Mathematics in Victorian Indigenous Communities: Stories, Practices, and Global Comparisons
Mathematics is often assumed to be a Western invention, but Indigenous peoples worldwide developed highly sophisticated mathematical systems rooted in culture, story, and practice. For Indigenous communities in Victoria — including the Wadawurrung, Wurundjeri, Gunditjmara, and Taungurung — mathematics was not abstract but deeply embedded in Country, ceremony, and daily survival.
Anthropologists such as Donaldson (2015) and Broome (2005) have shown that Aboriginal mathematics was expressed in counting systems, geometry, astronomy, trade, and kinship, offering a worldview that integrates number, space, and spirituality.
Mathematics in Victorian Indigenous Communities
Counting and Number Systems
Victorian Indigenous languages included number words, often structured relationally rather than abstractly. For example, Wadawurrung speakers described quantities in practical terms such as pairs, bundles, or body-based counts (Broome, 2005). Gunditjmara eel aquaculture required accurate counting of eels trapped in stone channels, demonstrating applied arithmetic (UNESCO, 2019).
Geometry in Ceremonial Grounds
Ceremonial bora rings and corroboree grounds show circular and symmetrical design, reflecting deep spatial knowledge. The Wurdi Youang stone arrangement (Wadawurrung Country) aligns with the sunset positions at solstices and equinoxes, indicating not only geometry but also astronomy (Hamacher & Norris, 2011).
Trade and Exchange
Trade across Victoria required arithmetic equivalence. Wadawurrung and Wurundjeri people exchanged Mount William greenstone axes in set numbers, with bundles of goods recorded and exchanged according to kinship law (Clark, 1995).
Timekeeping and Astronomy
Victorian Indigenous groups used lunar cycles (~29.5 days) and solar solstices to structure ceremonial calendars (Hamacher, 2012). Ecological maths guided harvesting: murnong (yam daisies) were collected seasonally, while eel migrations were predicted using lunar and seasonal observation (UNESCO, 2019).
Mathematical Stories in Victoria
Indigenous oral traditions encoded mathematical thinking:
Bunjil’s Laws (Kulin Nations): Marriage rules required strict kinship exclusions, a system resembling combinatorial logic (Broome, 2005).
Star Stories: Wurundjeri and Taungurung people observed Purra (Canopus) and the Pleiades (Seven Sisters), timing ceremonies and food gathering by stellar positions (Hamacher & Norris, 2011).
Tanderrum Ceremonies: Structured exchanges between groups followed predictable reciprocity, a form of social mathematics (Neale, 2017).
Mathematics Across Aboriginal Australia
Northern Australia
The Yolŋu of Arnhem Land developed kinship mathematics with moieties and subsections. This system, described by Donaldson (2015), can be represented through algebraic sets, defining who may marry whom.
Central Desert
The Arrernte and Pitjantjatjara used sand drawings to encode topographical and social information in geometric forms (Neale, 2017).
Western Australia
The Noongar recognised six distinct seasons, each defined by ecological markers. This reflects an advanced calendar system combining arithmetic and environmental mathematics (Rose, 1996).
International Indigenous Mathematical Systems
Māori (Aotearoa/New Zealand)
Māori tatau (counting) systems were applied to navigation and food storage, while spiral carvings (koru) show geometric principles (Donaldson, 2015).
Inca (South America)
The quipu, a knotted cord system, functioned as a numerical and algebraic device for record-keeping (Neale, 2017).
Maya (Central America)
The Maya developed a base-20 numerical system and highly accurate calendars based on astronomy (Flood, 1997).
Sámi (Scandinavia)
The Sámi used applied maths for reindeer herd counts, migration timing, and celestial navigation (Rose, 1996).
The Science of Indigenous Mathematics
Modern research highlights the scientific precision of Indigenous mathematics:
Geometry: evident in stone arrangements like Wurdi Youang (Hamacher & Norris, 2011).
Arithmetic: applied in trade bundles and kinship obligations (Clark, 1995).
Probability and Prediction: seasonal cycles tied to flora and fauna reflect forecasting models (Broome, 2005).
Fractal Design: Aboriginal art often uses repeating recursive patterns, similar to fractal mathematics in African design (Donaldson, 2015).
Impacts of Colonisation
Colonisation disrupted mathematical traditions:
European observers dismissed Aboriginal number systems as “primitive” (Reynolds, 1987).
Missions replaced Indigenous education with Western arithmetic, silencing cultural approaches (Barwick, 1998).
Dispossession destroyed practices tied to environment — eel counting at Budj Bim, yam harvesting cycles, and quarry trading systems (Clark, 1995).
Contemporary Revival
Today, Aboriginal educators reintroduce mathematics through cultural frameworks:
Budj Bim eel traps are taught as engineering and mathematical marvels (UNESCO, 2019).
Wurdi Youang is included in astronomy curricula, connecting geometry with solar observation.
Victorian schools incorporate Indigenous maths stories to strengthen both cultural identity and STEM education (Hamacher, 2012).
Conclusion
Mathematics in Victorian Indigenous communities was deeply embedded in environment, law, and ceremony. From eel traps to stone arrangements, kinship to calendars, Indigenous people practised sophisticated mathematical systems long before European colonisation.
When compared globally — from the Incan quipu to Māori spiral carvings — it is clear that mathematics is a universal human practice, expressed in diverse cultural forms. Recognising Indigenous mathematics highlights its sophistication and ensures these systems contribute to both cultural renewal and modern education.
Reference List
Barwick, D. (1998). Rebellion at Coranderrk. Canberra: Aboriginal History Inc.
Broome, R. (2005). Aboriginal Victorians: A History Since 1800. Sydney: Allen & Unwin.
Clark, I. D. (1995). My Country of the Corner: The History of the Djadja Wurrung 1837–1901. Melbourne: MUP.
Donaldson, M. (2015). The Mathematical World of the First Australians. Sydney: UNSW Press.
Flood, J. (1997). Archaeology of the Dreamtime. Sydney: Harper Collins.
Hamacher, D. W., & Norris, R. P. (2011). “Bridging the Gap through Australian Aboriginal Astronomy.” Australian Journal of Social Issues, 46(1).
Hamacher, D. (2012). Aboriginal Astronomy: Embracing Both Science and Culture. Canberra: Aboriginal Studies Press.
Neale, M. (2017). Songlines: The Power and Promise. Canberra: National Museum of Australia.
Reynolds, H. (1987). The Law of the Land. Ringwood: Penguin.
Rose, D. B. (1996). Nourishing Terrains: Australian Aboriginal Views of Landscape and Wilderness. Canberra: Australian Heritage Commission.
UNESCO. (2019). Budj Bim Cultural Landscape World Heritage Nomination. Paris: UNESCO.
Written, Researched and Directed by James Vegter 16/09/2025
Magic Lands Alliance
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Magic Lands Alliance acknowledge the Traditional Owners, Custodians, and First Nations communities across Australia and internationally. We honour their enduring connection to the sky, land, waters, language, and culture. We pay our respects to Elders past, present, and emerging, and to all First Peoples communities and language groups. This article draws only on publicly available information; many cultural practices remain the intellectual property of communities.