Book Cover design by Brian Barth, Smithsonian Books
Chinese paperback Math and the Mona Lisa

Hardback Edition
Released April 2004
Seven Printings

Paperback Edition
Released March 2006


Additional Reviews

“ A Beautiful Marriage of Science and Art ”     

Finally, finally as though waiting to open a treasure, Bulent Atalay brings to the world through his genius, the beautiful marriage of science and art in his book, Math and the Mona Lisa. He achieves his purpose of introducing the reader to the fundamental principles of symmetries and shapes inherent in the nature of the universe and as seen through science and viewed in art.  The reader travels this journey of understanding with Leonardo da Vinci as the guide teaching us the exquisite aesthetics of mathematical principles. As these principles are innate in all human consciousness this book is a must read for all.

The world can be grateful for Math and the Mona Lisa as it inspires all of humanity to see the wisdom and perfection that underlies the structure of the universe, especially at this juncture in history when there appears to be chaos everywhere. As an artist who uses these universal principles in the structure of my work, I am especially grateful.

Caroline H. Orner, Maryland

“A fascinating read for even non-math types”     

Dr. Atalay's knowledge of Leonardo is obviously well known, but what struck me about Math and the Mona Lisa is the way he was able to present theories of science, math, and art in such a way that the layperson can both understand the concepts, and be thrilled by the narrative. A really terrific book.

Lauri Berkenkamp, Vermont

Unlike The Da Vinci Code, this book is for real...    

A professor of physics, author Atalay blessed his readers with a succinct history of science & art throughout the ages, emphasizing in particular the contributions of Leonardo da Vinci. We are provided 13 Chaps., 16 color plates & several cartoons to intimately introduce Leonardo da Vinci, his birth, & life & times entwined with an invaluable pensive view of the nature of art & science, & the science of art. Atalay ruminates on previous & subsequent renowned scientists, philosophers & artists, including present-day physicists wrestling with quantum mechanics, etc.

For those interested in science & art & seek intimate glimpses into lives & times of the world's greatest thinkers as Aristotle, Archimedes, Michelangelo, Galileo, Newton, de Broglie, Einstein, Schroedinger, etc. this is your book.

Several provocative math/phsics concepts are used to illuminate uncanny conceptual skills of scientists, but this is not a primer on physics, math or art. Nonetheless, it is an important book, one that requires an author to be personally & deeply immersed in the world of science.  Atalay has done this admirably & publishers don't get any better. Enjoy.

Russell A. Rohde, MD, West Covina, California.  July 4, 2006

“Interesting Mixture of Art, Mathematics and Science”     

With Leonardo Da Vinci as his central figure and human creativity as his main focus, the author melds mathematics and art in interesting ways. The book contains quite a variety of topics, including but not limited to: snippets of Leonardo's life - focusing mainly on art and science, geometrical analyses of various works of art, discussions on various artists and scientists from throughout the ages and a brief history of physics. The golden ratio is shown to play a very important role in various artistic masterpieces, and, indeed, is shown to exist in the structure of the human body. Not being an artist myself, by any stretch of the imagination, I learned quite a bit from reading this book. The author, a theoretical physicist and accomplished artist, has synthesized a book which is a model of clear writing. It should be of interest to a very broad audience, but particularly those with a penchant for art, mathematics and science. .

G. Poirier, Ottawa, Ontario, Canada. May 16, 2006

“Leonardo would have approved”     

For me reading Bulent Atalay’s book was nothing short of a sublime experience that transported me back to my undergraduate physics classroom twenty odd years ago. I was as an aspiring scientist enrolled in Professor Atalay’s ‘University Physics’ class. I had initially walked into the room expecting two semesters of obscure and interminable formulas of physics. Instead of just the material of that arcane subject, I found myself immersed in a holistic education — along with the physics and math there was also frequent references to art, music, literature and the classics, and all interrelated. I left with an appreciation of the humanities, as well as with stronger mathematical skills, and yes, physics as well!!! I had experienced the ‘Atalay magic.’

