# Mathematical Treasure: An Indonesian Zero

Author(s):
Frank J. Swetz (The Pennsylvania State University) and Shaharir bin Mohamad Zain (National University of Malaysia)

It is almost certain that in most ancient societies the concept of nothingness was known. Thus, the languages and, ultimately, the number systems of early cultures had to find means of expressing the absence of goods or quantities; such terms for the concept of zero have included Shūnya, nulla, nadaṣifr, zevero, zip, and zilch. Knowledge of the abstract idea of zero appears to have predated the employment of a symbol for zero in place-value numeral systems although, as may be obvious to readers, simply leaving an empty space as a placeholder in a written number can lead to ambiguities of understanding. Some scholars have attempted to trace not only the invention of zero symbols in the world’s various systems of numeration but specifically the earliest appearances of “$0$” as the mark used to denote zero. For example, other Mathematical Treasures in Convergence examine a stone in Cambodia marked with the Khmer year $605$ (683 CE) and early examples of zero symbols found in India. This article discusses a zero symbol found on the island of Sumatra in modern-day Indonesia.

In 1918, the French archaeologist George Cœdès (1886–1969) posited the existence of a dominant but previously unknown Old Malay empire in Southeast Asia, one that pre-dated the Khmers of Cambodia. Continuing exploration has confirmed this kingdom’s existence. Named Sriwijaya, it was ruled by a maharaja, centered on the island of Sumatra, and flourished in the period CE 650–1377. As indicated by the map below, it was a major trading and maritime power that controlled the sea lanes from Madagascar, across the Indian ocean and the Straits of Malacca, through the whole of the South China Sea, and to the islands of the Philippines. Sriwijaya also became an early center of Buddhist teaching and proselytizing.

Influence and expansion of the Srivijayan [Sriwijan] empire by the eighth century CE.
Map created by Gunawan Kartapranata and available from Wikimedia Commons

A major trading partner with China, Sriwijaya supplied the Celestial Empire with luxury goods: gold, silver, and ivory as well as much-sought-after pepper and other exotic spices. In the 7th century, a Chinese monk, Yijing, reported on the grandeur and wealth of this exotic empire. Arab ships plied its waters, and perhaps the fabled adventurer Sinbad the sailor was attracted to the kingdom’s prestige and wealth. Continued researches—such as the investigations by Cœdès and his countrymen; socio-archaeologist Louis-Charles Damais; and British historian O.W. Wolters—have more fully affirmed and documented evidence of the existence of this early Old Malay maritime power. Archaeological explorations have uncovered a rich trove of Sriwijayan artifacts and records. Of particular relevance here, three dated ceremonial stones thought to have been used in Buddhist purifying rituals have been retrieved. They bear the numerals $605$, $606$, and $608$, denoting years as reckoned in the Hindu Saka era calendar, which translate into our Common Era calendar as the dates 683, 684, and 686. The earliest of these inscriptions is shown below. Thus an early 7th-century date for the appearance of zero has been again confirmed.

Keduka Bukit Stone, uncovered by a Dutch colonial officer in 1920 at Paembang, Sumatra, Indonesia. The inscription is in the Old Malay language and bears the date 605, which some experts contest, claiming that it reads 604. In either instance, its zero is a competitor to the Khmer Sambor Stone. This artifact is now housed at the Indonesian National Museum in Jakarta. Photograph by Gunawan Kartapranata and available from Wikimedia Commons via the Creative Commons Attribution-Share Alike 4.0 International license.

##### References

Aczel, Amir. 2015. Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers. New York: Palgrave Macmillan.

Cœdès, George. 1918. Le royaume de Çrīvijaya. Bulletin de l’École française d'Extrême-Orient 18(6): 1–36.

Cœdès, George. 1931. A propos de l'origine des chiffres arabes. Bulletin of the School of Oriental Studies 6(2): 323–328.

Diller, Anthony. 1995.  Sriwijaya and the First Zeros. Journal of the Malaysian Branch of the Royal Asiatic Society 68(1): 53–66.

Swetz, Frank J., and Shaharir bin Mohamad Zain. 2022, July 28. The Elusive Origin of Zero. Scientific American Online.

Zain, Shaharir bin Mohamad. 2001. A Note on the Decimal Numeral System. The Humanistic Mathematics Network Journal 24: 36-42.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University) and Shaharir bin Mohamad Zain (National University of Malaysia), "Mathematical Treasure: An Indonesian Zero," Convergence (September 2022)