Culture, history and language · Scope

Can knowledge built into practices such as weaving, building or navigation count as mathematics?

Many communities use sophisticated patterns, measurements and calculations in crafts and navigation without writing them as theorems. Ethnomathematics, a field associated with Ubiratan D'Ambrosio, studies such practices. This question asks where the boundary of mathematics lies.

Claims

If a practice reliably uses number, pattern, symmetry or measurement, it contains mathematical knowledge, whether or not it is written as a theorem.
Recognising such knowledge widens our understanding of what mathematics is and who does it.

Counterclaims

Mathematics as an area of knowledge is defined by proof and generality; skilful practice without justification is valuable knowledge, but of a different kind.
Outsiders may 'find' mathematics in a practice that its practitioners would describe quite differently.

Real-life situations from mathematics

Inca khipu

The Inca recorded numbers using knotted cords called khipu, with a place-value system in base 10. Scholars are still working out whether some khipu also recorded words.

Polynesian wayfinding

In 1976 the voyaging canoe Hōkūleʻa sailed from Hawaiʻi to Tahiti navigated by Mau Piailug using stars, swells and birds, without instruments, showing the accuracy of traditional navigation knowledge.

Check dates and figures in a reliable source before you use them, and cite that source.

Use this in your TOK work

Essay. Fits titles about indigenous knowledge, the boundaries of areas of knowledge or practical versus theoretical knowledge.

Exhibition. A woven textile with a repeating pattern, or a photo of a traditional navigation chart, suits the indigenous societies theme.

Link it to the prescribed title or the exhibition prompt you are working on, in your own words. See using maths examples in your essay and choosing exhibition objects.

Themes and study heading

Knowledge and indigenous societies Knowledge and language Scope

What mathematics is about, and where its edges lie.