts but eventually created a crane-like arms system instead.
  • The project to divert the Arno failed due to the ditches being shallower than expected and collapsing during a storm.
  • Leonardo's interest in hydraulic engineering did not end there, and he went on to design a canal between Florence and the Mediterranean Sea to bypass the silted-up and rapid parts of the Arno River.
  • Leonardo also provided technical assistance to the ruler of Piombino to drain the surrounding marshes using both diversion methods and an ambitious centrifugal pump idea.


“This inability to ground his fantasies in reality has generally been regarded as one of Leonardo’s major failings. Yet in order to be a true visionary, one has to be willing to overreach and to fail some of the time. Innovation requires a reality distortion field. The things he envisioned for the future often came to pass, even if it took a few centuries. Scuba gear, flying machines, and helicopters now exist. Suction pumps now drain swamps. Along the route of the canal that Leonardo drew there is now a major highway.”

Chapter 25 Michelangelo and the Lost Battles


  • Leonardo and Michelangelo were both vying for commissions in Florence around 1504, with Leonardo working on a battle scene for the Signoria and Michelangelo creating designs for the Medici's council hall.
  • Leonardo's design featured a large-scale mural of the Battle of Anghiari, while Michelangelo created cartoons for tapestries depicting the Battle of Cascina.
  • The competition between the two artists was intense and attracted much attention, with young artists such as Raphael traveling to Florence to study their works.
  • Leonardo's unfinished battle scene is considered one of the most influential lost paintings in history, and it helped shape the High Renaissance by demonstrating the importance of individual artistic style and genius.
  • Both artists abandoned their projects due to various reasons, including difficulties with materials and competing visions for the works.
  • The competition between Leonardo and Michelangelo raised the status of artists and paved the way for recognition of their individual styles and personalities.

Chapter 26 Return to Milan


  • Leonardo returned to Milan in 1508 after a lengthy absence due to an inheritance dispute in Florence.
  • He was welcomed back by his patron, Ludovico Sforza, who had been deposed and replaced by the French ruler, Louis XII.
  • Leonardo sought the favor of Charles d'Amboise, the French governor, and sent Salai to Milan to deliver a letter requesting an apartment and assurance of continued salary.
  • Leonardo was no longer interested in painting commissions and instead focused on scientific endeavors such as anatomy, geology, water studies, bird studies, optics, astronomy, and architecture.
  • He also designed mechanical devices for pageants and festivities, including a lion that opened its chest to release golden lilies.
  • Leonardo's scientific interests included plans for expanding a palace hall for festivities, a garden of delights with flowing water and various entertainments, and military machinery.
  • The intellectual ferment in Milan attracted artists, scientists, and inventors, making it an ideal environment for Leonardo.
  • Milan provided Leonardo with patrons who appreciated his diverse talents and indulged his intellectual pursuits, as well as grand pageants and festivities that showcased his engineering skills.
  • Leonardo's return to Milan marked a turning point in his career as he shifted away from painting commissions and towards scientific exploration and invention.

Chapter 27 Anatomy, Round Two


  • Leonardo's anatomical studies included dissections of over thirty human and animal bodies.
  • He made detailed drawings and notes, focusing on muscles, bones, nerves, veins, and joints.
  • He noticed the similarities between plant seeds and human embryos and made an analogy between the umbilical cord of a seed and that of a fetus.
  • Leonardo was aware that his fetus drawing had a spiritual quality but did not share his discoveries widely, leading to minimal impact on the history of science.
  • He lacked understanding of the collaborative nature of knowledge growth and the importance of dissemination for scientific progress.
  • His anatomical studies were surpassed by Andreas Vesalius' publication of On the Fabric of the Human Body twenty-five years after Leonardo's death.


“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.”

Chapter 28 The World and Its Waters


  • Leonardo's geological studies led him to question the biblical story of the Flood and propose that fossils were formed over long periods of time through geological processes such as erosion and sedimentation.
  • He observed that fossilized shells are often found in layers and that their presence in high places could not be explained by a single flood. Instead, he proposed that the earth's crust had shifted over time to create mountains and expose previously submerged rock layers.
  • Leonardo also studied the reflection of light from the earth on the moon and concluded that the moon reflects the light of the sun in the same way that the earth does. He realized that the sky appears blue due to the scattering of sunlight by water droplets or particles in the atmosphere.
  • He planned to write a treatise on astronomy but never completed it. Instead, he made notes on various astronomical phenomena, including the motion of the sun and the phases of Venus.
  • Leonardo's observations and theories on geology, fossils, and the color of the sky were significant advances for his time and contributed to the development of these fields in later centuries. However, some of his ideas, such as his belief that the moon does not emit its own light, were later found to be incorrect.


