Finding Zero

by Amir D. Aczel

  9

  When I returned from India, it seemed to me that my research was at a dead end. The ancient Indians of the ninth century had a zero, but this zero was concurrent with the Arab empire centered at Baghdad—the caliphate—whose traders connected East and West. The zero could have been invented anywhere: in the East and brought west by Arab traders; in Europe and transported to India through the same Arab naval commerce; or invented by Arab mathematicians themselves and then taken both east and west through Arab trade. If the Bakhshali manuscript were to be carbon dated and was found to be much more ancient than the Gwalior zero, this might settle the problem. But who was I to convince the stubborn British authorities to allow me to carry out what they thought was an invasive analysis of a priceless artifact? Others have attempted to do so and failed.

  I felt resigned to the fact that I might never resolve who invented the zero. I wanted to go on with my studies but had little going for me at this point. Should I look for another research project? I asked myself. Debra was very supportive, however, and suggested that I keep trying. But I was losing faith in my ability to research this topic any further. I simply could find nothing more about the zero. There wasn’t anything I could do that would move my search forward; all my attempts were futile. I felt frustrated, angry, and depressed after devoting so much time to this search. So reluctantly I started looking for other research topics, encouraged by my friends and colleagues who felt I needed a subject other than the numerals to occupy my mind.

  I found a compromise. The zero was beyond my reach, but I could look at other number systems and study them. The Etruscans—a mysterious Italic people obsessed with death and funerary arts whose culture flourished between the eighth and third centuries BCE in what is now Tuscany and a part of Umbria—had their own number system, which had never been fully deciphered. So I began to look at Etruscan numbers with renewed research vigor. Playing-dice made of bone had been discovered in Etruscan archaeological sites, and these provided hints about the shape of the numerals from one to six. All of these numbers were letters in the Etruscan alphabet, but the alphabet itself had not been deciphered, so we are not sure of the shape of all the Etruscan numerals—there has simply been a paucity of finds for us to be able to draw a clear-cut conclusion. I found this fact intriguing. And after a month of intense work, I made progress on discerning a similarity between Etruscan and Greek letters. For example, the Etruscans had no g sound, so they imported the Greek letter gamma to stand for their letter C. When the Etruscan civilization was subsumed into the Roman Republic in the first two centuries BCE, C came to stand for the number 100—thus completing a circuitous route from Greece to Etruria and finally to Rome. This was interesting research, but it wasn’t the exciting quest for the primal zero.

  Then something unexpected happened. While Debra and I shared a meal one day—she had come home for lunch to cheer me up—she suggested that I might look further into the story of the Gwalior zero, the oldest known zero in India, which I had recently seen. Unbeknownst to us at the time, this suggestion would bring about the needed breakthrough in my stalled project.

  Following her suggestion, I looked again at the Gwalior zero, and to my surprise found an excellent online description of this artifact by the mathematician Bill Casselman of the University of British Columbia. So I called him up, out of the blue, to ask him to tell me more about Gwalior. He answered my call with alacrity, and through our pleasant, long conversation I learned that he had a surprisingly extensive familiarity with the history of numbers. It also turned out that he had been a doctoral student of the celebrated Japanese American number theorist Goro Shimura of Princeton, whom I had interviewed for my earlier book about Fermat’s Last Theorem. This was a fortuitous connection to have discovered between us, and I hoped Casselman would become a friend.

  He told me he was sure that an earlier zero than Gwalior’s had been discovered in Cambodia and published many decades ago by the French archaeologist George Cœdès. Casselman didn’t know more about this finding, he confessed, and suggested that I try to find out the whole story. I almost fell out of my chair when I heard him say this—I realized immediately that Cœdès had to have been the archaeologist that Laci had read about many years before. I had finally stumbled onto his trail almost by chance.

  I was bewildered. How could I not have found it all on my own? Hadn’t I been carefully looking into the history of the zero for so many months? And to embarrass myself further, I later even discovered that the book sitting right on top of my desk, The Universal History of Numbers by French researcher Georges Ifrah, had several references to the work of Cœdès—and I had completely missed them. I sat motionless for a minute, rubbing my eyes in disbelief. How could I have been so careless? And then I went to the fridge and poured myself a strong, icy drink. Once again, Laci had led me in the right direction—even if it had taken me four decades to find out where he was trying to point me.

  I spent the following weeks working frantically to learn as much as I could about this little-known (to me, and to the general public—in scholarly circles he was well-known) French archaeologist and linguist who had changed our understanding of the history of mathematics—without, himself, being a mathematician. Cœdès was a fascinating character: a man with immense gifts of language and interpretation, who cared deeply about history and about righting the wrongs perpetrated by bigoted scholars. Cœdès discovered a much earlier zero than the Gwalior, analyzed and published it, and corrected our understanding of the history of numbers.

  But it turned out that Cœdès’s artifact with the early Cambodian zero had been lost. I now felt a need to find it again, to see it and bring it to the attention of the world: the first known zero—a testament to humanity’s great intellectual discovery that led to the creation of our modern digitally ruled world, and proof that the East, not Europe or the Arabs, had it first.

