Non-European Mathematics

From George Gheverghese Joseph’s excellent book ‘The Crest of the Peacock: Non-European Roots of Mathematics’:

The concept of mathematics found outside the Graeco-European praxis was very different. The aim was not to build an imposing edifice on a few self-evident axioms but to validate a result by any suitable method. Some of the most impressive work in Indian and Chinese mathematics examined in later chapters, such as the summations of mathematical series, or the use of Pascal’s triangle in solving higher-order numerical equations, or the derivations of infinite series, or “proofs” of the so-called Pythagorean theorem, involve computations and visual demonstrations that were not formulated with reference to any formal deductive system. The view that mathematics is a system of axiomatic/deductive truths inherited from the Greeks, and enthroned by Descartes, has traditionally been accompanied by the following cluster of values that reflect the social context in which it originated:

  1. An idealist rejection of any practical, material(ist) basis for mathematics: hence the tendency to view mathematics as value-free and detached from social and political concerns
  2. An elitist perspective that sees mathematical work as the exclusive preserve of a high-minded and almost priestly caste, removed from mundane preoccupations and operating in a superior intellectual sphere

Mathematical traditions outside Europe did not generally conform to this cluster of values and have therefore been dismissed on the grounds that they were dictated by utilitarian concerns with little notion of rigor, especially relating to proof.