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Mathematical Treasure: Indonesian Zeros

Frank J. Swetz (The Pennsylvania State University), Shaharir bin Mohamad Zain (National University of Malaysia), and Iwan Pranoto (Institut Teknologi Bandung, Indonesia)

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 stele in Cambodia marked with the Khmer year \(604\) (682–683 CE) and early examples of zero symbols found in India. This article discusses zero symbols found in modern-day Indonesia, including the inscription on the Kedukan Bukit stone discovered on the island of Sumatra.

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. 

Map of the Srivijaya Empire from Wikipedia.
Figure 1. Influence and expansion of the Srivijayan [Sriwijan] empire by the eighth century CE.
Map created by Gunawan Kartapranata and available from Wikimedia Commons
via the Creative Commons Attribution-Share Alike 3.0 Unported license.

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. The stones, known as Kedukan Bukit, Talang Tuo, and Kota Kapur, bear the numerals \(604\), \(606\), and \(608\) respectively, 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 the zero symbol has been again confirmed.

The earliest of the three stones, known as the Kedukan Bukit inscription, showing an Old Malay zero symbol.
Figure 2. Kedukan Bukit Stone, uncovered by a Dutch colonial officer in 1920 in Palembang, Sumatra, Indonesia. The inscription is in the Old Malay language and bears the date 604. (A discussion of the controversies over its dating appears below.) The stone’s zero symbol thus corroborates the evidence of an early zero on the Khmer Sambor Stone. This artifact is now housed at the Indonesian National Museum in Jakarta. Photograph by Iwan Pranoto.

Talang Tuo inscription showing the date 606.
Kota Kapur inscription showing the date 508.
Figure 3. Talang Tuo inscription bearing the “606” numeral notation (top); Kota Kapur
inscription bearing the “608” numeral notation (above). Photographs by Iwan Pranoto.

In [Cœdès 1930, p. 34], Cœdès translated the Kedukan Bukit inscription and hesitantly interpreted the numerical symbol as 605. However, immediately after expressing the numeral as 605, Cœdès added a footnote describing his uncertainty about the unit digit 4 or 5, although, in the end, he determined that 5 was more likely. To be precise, he said:

Le chiffre des centaines est sûr (v. infra, p. 51) ; quant à celui des unités, ce ne peut être que 4 ou 5, mais 5 est plus probable.

This paper is widely recognized as the definitive authority on translating the Kedukan Bukit inscription, and its findings conclusively established that the inscription was created in the 605 Saka year. Regrettably, some scholars tended to concentrate solely on the number 605 and disregarded Cœdès's cautionary statements in the footnote. Meanwhile, Cœdès translated the Sambor inscription from Cambodia and consistently decoded the similar numerical symbol on it as 605 as well [see Cœdès 1930, Plate VII]. Cœdès included photographs of the two numeral notations in the inscriptions of Kedukan Bukit and Sambor, as shown in Figure 4. (In his 2015 Mathematical Treasure on The Cambodian Zero, Frank Swetz reported on the Sambor inscription containing zero placeholders by referring to Amir Aczel’s works.) As observed in both photographs, the digits of the two numbers are similar, except that the Sambor inscription utilizes the dot or bindu as the representation of zero. In contrast, the zero notation on the Kedukan Bukit stone is a small hollow circle, which is commonly used today.

Detail of Kedukan Bukit inscription, showing the date 604.
Detail of the Sambor (Khmer) inscription, showing the date 604.
Figure 4. Numeral notations carved in the Kedukan Bukit stone (top)
and Sambor inscription (above) [Cœdès 1930, Plate VII].

Thus, the question is whether the year inscribed on the Kedukan Bukit stone was \(604\) or \(605\). The seminal work of Damais [1952] plays an important role in resolving this matter. In it, Damais listed the writing of numerical symbols in various inscriptions collected at that time, not only those found in Sumatra, but also those found in Java, Sunda, and Bali. Damais thoroughly listed and sorted each number symbol from 0 to 9 based on the year in which it was written. This representation enables us to examine the evolution of the writing of each number. Due to Damais’s comparative table, the distinction between the numeral notations for \(4\) and \(5\) becomes evident. Since Damais’s work was done two decades after Cœdès wrote his 1930 paper, it is understandable that the difference between the symbols 4 and 5 might not have been apparent to Cœdès. But, thanks to Damais’s efforts, we can now understand that numeral symbols 4 and 5 both represent similar body parts, but the symbol for 5 is distinguished by a stroke at the top.

Thus, Damais [1952], Soutif [2008], and Boechari [2018] have concluded that the Kedukan Bukit inscription from Indonesia dates to \(604\) Saka, not 605 Saka. Moreover, Soutif confirmed that the Sambor inscription from Cambodia and the Kedukan Bukit inscription are both from 604 Saka. To further corroborate this fact, Figure 5 lists numeral notations in various inscriptions from the islands of Sumatra and Java, organized by their year of inscription. By analyzing the distinct differences between the symbols 4 and 5 as represented on this table, it is possible to convince ourselves that the final digits of the numeral notations of both the Kedukan Bukit and Sambor inscriptions (Figure 4) are indeed 4.

Comparative table of medieval Indonesian inscriptions for the numerals 4 and 5.
Figure 5. The evolution of the numeral notations 4 and 5 in inscriptions
found in Sumatra and Java. Table provided by Iwan Pranoto.

On the one hand, the above findings confirm that the oldest zero placeholder and decimal number writings found thus far are in the numeral notations 604 carved in the 7th-century Kedukan Bukit and Sambor inscriptions from Indonesia and Cambodia, respectively. On the other hand, the earliest recorded instance of the zero placeholder in the Indian subcontinent dates back to 9th-century Gwalior, yet it had already been utilized in multiple instances in 7th-century Southeast Asia. This finding suggests the proposition that, in Maritime Asia, number knowledge was disseminated and cross-pollinated concurrently, rather than being passively absorbed.

This Mathematical Treasure was updated in January 2024 by Dr. Iwan Pranoto. The photographs above may be used in your classroom; for all other uses, please contact Dr. Pranoto.


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

Boechari. 2018. Melacak sejarah kuno Indonesia lewat prasasti. Kepustakaan Populer Gramedia.

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

Cœdès, George. 1930. Les Inscriptions Malaises de Çrīvijaya - Persée. Bulletin de l’Ecole Française d’Extrême-Orient 30:29–80.

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

Damais, Louis-Charles. 1952. I. Études d’épigraphie indonésienne. Bulletin de l’École française d’Extrême-Orient 46 (1):1–106.

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

Soutif, Dominique. 2008. Dénombrer les biens du dieu: Étude de la numération du vieux khmer (VIe-XIIe siècles śaka). Journal of Cambodia Research, no. 10:51–80.

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.

Zain, Shahrir bin Mohamad, and Zahrin Affandi Mohd Zahrin. 2019. Sistem Angka Perpuluhan yang Diketahui Tertua di Dunia: Angka Malayonesia (The World’s Oldest Known Decimal Numeral System: The Malayonesian Numerals). Journal of Science and Mathematics Letters 7:52–65.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), Shaharir bin Mohamad Zain (National University of Malaysia), and Iwan Pranoto (Institut Teknologi Bandung, Indonesia), "Mathematical Treasure: Indonesian Zeros," Convergence (September 2022)