"Examples of the Catholic church commenting on, or intervening in, the development of mathematics:" Counter-reformation issues in the 17th century around transubstantiation/consubstantiation interpretation of the eucharist directly influenced attitudes toward the techniques of indivisibles that were seen as closely related to atomism and therefore opposed on doctrinal grounds by many catholic theologians based on canon 2 of the 13th Session of the Council of Trent in the preceding century.
The said canon was a particularly doctrinaire endorsement of the pagan Aristotelian doctrine of hylomorphism. The doctrine postulates a pseudoscientific substratum ("hylo") underpinning all forms (that's the "morph" part), or a kind of primordial undifferentiated Play-Do. Such a speculative scheme is somewhat analogous to ether, similarly rejected by scientists in the 19th century. Meanwhile, protestants envisioned less literal interpretations (such as consubstantiation) that tolerated elements of atomism.
The result was that in catholic Italy, developments in indivisibles and the techniques leading to the emerging infinitesimal calculus came to a virtual stop whereas mostly protestant lands tolerated such mathematical activity leading to the development of the infinitesimal analysis:
en 1700, c'est le vide intégral en ce qui concerne la pratique des mathématiques nouvelles en Italie (page 183 in Robinet).
The reference is Robinet, A. (1991) La conqu^ete de la chaire de mathématiques de Padoue par les leibniziens. Revue d'Histoire des Sciences, 44(2), 181--201.
le grand nombre des mathématiciens de [l'Ordre] resta jusqu'`a la fin du XVIII$^e$ si`ecle profondément attaché aux méthodes euclidiennes (page 77 in Bosmans).
The reference is Bosmans, H. (1927) André Tacquet (S. J.) et son traité d''Arithmétique théorique et pratique.' Isis, 9(1), 66--82.
These and related issues are discussed in detail in this 2018 publication in Foundations of Science which is also available on the arxiv.
