Around the time that he reached the unnerving milestone of turning thirty, Leonardo da Vinci wrote a letter to the ruler of Milan listing the reasons he should be given a job. He had been moderately successful as a painter in Florence, but he had trouble finishing his commissions and was searching for new horizons. In the first ten paragraphs, he touted his engineering skills, including his ability to design bridges, waterways, cannons, armored vehicles, and public buildings. Only in the eleventh paragraph, at the end, did he add that he was also an artist.

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.

I asked […] Martin Clayton, whether he thought [Maestro Da Vinci] 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.

I embarked on this book because [Maestro 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. Benjamin Franklin, a previous subject of mine, was a Leonardo of his era: with no formal education, he taught himself to become an imaginative polymath who was Enlightenment America’s best scientist, inventor, diplomat, writer, and business strategist. He proved by flying a kite that lightning is electricity, and he invented a rod to tame it. He devised bifocal glasses, enchanting musical instruments, clean-burning stoves, charts of the Gulf Stream, and America’s unique style of homespun humor. Albert Einstein, when he was stymied in his pursuit of his theory of relativity, would pull out his violin and play Mozart, which helped him reconnect with the harmonies of the cosmos. [Maestro Lovelace], whom I profiled in a book on innovators, combined the poetic sensibility of her father, Lord Byron, with her mother’s love of the beauty of math to envision a general-purpose computer. And [Steve Jobs] climaxed his product launches with an image of street signs showing the intersection of the liberal arts and technology. Leonardo was his hero. “He saw beauty in both art and engineering,” Jobs said, “and his ability to combine them was what made him a genius.

In fact, [Maestro Da Vinci’s] genius was a human one, wrought by his own will and ambition. It did not come from being the divine recipient, like Newton or Einstein, of a mind with so much processing power that we mere mortals cannot fathom it. 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,

At first I thought that [Maestro Da Vinci’s] susceptibility to fantasia was a failing, revealing a lack of discipline and diligence that was related to his propensity to abandon artworks and treatises unfinished. To some extent, that is true. 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.

[Maestro Da Vinci] crammed every inch of his pages with miscellaneous drawings and looking-glass jottings that seem random but provide intimations of his mental leaps. Scribbled alongside each other, with rhyme if not reason, are math calculations, sketches of his devilish young boyfriend, birds, flying machines, theater props, eddies of water, blood valves, grotesque heads, angels, siphons, plant stems, sawed-apart skulls, tips for painters, notes on the eye and optics, weapons of war, fables, riddles, and studies for paintings.

My favorite gems in [Maestro Da Vinci’s] notebooks are his to-do lists, which sparkle with his curiosity. One of them, dating from the 1490s in Milan, is that day’s list of things he wants to learn. “The measurement of Milan and its suburbs,” is the first entry. This has a practical purpose, as revealed by an item later in the list: “Draw Milan.” Others show him relentlessly seeking out people whose brains he could pick: “Get the master of arithmetic to show you how to square a triangle…Ask Giannino the Bombardier about how the tower of Ferrara is walled…Ask Benedetto Protinari by what means they walk on ice in Flanders…Get a master of hydraulics to tell you how to repair a lock, canal and mill in the Lombard manner…Get the measurement of the sun promised me by Maestro Giovanni Francese, the Frenchman.” He is insatiable.

That followed [Maestro Da Vinci’s] injunction to begin any investigation by going to the source: “The one who can go to the fountain does not go to the water-jar."