Toward a History of Mathematics Focused on Procedures

Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze, David M Sherry

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

Abraham Robinson’s framework for modern infinitesimals was developed half a century ago. It enables a re-evaluation of the procedures of the pioneers of mathematical analysis. Their procedures have been often viewed through the lens of the success of the Weierstrassian foundations. We propose a view without passing through the lens, by means of proxies for such procedures in the modern theory of infinitesimals. The real accomplishments of calculus and analysis had been based primarily on the elaboration of novel techniques for solving problems rather than a quest for ultimate foundations. It may be hopeless to interpret historical foundations in terms of a punctiform continuum, but arguably it is possible to interpret historical techniques and procedures in terms of modern ones. Our proposed formalisations do not mean that Fermat, Gregory, Leibniz, Euler, and Cauchy were pre-Robinsonians, but rather indicate that Robinson’s framework is more helpful in understanding their procedures than a Weierstrassian framework.

Original languageEnglish (US)
Pages (from-to)1-21
Number of pages21
JournalFoundations of Science
DOIs
StateAccepted/In press - Sep 21 2016

ASJC Scopus subject areas

  • General
  • History and Philosophy of Science

Fingerprint Dive into the research topics of 'Toward a History of Mathematics Focused on Procedures'. Together they form a unique fingerprint.

  • Cite this

    Błaszczyk, P., Kanovei, V., Katz, K. U., Katz, M. G., Kutateladze, S. S., & Sherry, D. M. (Accepted/In press). Toward a History of Mathematics Focused on Procedures. Foundations of Science, 1-21. https://doi.org/10.1007/s10699-016-9498-3