“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. There he engaged in a dialogue between theories and experience, and when they conflicted he was receptive to trying a new theory. That willingness to surrender preconceptions was key to his creativity.”

“He also noted that the veins of humans narrow with age, but the springs and rivers of the earth continually enlarge their channels.30”

“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.”

Chapter 29 Rome


  • Leonardo spent most of his time in Rome (1513-1516) at the Villa Belvedere, which was a summer residence of Pope Leo X and his brother Giuliano de' Medici.
  • He did not paint any new works during this period but continued his scientific investigations, especially focusing on concave mirrors for various applications such as concentrating sunlight to produce heat.
  • Leonardo had conflicts with two German assistants, one of whom was building mirrors for him but was also working for others and denouncing Leonardo to the pope. Another German, Giovanni, criticized Leonardo's work and interfered with his anatomical studies.
  • The Medici influence waned in Rome when Giuliano died, and Leonardo was no longer a favorite of the Medici court. He followed Pope Leo X to Florence and Bologna for diplomatic meetings with King Francis I of France.
  • Leonardo made designs for rebuilding Florence and drew the Medici Palace with a new façade that faced the proposed grand plaza. However, he did not stay in Florence long and eventually went to France at the invitation of King Francis I.

Chapter 30 Pointing the Way


  • Leonardo's late paintings of Saint John the Baptist and the angel of the Annunciation feature a spiritual pointing gesture directed personally to the viewer, enhancing their spiritual intimacy while also showcasing seductive and sensuous elements.
  • These works challenge traditional perceptions by connecting the spiritual to the sensual and highlighting the ambiguity between spirit and flesh.
  • Saint John's portrait showcases Leonardo's mastery of chiaroscuro, enhancing mystery and conveying a powerful sense of John's role as witness to the true Light.
  • The pointing hand in the painting is sharply delineated, creating a visual disjuncture that makes it seem closer to the viewer.
  • Leonardo's lost Angel of the Annunciation painting featured an androgynous angel making a similar gesture, heralding the arrival of Christ.
  • The drawing known as the Angel Incarnate is a controversial work depicting a transgender version of the angel with female breasts and a large erect penis, highlighting Leonardo's exploration of the ambiguous border between flesh and spirit and feminine and masculine.

Chapter 31 The Mona Lisa


  • The Mona Lisa is a portrait of Lisa Gherardini, wife of Florentine merchant Francesco del Giocondo, commissioned around 1503 and completed around 1517.
  • Leonardo's innovative use of sfumato, or the gradual blending of colors and tones, creates an illusion of depth and lifelike quality in the painting.
  • Lisa's enigmatic smile has captivated viewers for centuries, inspiring numerous interpretations and theories about its meaning.
  • Leonardo's expertise in optics and anatomy influenced the depiction of light and shadow in the Mona Lisa, as well as the subtlety and realism of Lisa's features.
  • The painting's composition and setting reflect Leonardo's interest in the natural world and the interconnectedness of all things.
  • The Mona Lisa's enduring popularity and influence can be attributed to its emotional engagement with viewers, as well as its innovative techniques and timeless themes.

Chapter 32 France


  • Leonardo's birthplace, Vinci, is a small hill town in the Tuscan region of Italy.
  • He was born out of wedlock and grew up in the household of his granduncle, Antonio, who ran a successful inn.
  • Leonardo received an informal education from local teachers and possibly even attended the prestigious University of Bologna for a short time.
  • He began his artistic career as an apprentice in Florence under Andrea del Verrocchio, where he learned various techniques including oil painting and metalworking.
  • In his early twenties, Leonardo moved to Milan to work for Ludovico Sforza, the ruling duke of Milan. He spent the next seventeen years there, producing some of his most famous works such as The Last Supper and the Mona Lisa.
  • During this period, Leonardo also conducted extensive scientific studies on various topics including anatomy, geology, optics, and engineering.
  • In 1502, Leonardo was summoned to Rome by Pope Leo X to work on decorations for the Sistine Chapel. He worked on the project for several years but left without finishing it due to a dispute with Michelangelo.
  • In 1506, Leonardo returned to Milan and continued his scientific studies while also working on various painting commissions.
  • In 1513, Leonardo moved to France at the invitation of King Francis I. He spent the remainder of his life there, working primarily as a military engineer and advisor to the king.
  • Leonardo's notebooks contain a wealth of ideas and studies on various topics, including art, science, mathematics, and engineering. They provide insight into his thought processes and show his wide-ranging interests.
  • Leonardo died on May 2, 1519, at the age of sixty-seven. His final will and testament specified that he wanted to be buried in the church at Amboise, where his remains may still be located.
  • Leonardo's influence on art and science is immeasurable. He is considered a pioneer in both fields and his work continues to inspire artists and scientists to this day.


