Informal mathematics

Informal mathematics

Informal mathematics, also called naïve mathematics, has historically been the predominant form of mathematics at most times and in most cultures, and is the subject of modern ethno-cultural studies of mathematics. The philosopher Imre Lakatos in his Proofs and Refutations aimed to sharpen the formulation of informal mathematics, by reconstructing its role in nineteenth century mathematical debates and concept formation, opposing the predominant assumptions of mathematical formalism.[1] Informality may not discern between statements given by inductive reasoning (as in approximations which are deemed "correct" merely because they are useful), and statements derived by deductive reasoning.

Contents

Terminology

Informal mathematics means any informal mathematical practices, as used in everyday life, or by aboriginal or ancient peoples, without historical or geographical limitation. Modern mathematics, exceptionally from that point of view, emphasizes formal and strict proofs of all statements from given axioms. This can usefully be called therefore formal mathematics. Informal practices are usually understood intuitively and justified with examples—there are no axioms. This is of direct interest in anthropology and psychology: it casts light on the perceptions and agreements of other cultures. It is also of interest in developmental psychology as it reflects a naïve understanding of the relationships between numbers and things. Another term used for informal mathematics is folk mathematics, which is ambiguous; the mathematical folklore article is dedicated to the usage of that term among professional mathematicians.

The field of naïve physics is concerned with similar understandings of physics. People do use mathematics and physics in everyday life, without really understanding (or caring) how mathematical and physical ideas were historically derived and justified.

History

There has long been a standard account of the development of geometry in ancient Egypt, followed by Greek mathematics and the emergence of deductive logic. The modern sense of the term mathematics, as meaning only those systems justified with reference to axioms, is however an anachronism if read back into history. Several ancient societies built impressive mathematical systems and carried out complex calculations based on proofless heuristics and practical approaches. Mathematical facts were accepted on a pragmatic basis. Empirical methods, as in science, provided the justification for a given technique. Commerce, engineering, calendar creation and the prediction of eclipses and stellar progression were practiced by ancient cultures on at least three continents.

See also

References

  1. ^ Imre Lakatos, Proofs and Refutations (1976), especially the Introduction.

Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Mathematics, Form and Function — is a survey of the whole of mathematics, including its origins and deep structure, by the American mathematician Saunders Mac Lane. Contents 1 Mac Lane s relevance to the philosophy of mathematics 2 Mathematics and human activities …   Wikipedia

  • mathematics, foundations of — Scientific inquiry into the nature of mathematical theories and the scope of mathematical methods. It began with Euclid s Elements as an inquiry into the logical and philosophical basis of mathematics in essence, whether the axioms of any system… …   Universalium

  • List of mathematics articles (I) — NOTOC Ia IA automorphism ICER Icosagon Icosahedral 120 cell Icosahedral prism Icosahedral symmetry Icosahedron Icosian Calculus Icosian game Icosidodecadodecahedron Icosidodecahedron Icositetrachoric honeycomb Icositruncated dodecadodecahedron… …   Wikipedia

  • Cognitive science of mathematics — The cognitive science of mathematics is the study of mathematical ideas (concepts) using the techniques of cognitive science. It proposes to ground the foundations of mathematics in the empirical study of human cognition and metaphor.This… …   Wikipedia

  • Folk mathematics — can mean: * The mathematical folklore that circulates among mathematicians * The informal mathematics used in everyday life, as studied in ethno cultural studies of mathematics …   Wikipedia

  • Wikipedia:Manual of Style/Mathematics — This guideline is a part of the English Wikipedia s Manual of Style. Use common sense in applying it; it will have occasional exceptions. Please ensure that any edits to this page reflect consensus. Shortcuts: WP:MSM MO …   Wikipedia

  • Marang Center for Mathematics and Science Education — Marang Centre for Mathematics and Science Education Address 27 St. Andrews Road, Parktown Johannesburg, 2193 Private Bag 3, Wits 2050 South Africa Information Established 2005 Head of school Prof. Ruksana Osman …   Wikipedia

  • Philosophy of mathematics — The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of …   Wikipedia

  • Function (mathematics) — f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a …   Wikipedia

  • Language of mathematics — The language of mathematics is the system used by mathematicians to communicate mathematical ideas among themselves. This language consists of a substrate of some natural language (for example English) using technical terms and grammatical… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”