Mathematics in Nature

  • Ole Ravn
  • Ole Skovsmose
Part of the History of Mathematics Education book series (HME)


This chapter gives the Renaissance and rationalist philosophers of the 16th and 17th century have the word. The Renaissance is generally characterised by the belief that human reason can provide insight in the organisation of the world. The world was still considered God’s creation, but it became increasingly common to view it as machine, which functioning the deity has not interfered with since its creation.

The chapter starts out with an account of the so-called scientific revolution and the break with Aristotelian physics that it represents. The move from a geocentric to a heliocentric worldview becomes analysed in detail. The use of mathematics for describing nature is a central element in this move, and the chapter examines the tying together of explanations of nature and mathematics that took place during this tumultuous time. Infinitesimals challenged mathematical ontology. If mathematics is the “language of nature,” infinitesimals must somehow relate to entities in reality. But as such, they are rather unmanageable, for how can a world that has actual extension be built by units so small that they have no extent? How many infinitesimals have to be added up in order to turn into a natural object?


Geocentric worldview Heliocentric worldview Infinitesimals Laws of nature Newton’s Principia Renaissance Scientific revolution Unnatural mathematics 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ole Ravn
    • 1
  • Ole Skovsmose
    • 1
    • 2
  1. 1.Department of Learning and PhilosophyAalborg UniversityAalborgDenmark
  2. 2.Department of Mathematics EducationState University of São Paulo, (Universidade Estadual Paulista, Unesp)São PauloBrazil

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