Encyclopedia of Mathematics Education

2020 Edition
| Editors: Stephen Lerman


  • Mike O. J. ThomasEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-3-030-15789-0_8


The word algorithm probably comes from a transliterated version of the name al-Khwarizmi (c. 825 CE), the Arabic mathematician who described how to solve equations in his publication al-jabr w’al-muqabala. An algorithm comprises a step-by-step set of instructions in logical order that enable a specific task to be accomplished. Due to its nature, it can be programmed into a computer, although some problems may not be computable or solvable by an algorithm. In his famous paper, Turing (1936) showed, among other things, that Hilbert’s Entscheidungsproblem can have no solution. He did this by proving “that there can be no general process for determining whether a given formula U of the functional calculus K is provable, i.e., that there can be no machine which, supplied with any one U of these formulae, will eventually say whether U is provable” (1936, p. 259).

An example of a simple well-known algorithm is that for sorting a sequence of real numbers into descending (or with a...


Algorithm Computing History of mathematics Instrumental understanding Representation 
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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of MathematicsThe University of AucklandAucklandNew Zealand

Section editors and affiliations

  • Bharath Sriraman
    • 1
  1. 1.Department of Mathematical SciencesThe University of MontanaMissoulaUSA