Math and the Mona Lisa: The Art and Science of Leonardo da Vinci

Math and the Mona Lisa: The Art and Science of Leonardo da Vinci

by Bulent Atalay

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   Leonardo da Vinci was one of history's true geniuses, equally brilliant as an artist, scientist, and mathematician. Readers of The Da Vinci Code were given a glimpse of the mysterious connections between math, science, and Leonardo's art. Math and the Mona Lisa picks up where The Da Vinci Code left off, illuminating Leonardo's…  See more details below


   Leonardo da Vinci was one of history's true geniuses, equally brilliant as an artist, scientist, and mathematician. Readers of The Da Vinci Code were given a glimpse of the mysterious connections between math, science, and Leonardo's art. Math and the Mona Lisa picks up where The Da Vinci Code left off, illuminating Leonardo's life and work to uncover connections that, until now, have been known only to scholars.

   Bülent Atalay, a distinguished scientist and artist, examines the science and mathematics that underlie Leonardo's work, paying special attention to the proportions, patterns, shapes, and symmetries that scientists and mathematicians have also identified in nature. Following Leonardo's own unique model, Atalay searches for the internal dynamics of art and science, revealing to us the deep unity of the two cultures. He provides a broad overview of the development of science from the dawn of civilization to today's quantum mechanics. From this base of information, Atalay offers a fascinating view into Leonardo's restless intellect and modus operandi, allowing us to see the source of his ideas and to appreciate his art from a new perspective.

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Editorial Reviews

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“The broad sweep of Professor Atalay's brilliant mind brings us an approach to understanding the Vincian genius that is so insightful, so original, and so well-reasoned that it immediately becomes an essential volume in the canon of Leonardiana. I read this monumental achievement in awe of the author's perceptions.”—Sherwin Nuland, author of Leonardo da Vinci and winner of the 1994 National Book Award for How We Die.

“A masterful examination of the differences and similarities in the sciences and the arts, as embodied by that genius of both fields: Leonardo da Vinci. Professor Bülent Atalay has penetrated Leonardo's mind, in a way that is both highly readable and very informative.”—Jamie Wyeth

“Bülent Atalay takes us on a delightful romp through millenia and across continents, bringing together art, architecture, science, and mathematics under the umbrella of Leonardo's genius. His writing is informed by his artist's eye for beauty, his historian's appreciation of context, and his scientist's love of order and symmetry. I read Atalay's description of Leonardo's The Last Supper not long after having visited the masterpiece in Milan, for the first time since its restoration. His words added an unexpected poignancy to that sublime experience. Leonardo is the prototype for the renaissance man—artist, architect, philosopher, scientist, writer. There are few like him today, but Atalay is indeed a modern renaissance man, and he invites us to tap the power of synthesis that is Leonardo's model.”—William D. Phillips, winner of the 1997 Nobel Prize in Physics.

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Math and the Mona Lisa

The Art and Science of Leonardo da Vinci
By Bulent Atalay

HarperCollins Publishers, Inc.

Copyright © 2006 Bulent Atalay
All right reserved.

ISBN: 0060851198

Chapter One

Leonardo Fiorentino:
A Life Well Spent

Late medieval and early Renaissance Italy witnessed many changes, including a revival of the mercantile economy, the emergence of a vernacular literature, and the first serious efforts to recover the classical tradition of learning. Feudalism, with the landed nobility controlling the lives and destinies of the populace, began to lose its grip. The Holy Roman Empire and the Roman Catholic Church increasingly failed to provide social and political stability. National monarchies, especially those of France and England, rose in importance, and in Italy, the city-state became the preferred form of political organization. One city-state, Florence, located in north central Italy, took the lead in projecting the new indefatigable spirit of humanism, a return to the classical ideal of man being the measure of all things; it became the incontestable intellectual capital of Renaissance Europe. The city's preeminence was displayed in literature -- with Petrarch, Dante, and Boccaccio -- but most prominently in painting, sculpture, and architecture. The brilliant painter Giotto appeared early in this remarkable period. The next hundredyears gave rise to the artist Masaccio and architects Alberti and Brunelleschi; then, toward the end of the fifteenth century, the matchless trio of Leonardo, Michelangelo, and Raphael burst onto the scene.