Everyone cannot take a course from Atalay. But Math and the Mona Lisa echoes the style of his classroom. His book revolves around Leonardo’s passions, but most importantly it presents a way to think beyond the box. He serves as a gifted guide for an extraordinary intellectual journey. In some ways it surpasses many of the inventions of others portrayed in the book by creating a vehicle through which the lay reader can penetrate the mind of the creative genius. The book can inspire all of us to continue questioning, to continue discovering, to continue seeking connections between seemingly unrelated disciplines in a way that adds more beauty to all of them. Leonardo would have approved…

Lisa Wright, Virginia

" A Gem for Leo"     

Although Math and the Mona Lisa addresses art and science in general, at its heart the book is a paean to Leonardo, and a celebration of his works from a unique perspective.  The author, Bulent Atalay, a remarkable scientist and artist who has been called a modern Renaissance man, clearly identifies with Leonardo, another scientist, artist, and engineer who was the definitive Renaissance man.  This special affinity makes the book more than an ordinary biography, and gives exceptional credibility to the author's views on the ways in which the concatenation and synthesis of art and science informed Leonardo's productions.  It is not coincidental that both Atalay and his hero, Leonardo, have produced art that is representationalist, because such work, like science, requires creativity constrained by reality.  Math and the Mona Lisa is not a lavish coffee-table tome.  Instead, it is a compact gem that covers its main theme clearly, concisely, and comprehensively.  It is small enough to fit into purse or coat pocket, and light enough to be easily portable.  Rather than killing time in queues, waiting rooms, and aircraft, a reader can find, throughout the book, a wide range of thought-provoking statements and allusions, some central and many peripheral to the principal topic of the book.  Even readers who are familiar with much of the content of the book may be pleased to see so many disparate ideas brought into meaningful association.  Yet the best things, such as this book, do not contain and provide all that we need, but inspire us to think and seek on our own.  Good things sometimes do come in small packages.

Barry Bressler, Ph.D., Fredericksburg, VA


“I don't have a Nobel [Prize] in Physics like Dr. [William] Phillips, but, ”     

… maybe that makes me a better, more an "Average Joe," reviewer. Mr. Atalay has written a wonderful book. It isn't just about math and the Mona Lisa but marries the history of art with the history of science in a delightful and insightful way. His digressions and endnotes are copious, entertaining and enlightening. I rank it with Margaret Livingstone's "Vision and Art, the Biology of Seeing", as must reads for painters and those interested in painting. But, this is not an easy read or a book to speed read. To wring the greatest benefit from your $16 investment, plan to take time to reflect on the contents and their implications.

Michael Reding, Albuquerque, NM


"Art and Science Synthesized in Leonardo's Mind and Method"     

This is a genuinely astonishing book. Its essential idea is that the dichotomy between art and science is a relatively modern idea, that the distinction is not present in Leonardo's method of looking at the world. I've read a lot of good histories of art, and even a good history of science or two, but I've never seen an organic history of both, and that's Atalay's achievement. The illustrations alone — showing the art in science and the science in art — are a wonder, and well worth the price of the book. A very elegant entertainment.

Nicholas Murray, New York

"An Ancient and Modern Parallel"     

In his marvelously written book on Leonardo da Vinci, Bulent Atalay, who is both physicist and artist, has drawn an intriguing parallel between Raphael's wondrous painting, "The School of Athens", and the equally famous photograph (within the physics community) of participants (including Einstein sitting front-and-center) at the 1927 Solvay Conference on Physics that focused on the revolutionary formulation of Quantum Mechanics that had been accomplished by Heisenberg, Schroedinger, Born, and Dirac between 1925 and 1927. Just as Socrates, Plato, Aristotle, and Alexander represented the "High Renaissance" of Athens, Leonardo, Michelangelo, Raphael the same for 15th century Italy, 1925-27 were truly heroic years for physics. Atalay writes extremely well, and is an exceptional expositor of difficult material, especially in mathematics and physics.

