FERMAT’S DILEMMA: WHY DID HE KEEP MUM ON INFINITESIMALS? AND THE EUROPEAN THEOLOGICAL CONTEXT

JACQUES BAIR, MIKHAIL G. KATZ, AND DAVID SHERRY

摘要：17世纪上半叶是一个知识发酵的时间，自然哲学战争伴随着宗教战胜兴起。我们通过研究一个叫做adequality的纯数学技术、以及它与不可分性和其他技术的关系来说明这一点。这个adequality技术是由可敬的法官皮埃尔·德·费马开创的。Andr 'e Weil指出，adequality在多项式的简单应用，可以单纯地用代数方法来处理，但像摆线曲线这样更一般的问题不能用代数方法来处理，还需要额外的工具——这可能会让数学家费马陷入麻烦。布雷格抨击Tannery篡改了费马的手稿，但正是布雷格篡改了费马的技术，把所有的项都移到左边，以便更好地符合布雷格自己强调双根思想的解释。我们用无限接近关系和standard part函数为费马的技术提供了现代表述。

关键词：充足性；原子论；摆线；亚纯性；不可分；无穷小；南特法令；特伦特13.2委员会

Abstract. 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. Andr`e 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.

Keywords: adequality; atomism; cycloid; hylomorphism; indivisibles; infinitesimal; jesuat; jesuit; Edict of Nantes; Council of Trent 13.2

http://dx.doi.org/10.1007/s10699-017-9542-y​dx.doi.orghttps://arxiv.org/abs/1801.00427​arxiv.orghttps://mathscinet.ams.org/mathscinet-getitem?mr=3836239​mathscinet.ams.org