  I was now ready to get on the road again, and I finally had a starting point. But who was this scholar, George Cœdès, who made such a powerful discovery now presumed lost?

  George Cœdès was born on August 10, 1886, in the elegant 16th arrondissement in Paris, just across the Seine from the Eiffel Tower, which would be erected when he was three years old. His father was a wealthy stockbroker. His grandfather, a Hungarian Jewish immigrant named J. Kados, was an artist who was determined to start a new life in France; he had left everything behind him on abandoning his native Hungary, including his name, which he changed to make it sound French. His grandson, George, would throughout his life maintain the ligature between the o and the e in Cœdès, as well as on the accent grave on the second e. And he insisted it be pronounced as sehdehss.

  Raised in comfort in Paris, George eschewed a career in finance, a field his father had encouraged him to study, and decided instead to learn languages. His mother was born to a Jewish family in Strasbourg with deep roots in Alsace-Lorraine, a part of France bordering Germany where German is still spoken with some frequency today. Cœdès had good familiarity with German from his home and as a young man decided to study it. At 20, he spent a year traveling in Germany to master the language. He learned it so well that when he crossed the border back into France, the guards couldn’t believe he was French and not German. When he returned to Paris, Cœdès enrolled in a language instruction program to qualify him as a language teacher.

  He passed his national teacher’s qualifying exams with ease, and in May 1908 received his license to teach German in French secondary schools. But life was not easy for a Jew of foreign origin in France of the early twentieth century. The country was still reeling from the infamous Dreyfus trial, which had polarized society and caused a resurgence of anti-Semitism among both the elite and bureaucratic circles. Many French schools refused to hire the brilliant young bilingual teacher. Being ambitious and single-minded, George refused to give up, and after trying for positions at many schools, he finally was appointed to teach German a
t the Lyceé Condorcet in Paris and set out on the career of a high school language teacher. But soon events would take him on a different path.

  Shortly after he started teaching at the Lyceé, Cœdès was called to serve his country. In a sense, this was fortunate for him, since his call-up occurred in 1908, during a peaceful time not long before the outbreak of the Great War. But the French military was as anti-Semitic in that period as it had been for decades, making life difficult for the young officer. On leave, he could visit his doting parents and his school, where students remained attached to their now-absent favorite teacher.

  One day in Paris, Cœdès decided to spend his afternoon in the Louvre. Anyone who has ever visited the Louvre has been overwhelmed by the richness of the paintings, statues, and artifacts on display in this museum—perhaps the world’s greatest. On this early spring day in 1909, the 23-year-old George Cœdès entered the Louvre and went to the room displaying the Near Eastern Antiquities Collection. George abruptly stopped in front of the Babylonian stele depicting the Storm God. He studied the explanation of the display and was surprised to find that if he concentrated hard, he could deduce some connections between the words in French on the explanatory panel and the signs displayed on the stone artifact. He was even able to decipher the meaning of a few of the characters.

  Stunned by what he had been able to do, Cœdès realized he had a rare gift. With some effort, he could understand the meaning of ancient languages whose letters and signs were carved in stone on millennia-old artifacts. By the time he reached the room housing the Southeast Asian Collection, he was hooked. He knew he wanted to spend his life decrypting such ancient writings.

  Because of its colonial involvement in Southeast Asia, a region the French called Indochine, France had acquired a wealth of art and documents in its museum collections from Cambodia, Vietnam, Thailand, and Laos. Over the next few months until his discharge from military service, Cœdès spent every minute he could spare in some Parisian museum, armed with notebook and pen, copying writings in Old Khmer, the ancient Cambodian language that fascinated him the most. Six months later, Cœdès had become somewhat proficient in this language. As soon as he was released from the army, he enrolled at the École Pratique des Hautes Études in Paris to study Old Khmer as well as Sanskrit, the most important Indian language.

  That year, he published his first scholarly article. It was a brilliant linguistic analysis of a Cambodian stele from the third century, in both Sanskrit and Old Khmer, and it appeared in the prestigious Bulletin de l’École Française d’Extrême-Orient, a publication edited in Hanoi in French colonial Vietnam and named after the educational and research institute the French had established throughout Indochina.

  In the summer of 1911, Cœdès was awarded his doctorate from the École Pratique des Hautes Études and got his first job offer as a scholar. The École Française d’Extrême-Orient, which had published his first article, offered him a position as researcher in Hanoi. He immediately headed for Indochina.

  Cœdès was a careful, ambitious, and determined scholar from an early age. When he studied a subject, he did it thoroughly and completely, often sitting for hours at his desk inspecting ancient documents—copies of inscriptions, pencil rubbings of stone artifacts or steles—until he understood them completely. Slight, bespectacled, and with a pallid complexion, he looked like a born bookworm.

  Cœdès knew that the British scholar G. R. Kaye, whose papers he had read, was a man on a nasty mission. He realized how deeply Kaye despised India, a country that had welcomed him as a researcher and even allowed him to be the first to study the Bakhshali manuscript; Kaye had used his knowledge of Indian antiquities to argue that India followed the West in discoveries about mathematics. He had even used the discoveries of ancient Greek coins in India—proving Indian trade with Greece—to bolster his claims of European primacy, and his main issue for decades had been to oppose the idea that the nine numerals with a zero were invented in India.