Lester D. Taylor, Ph.D., Tucson, Arizona
Professor of Economics Emeritus , University of Arizona

"Lunch with Leonardo" or "C.P. Snow Revisted"     

Atalay's book just keeps unpacking as you read. He starts by describing C.P. Snow's two cultures and then provides a brief, but full, biography of Leonardo. Each chapter begins with a Leonardo quote that is unfolded within the chapter. In the end I felt a lot more intelligent about art and science and thought his use of Leonardo to make his case was quite smart indeed.

Joseph Richardson, Rochester, NY

"A Scientist Doing Art - an Artist Doing Science"     

Bulent Atalay, the author of this remarkable book, makes a compelling case for Leonardo being just as skilled as a scientist and engineer as he is known to have been as an artist. He writes that Leonardo was "a scientist doing art" seen in such geometric devices as the polyhedral shapes, the impeccable perspective, and in the geological formations found in his paintings. Atalay also writes that Leonardo was "an artist doing science," the evidence on display especially in the breath taking anatomical drawings. The author, himself an accomplished scientist and artist, may just be the perfect scholar to probe Leonardo's methodology. By revealing the results of his analysis in such convincing and readable form, Atalay has created an exceptionally powerful book that cannot fail to inspire, that cannot fail to become a classic. As a professional educator, I would recommend this book to anyone who values a good education.

BW Jones, Maryland

"The best I've read this year"      

Less about Leonardo and more about the mathematical properties of art, I can't recommend this book highly enough. Filled with vignettes such as the humorous story of Dutch art forger Han van Meegeren and other interesting asides, my only regret in reading Atalay's book is that it ended too quickly. The author's great advantage is that by being both a physicist and artist, he has managed to combine the two fields in a way that gives us both knowledge and feeling. Enjoyed it thoroughly and hope for more.

Louis G., Scientific American Book Club, June 30, 2004

"Extremely Fascinating Look into the Science of Art"      

This is a fascinating and insightful look into the world of artistic science and scientific art.   It is a wonderful insight into how science and art are deeply interconnected. It shows us how scientific principles are used in art and how art is hidden in science. The fact that the author is both a renowned physicist and an artist gives him a preferential point of view to tackle this topic. And he does this brilliantly.

I am a physician and a semi professional magician. For this very reason I feel an affinity towards Mr. Atalay's way of looking at things. Magic is also an art form that has its firm roots in physics, mathematics and chemistry. In particular the more advanced card effects often depend on well disguised quite marvelous mathematical principles.

While reading the chapter 'The Eye of the Beholder and the Eye of the Beheld' I was very intrigued by the leftward bias theory. [In the theory's application to a deck of cards] I thought it interesting that out of the 12 court cards in a standard poker deck, 8 of them (or 67%) show their left profile. What is, I believe, interesting is that all red cards (thus including all hearts) show their left side. Only four black cards show their right side, the 3 spades and the jack of clubs. Now, the hearts cards have always been associated with love and caring and the church while the spade cards with war and political power.   It might just be a coincidence, but it's nevertheless interesting.

All in all a fascinating book that you will treasure.

Giorgio E. Tarchini, MD/PhD Lake Lugano Switzerland
and New York, NY

Bulent Atalay's Mona Lisa     

... is an interesting exploration of the historical development of art and science and the effect each has had on the other, with particular reference to the inventive genius of Leonardo da Vinci. One does not have to be solely a scientist or a mathematician to enjoy Dr. Atalay's work, as the clarity of his exposition, his ease of discourse and the liveliness of his anecdotes combine to entertain and instruct even the general reader. I had the privilege of hearing Dr. Atalay lecture on the Fibonacci Series at Mary Washington University and his felicity of expression is admirably reflected in his book. I would highly recommend this work.

R. Inglis

Math and the Mona Lisa... most thought provoking book I have read     

Professor Atalay lucidly explains the mathematics of the Golden Mean which Leonardo both used in his art and eloquently wrote about in his notes which contain a fascinating array of scientific and engineering endeavors.

