Finding Zero (9 page)

While I did not know it at the time, Kaye would play a major role in my story. In the meantime, working under the assumption that the zero—the key to our entire number system—was an Eastern invention, I asked myself why this was so, and inexorably I had to link it with the unique logic that I perceived in Asia. My thesis was that the number system we use today developed in the East because of religious, spiritual, philosophical, and mystical reasons—not for the practical concerns of trade and industry as
in the West. In particular, nothingness—the Buddhist concept of Shunyata—and the Jain concept of extremely large numbers and infinity played paramount roles.

The earliest zero in India
is found in the city of Gwalior southeast of Agra, famed home of the Taj Mahal. Gwalior's history is steeped in legend. In 8 CE, Suraj Sen, the ruler of Madhya Pradesh, contracted a serious illness and was about to die. He was cured by a hermit named Gwalipa, and in gratitude, Sen founded a city and named it after the man who had saved his life. Gwalior has many temples built over the centuries, and it has a famous fort whose defense played a role in many conflicts throughout Indian history. The fort was almost impenetrable; it stands on a high plateau in the middle of the modern city, rising sharply to 300 feet above its surroundings. This made it very hard for enemies to reach it and breach its walls. In a Hindu place of worship called the Chatur-bhuja temple—“the temple to the four-armed god” (the four-armed god in Hindu tradition is Vishnu, the powerful maintainer of our world)—there is an inscription in Sanskrit on the wall that records that it was built in the year 933 of a calendar whose starting point was 57 BCE. This makes the year it was built 876 CE. The numerals 933 used here are surprisingly similar to our modern numbers. The inscription also records that the land grant for the temple had a length of 270 hastas (a measure of length). The 0 in 270 is the oldest zero that can be seen in India today.

So by 876 CE, the Indians had the crucially important use of a place-holding zero at their disposal in a number system that from our modern vantage point was perfect. Their system would
have enabled them to compute in a powerful, efficient, and unambiguous way. But would it be possible now to go still further back in time and find when the
first
zero had made its debut, the first exemplar of one of humanity's greatest intellectual inventions? I wanted to see it with my own eyes, to touch it, to feel it.

I left India with this remaining mystery unsolved. I learned much there, but nothing about where the key to the numbers—the primeval zero—came from, and when. If the oldest zero in India was from 876, then it was possible that it had come from Arabia—and had gone to Arabia from Europe—because the ninth century is well within the timeframe of extensive Arab sea trade. This was a time when Arab trade flourished, allowing for the possible transfer of goods—and ideas and information—across the realms the traders roamed, meaning between Europe and the East. Such transfer could well have taken place from east to west, or from west to east. And this was exactly the argument that the Western-biased Kaye had put forward in his lectures and articles. Lacking an earlier Eastern zero than that of Gwalior, Kaye's argument that our numbers with the zero numeral were either European or Arabic in origin could not be countered or disproved.

But if a zero could be found in the East that predated the emergence of Arab trade, this could provide strong support for the hypothesis that the zero was indeed an Eastern invention. This is why the Gwalior zero—important as it is—could not definitively determine who invented the most important component of our number system.

The oldest zero was of course the Mayan zero—but it was confined to Mesoamerica and went nowhere from there. And the
Gwalior zero was from the mid-ninth century—so it was no good as a historical landmark. If the Khandela inscription was ever to be rediscovered, it could bring the invention of the Indian zero down to 809 CE, as had been reported by people who claimed to have inspected it decades ago.
8
But because its date was still late, this wouldn't help much in finding a decisive, earlier zero that could settle the question of who invented the concept and the numeral.

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 at 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.