  Kaye held strong to the conclusion that since no datable artifacts had ever been found with definitive dates for zero earlier than the ninth century, our numbers must have been imported into India from Greece, or perhaps other places in Europe, or Arabia. The fact that he was the first researcher to study the Bakhshali had endowed him with academic clout, and he used it aggressively to convince other scholars that he knew much about India and that Indians could not possibly have preceded the West in designing a number system. In the highly biased, anti-Eastern British scholarly community, Kaye found many allies, and his views prevailed. But Cœdès was determined to prove Kaye wrong.

  10

  Cœdès defined the civilizations that thrived in Southeast Asia more than a thousand years ago as “Indianized”—he called them that because their peoples practiced Hinduism or Buddhism, followed Indian social customs, held Indian cultural values, and used Sanskrit in addition to their local languages. He noted the strong influence of India on the kingdoms of Angkor, Champa, and other dynasties of the region, which were in effect, according to his view, cultural extensions of India.

  By studying numerals found in ancient Cambodia and Indonesia, where his Indianized cultures thrived in the early centuries of the common era, Cœdès was able to support his theory that these civilizations used such numerals before their appearance in the West in the late Middle Ages. Numerals were found on many inscriptions from the eighth and ninth centuries analyzed by Cœdès, as were others found in India. But research in India proper also identified the key element of the numbers: the zero, discovered at Gwalior. Perhaps in the ruins of these Indianized civilizations, where so many stone inscriptions had been found, he might discover a zero predating that of Gwalior, Cœdès thought. In the meantime he spent much of his time studying the amazing culture that sprang up in the western part of Cambodia a millennium ago: the legendary civilization of Angkor.

  Angkor Wat is the largest temple or religious building—taking into account all the cathedrals and basilicas ever built—in the entire world. This gigantic, beautiful, and architecturally unique Hindu temple was built in the eleventh century—about the time that Notre Dame was completed in Paris—near the town of Siem Reap (Siam victorious) in western Cambodia. Unusually, Angkor Wat faces west, the opposite direction from that of all other Eastern temples. This fact has puzzled scholars for decades; one explanation for it is that it was dedicated to Vishnu, the Hindu god of the west. Because it was considered a monumental event in the history of Southeast Asia, the establishment of Angkor—the city of the Khmer empire that built the great temple—in the ninth century helped historians define the entire chronology of Cambodia:

  Pre-Angkor: from the first to the eighth centuries.

  Angkor: from the ninth to the thirteenth centuries.

  Post-Angkor: from the fourteenth through the twenty-first centuries.

  The region that gave rise to the powerful Angkorian civilization was divided in ancient times into various areas, each of them an independent or semi-independent kingdom. The kingdoms in the area of Southeast Asia during this time were Chenla, today’s Myanmar (Burma); the territory that is roughly present-day Vietnam was called Champa; and Cambodia of the ninth century, referred to in Chinese records as Fu-Nan (and by others as “Water Chenla”).

  Like Khajuraho in India, Angkor Wat was said to have become lost to the jungle when the Khmer empire disappeared, and was supposedly rediscovered by nineteenth-century French explorers. At least that is the story one hears about Angkor in the West. In 1846, the French missionary Father Charles Emile Bouillevaux rediscovered the magnificent lost legendary city of Angkor, including its temple, Angkor Wat. Five years later, the French explorer Henri Mouhot visited the site and made detailed observations of Khmer remains in the area.

  While it has no sexually explicit imagery, per se, Angkor Wat is adorned by thousands of alluring seminude female friezes of demigoddesses, or nymphs, called Apsara. Inscri
ptions here and elsewhere in Cambodia bear much numerical information in the form of dates and numbers of animals to be sacrificed, as well as measurements of lengths, widths, and heights. It seems that ancient southeastern Asian temples are also filled with symbols of sex and mathematics.

  Based on his research on Angkor, George Cœdès wrote the definitive book on Angkor Wat, titled simply Angkor. Even today, his book is by far the most comprehensive treatise on the lost civilization of ancient Cambodia. Cœdès described Angkor Wat as representing the height of the Dravidian style in architecture, which originated in southern India millennia ago. The temple itself is said to represent Mount Meru, the mythical home of the Hindu gods and thus an earthly likeness of a divine abode.

  Cœdès learned that linguists have determined that Old Khmer is thousands of years old, predating Thai. The indigenous cultures of Southeast Asia were advanced and had known how to make bronze for at least 1,500 years before contact with the civilization of India during the first centuries CE. Indian and Chinese influences in ideas and practices started here in the second and third centuries CE and then spread throughout the region. He learned that Chinese records from that time speak about Fu-Nan, in the lower reaches of the Mekong River, and Chenla, farther inland in the Mekong River basin. These references are in fact the only historical—rather than archaeological—ones we have for the civilization that grew in this region.