The Golden mean was a formula used directly or understood intuitively by almost all of the Renaissance artists. Although other Renaissance artists did not carry dissection of human anatomy to the extreme that Leonardo da Vinci did, Renaissance artists were the scientists of their day.

But "Math and the Mona Lisa" is not just another Leonardo da Vinci book. Dr. Atalay uses the Mona Lisa as a literary device to roam through the history of math and science as well as the history of art. As a scientist himself, Professor Atalay's descriptions make great scientists like Galileo, Newton, and Einstein seem real and understandable.

Yet Dr. Atalay is not a stranger to art. He has grown up simultaneously as an accomplished artist. Once the Queen of England asked him to publish a book of drawings of the English countryside.

 Dr. Atalay's education includes Eton, St. Andrews, Georgetown, Oxford and Princeton.

Dr. Atalay was born in Istanbul. His home town was the capital of the Roman Empire,Constantinople, Byzantium itself, and then the capital of the Ottoman Empire at the very border of Europe and Asia.

He recounts with awe, reverence and without prejudice the history of mathematics, art and science as they survived and flourished in the great seats of knowledge and learning in both the Europe and the Moslem world.

       — Ken Richards, Jr., Denver, Colorado

"The Intellectual Capacity of Leonardo"      

In reading Math and the Mona Lisa by Bulent Atalay, one comprehends the intellectual capacity of one of history's greatest scientist and artist, Leonardo da Vinci. Since his talents are expressed through both subjects, both sides of him are studied in order to truly appreciate his motivations and brilliance. More specifically, it is amazing to see how da Vinci's obsession with nature is expressed artistically and through scientific discoveries and inventions and how he utilizes his knowledge of anatomy and divine proportions in his art. Also, because the book approaches da Vinci holistically, his contemporaries, inspirations, and the men he influenced are also studied in great detail. It is for these reasons that I would definitely recommend this book to anyone who is interested in either the arts or the sciences. Because Atalay is pulling from his own knowledge of art, archaeology, and physics, the biography that he has written reads like a novel that can be enjoyed by people with a great range of interests.

Caroline Berson, Falls Church, Virginia

"Music for the Whole Brain "      

In the Prologue of Professor Bulent Atalay's wonderful book, he sites C.P. Snow's 1950s comment that the arts and the sciences had become mutually exclusive realms with little communication between them. Mr. Atalay's book joyfully corrects this state of affairs in ways only someone with developed skills in both realms could accomplish. This book is a great gift to those of us for whom math is as mysterious as life itself, or for the visual spatial learner who finds abstractions in mathematics difficult to grasp. It brings the art of image making together with the art of theorems and proofs to create a wholly accessible celebration of man's ability to perceive beauty, symmetry and form and to penetrate the mysteries of our natural world. Who better to use as an icon of these possibilities than Leonardo da Vinci who made no distinction between art, science, architecture, mathematics and technology but sought to elevate painting, especially, to its proper place in the sciences. Leonardo was the consummate conceiver, builder, observer and crafter of images. He is gaining immeasurable popularity at the moment not for the "Da Vinci Code" fad — which though a good read has nothing to do with the historical da Vinci — but for the model that his work presents for developing both sides of the human brain to its fullest. Leonardo da Vinci and the great artists of the European Renaissance inhabited the worlds of art, philosophy, natural science and mathematics equally. Unfortunately, art and music have become "electives," poorly funded in educational institutions and sadly considered superficial luxuries. Yet students and teachers of science and math in the USA struggle with "no child left behind" requirements in an attempt to help our kids compete globally in math and science. Professor Atalay's book will be a breath of fresh air to any teacher dedicated to helping his or her students fully develop their capacity to think. And to all of us, it is a magnificent symphony composed of music from the natural world.

Melinda Iverson, Seattle, Washington


Both artist and physicist, Atalay is perfectly suited to argue that while most artists intuitively use the scientific elements of perspective, proportion, shape, and symmetry in their work, Leonardo most likely did so consciously. This book attempts to synthesize art and science. After presenting the framework of science and math underlying art, Atalay examines Leonardo's model.

