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The trends discernible within the history of mathematics display a recurring one-sidedness. With an alternative non-reductionist ontology in mind this contribution commences by challenging the assumed objectivity and neutrality of mathematics. It is questioned by the history of mathematics, for in the latter Fraenkel et al. (Foundations of Set Theory, 2nd rev. ed., Amsterdam: North-Holland, 1973) distinguish three foundational crises: in ancient Greece with the discovery of incommensurability , after the invention of the calculus by Leibniz and Newton (problems entailed in the concept of a limit), and when it turned out that the idea of infinite totalities, employed to resolve the second foundational crisis, suffered from an inconsistent set concept. An alternative approach is to contemplate the persistent theme of discreteness and continuity further while distinguishing between the successive infinite and the at once infinite. Weierstrass, Dedekind, and Cantor define real numbers in terms of the idea of infinite totalities. Frege reverted to a geometrical source of knowledge while rejecting his own initial logicist position. Some theologians hold the view that infinity is a property of God and that theology therefore should mediate its introduction into mathematics. Avoiding the one-sidedness of arithmeticism (over-emphasizing number) and geometricism (over-emphasizing spatial continuity) will require that both the uniqueness of and mutual coherence between number and space is acknowledged. Two figures capture some of the essential features of such an alternative approach. Mediated by a Christian philosophy and a non-reductionist ontology, Christianity may therefore contribute to the inner development of mathematics.

DOI: 10.1007/978-3-319-70881-2_5

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