Fermat’s Dilemma: Why Did He Keep Mum on Infinitesimals? And the European Theological Context

Jacques Bair, Mikhail G. Katz, David Sherry

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


The first half of the 17th century was a time of intellectual ferment when wars of natural philosophy were echoes of religious wars, as we illustrate by a case study of an apparently innocuous mathematical technique called adequality pioneered by the honorable judge Pierre de Fermat, its relation to indivisibles, as well as to other hocus-pocus. André Weil noted that simple applications of adequality involving polynomials can be treated purely algebraically but more general problems like the cycloid curve cannot be so treated and involve additional tools–leading the mathematician Fermat potentially into troubled waters. Breger attacks Tannery for tampering with Fermat’s manuscript but it is Breger who tampers with Fermat’s procedure by moving all terms to the left-hand side so as to accord better with Breger’s own interpretation emphasizing the double root idea. We provide modern proxies for Fermat’s procedures in terms of relations of infinite proximity as well as the standard part function.

Original languageEnglish (US)
Pages (from-to)559-595
Number of pages37
JournalFoundations of Science
Issue number3
StatePublished - Sep 1 2018


  • Adequality
  • Atomism
  • Council of Trent 13.2
  • Cycloid
  • Edict of Nantes
  • Hylomorphism
  • Indivisibles
  • Infinitesimal
  • Jesuat
  • Jesuit

ASJC Scopus subject areas

  • General
  • History and Philosophy of Science


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