Scientific American Book Club Review

The quintessential Renaissance man, Leonardo da Vinci (1452-1519) was the first modern scientist--and a pioneer in fusing the worlds of science and art using mathematical insights. Inspired by Leonardo's achievements in both science and art, Bulent Atalay in Math and the Mona Lisa explores this process in detail.

Atalay identifies "Leonardo's Model"--Leonardo's attitude that nature could be best described scientifically. He shows how this attitude, in later centuries, inspired both an "aesthetics of mathematics" — the beauty in numbers perceived by physicists and mathematicians--as well as a "mathematics of aesthetics"--the perspective, proportion, symmetry, and other characteristics of art that can be expressed mathematically. The author fleshes out these concepts by providing examples both from Leonardo's own work and that of his intellectual heirs.

Take, for example, the golden ratio phi (1.618...), a quantity that is not only observed in nature (as in the dimensions of a nautilus shell) but that arises frequently in classical architecture and painting. Almost certainly aware of the aesthetic attractions of this ratio, Leonardo used it in the dimensions of two of his most famous paintings, The Last Supper and Mona Lisa , as well as in his sketch The Vitruvian Man . In the Mona Lisa , the subject's torso can be inscribed in a so-called golden triangle with angles 72:-36:-72:. Atalay also shows how Leonardo harnessed his understanding of optics to refine the art of perspective and use it in his own works.

In his guise as inventor, Leonardo was no less sensitive to the subtle interplay between science and art. While most of his notebooks have been lost, the surviving pages display a staggering number of inventions drawn with mathematical precision: the dynamics of vortices in water, the trajectories of cannonballs, the design of odometers, portable bridges, a prototype of an army tank, a bicycle, a helicopter design, a parachute, and more — thereby pioneering a mathematical worldview that would inspire Galileo, Newton, and Einstein.

Math and the Mona Lisa offers a deft analysis of the mathematical themes that bind the artistic and the scientific.

American Artist   

Math and the Mona Lisa documents and celebrates the genius of Leonardo da Vinci, focusing on his use of natural proportions, patterns, shapes, and symmetries. Although artists tend to employ these principles of mathematics unconsciously, Leonardo [likely] did so... deliberately, revealing in his few but famous paintings a perfect synthesis of the two disciplines.

San Diego Union Tribune   

In his best seller "The Da Vinci Code," Dan Brown offers a glimpse of Leonardo da Vinci's scientific genius in what is, essentially, a murder mystery. For those inquiring minds who wanted to know more, [Math and the Mona Lisa] may be the book.

Atalay, a professor of physics, examines the art and science of Leonardo, suggesting that while other great artists unconsciously employed certain symmetries and regularities in their work, da Vinci actually comprehended the underlying science and used it to full effect.

This is a richly detailed ... look at the interplay of art and science and the Renaissance man who brought them together brilliantly. There's no murder here, but plenty of mystery.

  da Vinci  and Friends: Curriculum Where Science and Art Meet

Physicist and artist Bulent Atalay, in his recent book, Math and the Mona Lisa: The Art and Science of Leonardo da Vinci, (Smithsonian Books, 2004) delves into questions of why da Vinci’s drawings and paintings have had such enduring appeal over the centuries. Atalay proposes that Leonardo made good intuitive use of the Divine Proportion or golden ratio, in which the ratio of one line segment to a shorter segment is the same as the ratio of the longer segment to the combined segments. For centuries artists and philosophers have claimed that this ratio, 1.618, expresses a universal harmony found in nature (in nautilus shells), art (self-portraits by Rembrandt) and architecture (the Parthenon). Could this explain part of the appeal of Leonardo’s paintings of Mona Lisa or Last Supper? Read the book, reviewed in Smithsonian Magazine [April 2004].

Blake School  April 2004  Newsletter

Convergence: A Magazine of the Mathematical Association of America 

This is not a sequel to The Da Vinci Code.  In his book, author Atalay, himself a physicist and recognized artist, makes the case for Leonardo da Vinci as the first modern scientist.  By his power to observe, record and communicate the intricacies of nature and the world around him, Leonardo emerges as the ultimate artist-scientist-engineer.  In his perceptions and creations, he intuitively captures the mathematical essences of perspective, proportion, patterns, shapes and symmetries that underlie art and nature.

