Examples of possible theological influences upon the development of mathematics are indicated. The best known connection can be found in the realm of infinite sets treated by us as known or graspable, which constitutes a divine-like approach. Also the move to treat infinite processes as if they were one finished object that can be identified with its limits is routine in mathematicians, but refers to seemingly super-human power. For centuries this was seen as wrong and even today some philosophers, for example Brian Rotman, talk critically about “theological mathematics”. Theological metaphors, like “God’s view”, are used even by contemporary mathematicians. While rarely appearing in official texts they are rather easily invoked in “the kitchen of mathematics”. There exist theories developing without the assumption of actual infinity the tools of classical mathematics needed for applications (For instance, Mycielski’s approach). Conclusion: mathematics could have developed in another way. Finally, several specific examples of historical situations are mentioned where, according to some authors, direct theological input into mathematics appeared: the possibility of the ritual genesis of arithmetic and geometry, the importance of the Indian religious background for the emergence of zero, the genesis of the theories of Cantor and Brouwer, the role of Name-worshipping for the research of the Moscow school of topology. Neither these examples nor the previous illustrations of theological metaphors provide a certain proof that religion or theology was directly influencing the development of mathematical ideas. They do suggest, however, common points and connections that merit further exploration.
If the inline PDF is not rendering correctly, you can download the PDF file here.
Aigner, Martin, Ziegler, Günter. (2009). Proofs from THE BOOK, Berlin, New York: Springer-Verlag.
Barrow, John D. (2000). The Book of Nothing. Vacuums, Voids, and the Latest Ideas about the Origin of the Universe, London: Vintage Books.
Benacerraf, Paul, Putnam, Hilary. (1983). Philosophy of Mathematics: Selected readings. Second edition. Cambridge University Press.
Borel, Emile. (1972). Œvres de Émile Borel. Paris: Centre National de la Recherche Scientifique.
Breger, Herbert. (2005). God and Mathematics in Leibniz’s Thought. In Koetsier & Bergmans (2005), 485–498.
Brouwer, L.E.J. (1949). Consciousness, Philosophy and Mathematics. Proceedings of the 10th International Congress of Philosophy, Amsterdam 1948 III, 1235–1249; also in Brouwer 1975, 480–494.
Brouwer, L.E.J. (1975). Collected works I. Philosophy and Foundations of Mathematics (ed. A. Heyting). Amsterdam: North-Holland.
Byers, William. (2007). How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics. Princeton University Press.
Dalen, Dirk van. (1999). Mystic, geometer, and intuitionist. The life of L.E.J. Brouwer. 1: The dawning revolution. Oxford: Clarendon Press.
Dauben, John. (1977). Georg Cantor and Pope Leo XIII: Mathematics, Theology, and the Infinite, Journal of the History of Ideas 38, No. 1, 85–108.
Ferreirós, Jose. ΄Ο Θεὸς ΄Αριϑμετίζει: The Rise of Pure Mathematics as Arithmetic with Gauss. In Goldstein et al (2007).
Goldstein, C., N. Schappacher, J. Schwermer (eds.) 2007. The Shaping of Arithmetic after S.F.Gauss’s Disquisitiones Arithmeticae. Berlin, Heidelberg, New York: Springer 2007.
Graham, Loren. (2011). The Power of Names, Theology and Science vol. 9, No. 1, 157–164.
Graham, Loren & Kantor, Jean-Michel. (2009). Naming Infinity. A True Story of Religious Mysticism and Mathematical Creativity. Harvard University Press.
Hersh, Reuben. (1991). Mathematics has a front and a back. Synthese, 88, 127–133.
Hibert, David. (1926). Über das Unendliche, Mathematische Annalen 95, 161–190. Translated in On the infinite, Jean van Heijenoort (ed.) From Frege To Gödel: A Source Book in Mathematical Logic, 1879–1931. Harvard University Press 1967.
Jenson, Robert W. (1997). Systematic Theology, Volume 1: The Triune God. Oxford: Oxford University Press.
Kahneman, Daniel. (2011). Thinking, Fast and Slow. Farrar, Straus and Giroux.
Kantor, Jean-Michel. (2011). Mathematics and Mysticism, Name Worshipping, Then and Now”, Theology and Science vol. 9, No. 1, 149–156.
Koetsier, Theun & Luc Bergmans (eds.). (2005). Mathematics and the Divine: A Historical Study, Elsevier.
Krajewski, Stanisław. (2011). Czy matematyka jest nauką humanistyczną? [Does mathematics Belong to the Humanities?, in Polish]. Kraków: Copernicus Center Press.
Mycielski, Jan. (1981). Analysis Without Actual Infinity. Journal of Symbolic Logic 46, no. 3, 625–633. doi: 10.2307/2273760.