# Mathematical Treasure: The Cambodian Zero

Author(s):
Frank J. Swetz (The Pennsylvania State University)

The popular numbering system used in most of the world today is based on the “Hindu-Arabic numerals,” now often called the “Indo-Arabic numerals.” This system of symbols originated in the central Indian city of Gwalior and has been dated back to the year 876 CE. One of the outstanding mathematical features of this system is the introduction of the symbol “0” as a placeholder within a string of digits. The Hindu name for this symbol was sunya, meaning void. In Arabic, the word for void was sifr, which, in Medieval Latin, became zephirum. By the late Middle Ages zephirum had been shortened in Italian and French to zero, the word we recognize and use today in English. (The Arabic sifr is also the root for the English word cipher.)

But for years the story circulated that the Gwalior zero was not the first zero placeholder; that a predecessor existed in Cambodia. Further details were lacking and the status of the “first” zero remained a mystery. In a dogged research project lasting over four years, Amir Aczel (1950-2015) located and documented the existence of this zero, a Khmer zero used in a stone inscription denoting the Khmer year 605 (683 CE). The photo images here were taken in Cambodia and provided to Convergence by Amir Aczel and his wife, Debra Aczel. The chronological inscription is contained on a stone stele first discovered in 1891 and designated in archaeological coding as K-127.

Figure 1. Can you spot the zero on Stele K-127? (Photograph: Amir Aczel, Debra Aczel)

Figure 2. The Khmer symbols above denote the year 605. The image above is from a rubbing of the numeral 605 from the stele.

Figure 3. Can you spot the zero now? (Photograph: Amir Aczel, Debra Aczel)

The inscription was deciphered and its numerical significance noted by the French philologist, historian, and archaeologist Georges Coedès (1886-1969) in 1931. Intervening wars and political disruptions obscured this historical find until Aczel’s search.

#### References

For further information on this zero and the search that located it, see:
Amir Aczel, Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers, New York: Palgrave Macmillan, 2015.

For information about Georges Coedès, see:
Coedès Collection, National Library of Australia, Canberra.

#### Acknowledgment

We thank Amir and Debra Aczel for use of their images of the Khmer zero. These images may be used in your classroom; no other use is permitted without the express written permission of Debra Aczel.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: The Cambodian Zero," Convergence (October 2015)