Math and the Mona Lisa attempts to present science through art and art through science.  In the process, it takes the reader on an historical tour of many mathematical concepts and their applications: from the origins of counting and measurement to the recognition and construction of regular and semi-regular polyhedra to the development of quantum mechanics.  Penrose tilings and logarithmic spirals are considered alongside the work of M.C. Escher and Salvador Dali.  Prominent in these considerations is the emergence of the “golden proportion” and its manifestations in the golden rectangle, the golden triangle, the golden pyramid and the spirals of phyllotaxis; as well as its appearance in the works of many prominent artists.  Indeed, this is a good primer on the golden proportion.  Of course, the life and work of Leonardo da Vinci, the main focus of the text, is fully reviewed and analyzed.  His creative genius is both clarified and magnified. A series of appealing, colorful illustrations are included.

This is a serious book about a serious topic.  Information is often dense and always thought provoking.  At times, it is not an easy read.  However, for those who choose to explore this book, it will provide an enriching experience.

Frank J. Swetz, Professor Emeritus, Pennsylvania State University

"Math and the Mona Lisa... is an interesting book that explores the relationship between art and science/math, using Leonardo da Vinci (a master at both) as a template and prototypical example.  In addition to providing insights into da Vinci’s life and art (which many who have read the da Vinci Code may want to know more about), this book also provides a fine example into the artistic side of science (or the scientific side of art) and the sheer beauty and interest that both hold.

I highly recommend [the book]…"

       — Daniel Moore, January 31, 2005

"In this engaging book, physicist Atalay... attempts to illuminate the mind of Leonardo da Vinci, all the while proving that the more one investigates the enigma of genius, the more enigmatic genius becomes. Leonardo is a convenient if quintessential foil rather than the true focus. The heart of the book is science, with a far greater discussion of math and physics than any work of art. There are two recurring themes: that our universe is mathematical and that there is beauty in this universe. Science and art are both investigations of this beauty, and their confluence is wondrously manifested in the exploits of scientist-artist Leonardo... a passionate account of scientific study in the West and Leonardo's place within it."

       — A. V. Coonin, CHOICE

"Dr. Atalay was the most influential teacher in my life. He taught me to look at physics from a whole new perspective. I remember the stories and relationships that he taught me. For me, this book was a step back in time. Now I am teaching my own group of students about the history and theory of math and science. This book will be an essential component of my class. I look forward to introducing the next generation [to] Dr. Atalay's work."

      Heather Baxter, High School Math and Physics Teacher, Dallas, Texas


"At Play in the Field of Ideas "

"... one of the books newly arrived here at Happiness Central will be commandeering a nice chunk of relaxation time, and I couldn't be more glad: I'm settling in with Math and the Mona Lisa, a marvelous piece of work that's already found hands several times this week when I really should have been doing other stuff. (Noticed a testy tone in a few of my posts lately? Try prying me away from reading I'm really enjoying, then count your fingers. Dangerous business, friends.)

Professor Bulent Atalay ranges all around the landscape -- math and art, physics and one of history's most fascinating figures, making connections everywhere. If you're a scientifically minded soul who'd like to bring greater skills to your appreciation of art, or an artist who suspects that math phobia might be depriving you of some of life's finer things, you need to check this one out. Dr. Atalay's students and lecture attendees are some extremely lucky people. (And I'm lucky to know the person who sent a copy along for my enjoyment -- many thanks, again.)"

      Angela Gunn, usatoday_TECH_SPACE, February 2006

"I have just finished reading the manuscript and it is a masterpiece.  It holds together wonderfully,... the reader will travel far."

      Vincent Burke, former Science Editor, Smithsonian Institution Press,
currently Life Sciences Editor, Johns Hopkins University Press

Eight Additional Reviews and Essays on Math and the Mona Lisa ...

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