An explosive catalyst for the change was the invention, by Johannes Gutenberg, of the printed book in 1455.1 Before the print revolution, Europe's libraries contained 30,000 volumes. Within fifty years the number of books had increased to three million. The Renaissance also saw the European voyages of discovery, resulting in dramatic expansion in the size of the known world. The Protestant Reformation ignited further intellectual commotion, with an attendant eruption of various dissident sects. Finally, the Renaissance artist, who saw the need to describe nature in the way it really presented itself and not in some idealized or ecclesiastically dictated way, was instrumental in the launching of modern science.

The changing intellectual milieu of the Renaissance spread quickly to Rome, Milan, and Venice. One ingredient for its accelerated development in Italy came with the conquest of Constantinople by the Ottoman Turks in 1453. A number of significant Byzantine scholars migrated to Italy at the invitation of the Italian humanists, among them, Theodore Gaza, John Argyropoulos, and the most influential of all, Demetrius Chalcondyles. These scholars brought with them the first serious efforts to recover the classical tradition of learning and afforded Italian humanists access to the classic Greek texts and manuscripts preserved in Constantinople.

Any discussion on the ascent of civilization must necessarily include the rise of the university. Toward the end of the eleventh century the first of the studia generalia, precursors of universities,2 had appeared in Bologna. In the twelfth century others began in Paris, Oxford, Modena, and Parma, and in the thirteenth century in Cambridge, Padua, Siena, Salamanca, Perugia, and Palermo. The universities did not give rise to the Renaissance, but they benefitted significantly from it. While the Italian universities were the first to be founded in Europe they were the last to be liberated from the scholastic tradition grounded in the works of Aristotle. Their doctrine was salutary for the rebirth of rigorous intellectual discourse in the manner of the ancient philosophers, but it focused mostly on theological issues in a doctrinaire way. Thus the early emergence of universities in Italy with their scholastic tradition has to be regarded as a red herring for the development of science in Italy.3

Not much is known about Leonardo da Vinci's personal life. According to his earliest biographer, Giorgio Vasari, he was an uncommonly handsome man, well-built, full of charm and grace, but he left no definitive image of himself. One reasonable candidate for a Leonardo likeness is a red chalk drawing, found in Turin in the mid-nineteenth century and believed by many to be a self-portrait of Leonardo in his old age. There is a mesmerizing quality in the eyes, simultaneously exuding wisdom, sadness, and acute intelligence that only a truly insightful psychologist-artist could capture (Plate 1). Another possible likeness, also from his mature years, is a colored chalk profile portrait thought to be by one of his pupils; David Alan Brown, of the National Gallery of Art, Washington, D.C., makes a compelling case for the subject of this work.

Leonardo lived his sixty-seven years in a time of frequent wars and political and social upheaval, but also in a period of artistic and intellectual ferment unrivaled since the Golden Age of Greece. He embodied the Renaissance spirit. In his own time he was known as II Fiorentino (the Florentine), although by the late sixteenth century Giorgio Vasari was already referring to him as "Leonardo da Vinci."

It is not known exactly where Leonardo was born, but convincing arguments have been offered by a number of biographers that he was born on April 15, 1452, in the Tuscan village of Anchiano, near the town of Vinci, on the outskirts of Florence. He was the illegitimate son of Ser Piero di Antonio da Vinci and a peasant girl named Caterina. The young couple never married, the boy living the first five years of his life with his mother, grandmother, and a peasant from Anchiano, whom the mother eventually did marry. Meanwhile, Ser Piero married Donna Albieri, a woman of his own station, and only when he found that his wife was infertile did he seek and gain guardianship of Leonardo.

During the next ten years the boy lived in his father's family home in Vinci, never gaining formal adoption or the benefit of the respected family name. There have been speculations by a number of authors -- including Sigmund Freud -- that in the home of his mother and maternal grandmother, and later in the home of his stepmother and step-grandmother, the boy perhaps received attention bordering on the worshipful. These factors have been offered as possible ingredients for his unusual psyche, his exquisite sensitivity, superhuman drive, surpassing intelligence, and probable homosexuality -- although this is all conjecture.


Excerpted from Math and the Mona Lisa by Bulent Atalay Copyright © 2006 by Bulent Atalay. Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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