n the late 1950s the British scientist and writer C. P. Snow delivered the Rede Lecture at Cambridge University and identified two disparate intellectual cultures: the intellectuals among the humanists (including artists and writers) and the intellectuals among the scientists (natural scientists and mathematicians).1 Snow claimed that communication between the two groups was strained at best and nonexistent at worst. At the beginning of the twenty-first century we find ourselves still discussing the chasm dividing Snow’s two cultures.
My own passions have always been varied. I am an artist, an occasional archaeologist, but primarily, a physicist—teaching and doing research in atomic physics, astrophysics, and nuclear physics. In art, my works were displayed in a number of exhibitions, including one-man shows in London and Washington, D.C., and collections of my lithographs found their way into Buckingham Palace (a gift of United States Ambassador Walter Annenberg to the Queen), the White House, and the Smithsonian Institution. As a theoretical physicist I have trained or taught at a number of universities—including Georgetown, Berkeley, Princeton, Oxford, and the Institute for Advanced Study. I am a person, I like to think, who lives in both cultures.
Five hundred years ago in Italy there were many intellectuals who developed expertise in diverse fields, and a number of these individuals were spectacularly good in many fields. The expression “Renaissance man” entered the Western vocabulary precisely to describe such people. One person, Leonardo da Vinci, more than any other, embodied that spirit, indeed transcended it. He was quite simply the best in the myriad fields with which he preoccupied himself.
Leonardo was a part-time artist, who might have worked on twenty paintings, a dozen of which survive; of these, only seven are of unchallenged provenance. Nonetheless, it is first as an artist that he is remembered. Indeed, one might argue about who is the third greatest artist in history—perhaps Rembrandt or Raphael, Monet or Picasso? About the first two, there is no argument. One can take Leonardo or Michelangelo, in either order. The level of their influence, their role as drivers, is that significant. As an engineer, Leonardo’s legacy includes a long list of actual and mental inventions that foreshadow future technologies by hundreds of years. Leonardo is inventing the future. Thus, he is the first and preeminent futurist.
The most extraordinary aspect of his genius, however, may just be that his general modus operandi actually prefigures the methodology of modern empirical science. Accordingly, I join in the trumpeting of a theme beginning to be heard among scientists, that Leonardo was the first modern scientist. There have been individuals with greater scientific legacies than Leonardo. Certainly Galileo, Newton, and Einstein are more prominent figures in the history of science, but science is the only reason for their attaining prominence. They made unprecedented discoveries and they published their results. In Leonardo’s day printing was in its infancy, and he had a relatively minor role in the production of only one book, De divina proportione. Had he been able to publish the scientific ruminations found in his manuscripts in his own time, our present level of sophistication in science and technology might have been reached one or two centuries earlier.
For Leonardo, the paragon artist-scientist-engineer, the astonishing variety of his interests are like the knots of a magnificent tapestry. Uncovering the internal dynamics of each of these interests and establishing the connections between them were his quest, and systematic experimentation, his method. Ultimately, in every aspect of his life—while doing science, engineering, and on the infrequent occasions when he did art—he was operating as the consummate scientist. And it was the cross-fertilization of ideas and their seamless integration that led to many of his astonishing achievements. The transcendent unity of science and art, and the expansive cross-semination, are the essence of Leonardo’s model.
Five hundred and fifty years after Leonardo’s birth we use Leonardo’s model to seek again the consilience of science and art—painting, architecture, sculpture, music, mathematics, physics, biology, and engineering—and to remedy as far as possible the disassociation that exists between cultures. We examine common themes and grounds among the interests of the artist and the scientist and the modes of expression adopted by each. The task involves applying elements of modern science and mathematics to the analysis of perspective, proportion, patterns, shapes, and symmetries underlying art and nature. It is important to point out at the outset, however, that in the case of the artist it is almost always unwittingly (but intuitively) that he imbues his works of art with these technical devices, often picked up as subliminal messages from nature. But in Leonardo’s case, it was most likely done with total awareness and forethought—in his art as well as his science. And so it is in the sciences now. The underlying mathematics and the principles of symmetry are not just useful, they are indispensable.
The chapters of Math and the Mona Lisa follow the development of fundamental science from the dawn of civilization, when numbers were invented, to ancient Greece, where science was born. We shall examine the significant role of Muslim scholars, who not only served as a conduit for the transfer of knowledge from the philosophers of antiquity to the scholars of the Renaissance, but who also invented some powerful tools of science and mathematics. The journey will take us through the Renaissance into the Scientific Revolution of the seventeenth century, through Galileo’s discoveries of the law of the pendulum and the law of free-fall and Newton’s discoveries of the universal law of gravitation and the formulation of the calculus. The scientific methodology of Leonardo continued into the twentieth century with Einstein formulating the theory of relativity and a number of extraordinarily gifted young physicists creating quantum mechanics.
Only after we establish the framework of the science and mathematics underlying art and science, and the differing approaches the artist and scientist take in describing nature, will we return to examine Leonardo’s modus operandi and his legacy as artist, scientist, and engineer. Thus, although Leonardo’s system, the “model,” serves as a unifying theme throughout the book, only three chapters are devoted exclusively to Leonardo. But if he were alive now, it is likely that it would have been many of the other chapters that he would have found especially interesting. The quintessential futurist, Leonardo would have glimpsed the whole from the vantage point of the modern scientist.
Math and the Mona Lisa presents science through art, and art through science, and approaches the larger goal of achieving a synthesis of the two fields. The qualities of timelessness and universality in Leonardo’s astonishing works speak eloquently for themselves. With Leonardo’s model providing the unifying thread, however, it becomes possible, first, to glimpse the man’s restless intellect, that extraordinary psyche; second, to see whence the ideas for his works of art came; and ultimately, to appreciate his art at a different level.