“On what may be the last page he wrote in his notebooks, Leonardo drew four right triangles with bases of differing lengths (fig. 143). Inside of each he fit a rectangle, and then he shaded the remaining areas of the triangle. In the center of the page he made a chart with boxes labeled with the letter of each rectangle, and below it he described what he was trying to accomplish. As he had done obsessively over the years, he was using the visualization of geometry to help him understand the transformation of shapes. Specifically, he was trying to understand the formula for keeping the area of a right triangle the same while varying the lengths of its two legs. He had fussed with this problem, explored by Euclid, repeatedly over the years. It was a puzzle that, by this point in his life, as he turned sixty-seven and his health faded, might seem unnecessary to solve. To anyone other than Leonardo, it may have been.”

Chapter 33 Conclusion


  • Leonardo was a genius who left many projects unfinished but finished works that prove his genius, including the Mona Lisa and anatomical drawings.
  • Genius involves creativity, the ability to apply imagination to intellect, and is universal in nature, spanning multiple disciplines.
  • Be curious, seek knowledge for its own sake, retain a childlike sense of wonder, observe details, start with the basics, see things unseen, go down rabbit holes, get distracted, respect facts, procrastinate, let the perfect be the enemy of the good, think visually, avoid silos, indulge fantasy, create for yourself, collaborate, make lists, and take notes on paper.
  • Embrace a mindset that is open to mystery and does not require sharp lines.


“Each moment incorporates what came right before and what is coming right after.”

“While some may see them as the crazy ones, we see genius. Because the people who are crazy enough to think they can change the world are the ones who do.”3”

“There have been, of course, many other insatiable polymaths, and even the Renaissance produced other Renaissance Men. But none painted the Mona Lisa, much less did so at the same time as producing unsurpassed anatomy drawings based on multiple dissections, coming up with schemes to divert rivers, explaining the reflection of light from the earth to the moon, opening the still-beating heart of a butchered pig to show how ventricles work, designing musical instruments, choreographing pageants, using fossils to dispute the biblical account of the deluge, and then drawing the deluge. Leonardo was a genius, but more: he was the epitome of the universal mind, one who sought to understand all of creation, including how we fit into it.”

“Be curious, relentlessly curious. “I have no special talents,” Einstein once wrote to a friend. “I am just passionately curious.”4 Leonardo actually did have special talents, as did Einstein, but his distinguishing and most inspiring trait was his intense curiosity. He wanted to know what causes people to yawn, how they walk on ice in Flanders, methods for squaring a circle, what makes the aortic valve close, how light is processed in the eye and what that means for the perspective in a painting. He instructed himself to learn about the placenta of a calf, the jaw of a crocodile, the tongue of a woodpecker, the muscles of a face, the light of the moon, and the edges of shadows. Being relentlessly and randomly curious about everything around us is something that each of us can push ourselves to do, every waking hour, just as he did.”

“Seek knowledge for its own sake. Not all knowledge needs to be useful. Sometimes it should be pursued for pure pleasure. Leonardo did not need to know how heart valves work to paint the Mona Lisa, nor did he need to figure out how fossils got to the top of mountains to produce Virgin of the Rocks. By allowing himself to be driven by pure curiosity, he got to explore more horizons and see more connections than anyone else of his era.”

“So did Einstein, who wrote to another friend, “You and I never cease to stand like curious children before the great mystery into which we were born.”5 We should be careful to never outgrow our wonder years, or to let our children do so.”

“If we want to be more like Leonardo, we have to be fearless about changing our minds based on new information.”

“While painting The Last Supper, Leonardo would sometimes stare at the work for an hour, finally make one small stroke, and then leave. He told Duke Ludovico that 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, “for their minds are occupied with their ideas and the perfection of their conceptions, to which they afterwards give form.” Most of us don’t need advice to procrastinate; we do it naturally. But procrastinating like Leonardo requires work: it involves gathering all the possible facts and ideas, and only after that allowing the collection to simmer.”


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