Understanding the relations between transcendence and mathematics: a resource essay for educators and students in Catholic universities to appreciate its deep meanings

References

• Aquinas, T. 1981. Summa Theologiae. Translated by the Fathers of the English Dominican Province. Notre Dame, IN: Christian Classics.
   Google Scholar
• Augustine of Hippo. 2010. On the Free Choice of the Will, On Grace and Free Choice, and Other Writings. Translated by P. King. Cambridge: Cambridge University Press.
   Google Scholar
• Belhoste, B. 1991. Augustin-Louis Cauchy: A Biography. Translated by F. Ragland. New York: Springer-Verlag.
   Google Scholar
• Bernard, de Chartres, Guillaume de Conches, Thierry de Chartres, and Guillaume de Saint-Thierry. 2004. Théologie et Cosmologie au XII^e Siècle; Traduit par Michel Lemoine et Clotilde Picard-Parra. Paris: Le Belles Lettres.
   Google Scholar
• Bernard of Clairvaux. 2020. On Consideration. Translated by G. Lewis. New York: Anthem.
   Google Scholar
• Bradley, J. 2011. “Theology and Mathematics – Key Themes and Central Historical Figures.” Theology and Science 9 (1): 5–26.
   Google Scholar
• Cantor, G. 1994. “On the Theory of the Transfinite. Correspondence of Georg Cantor and J. B. Cardinal Franzelin (1885–1886).” Fidelio 3 (3): 97–110.
   Google Scholar
• Caspar, M. 1993. Kepler. Translated by C.D. Hellman. New York: Dover Publications.
   Google Scholar
• Celeyrette, J. 2011. “Mathématiques et Théologie: L’Infini chez Nicholas de Cues.” Revue de Métaphysique et de Morale 2011/2 (70): 151–165.
   Google Scholar
• Cusa, N. 2007. On Learned Ignorance. Translated by G. Heron. Oregon: Wipf & Stock Publishers.
   Google Scholar
• Dauben, J. W. 1977. “Georg Cantor and Pope Leon XIII: Mathematics, Theology, and the Infinite.” Journal of the History of Ideas 38 (1): 85–108.
   Web of Science ®Google Scholar
• Dauben, J. W. 1983. “Georg Cantor and the Origins of Transfinite Set Theory.” Scientific American 248 (6): 122–131.
   Web of Science ®Google Scholar
• Davis, P. J. 2004. “A Brief Look at Mathematics and Theology.” Humanistic Mathematics Network Journal (Issue 27): Article 14. http://scholarship.claremont.edu/hmnj/vol1/iss27/14.
   Google Scholar
• Descartes, R. 1978. Discours de la Méthode. Paris: GF Flammarion.
   Google Scholar
• Descartes, R. 2010. “Letter of 15 April 1630 to Father Mersenne.” In Descartes, Oeuvres Philosophiques, Tome I – 1618-1637, edited by F. Alquie, 259–260. Paris: Garnier.
   Google Scholar
• Descartes, R. 2021. Méditations Métaphysiques. Paris: GF Flammarion.
   Google Scholar
• Eddington, A. S. 1928. The Nature of the Physical World. Cambridge: Cambridge University Press.
   Google Scholar
• Euler, L. 1960. Defense of the Divine Revelation Against the Objections of the Freethinkers, Leonhard Euleri Opera Omnia, Ser. 3, Vol. 12. Zurich: Orell-Fussli.
   Google Scholar
• Gutberlet, C. 1886. “Das Problem des Unendlichen.” Zeitschrift für Philosophie und philosophische Kritik 88: 179–223.
   Google Scholar
• Hahn, R. 2005. Pierre Simon Laplace, 1749–1827: A Determined Scientist. Cambridge, MA: Harvard University Press.
   Google Scholar
• Heisenberg, W. 1971. Physics and Beyond: Encounters and Conversations. New York: Harper and Row.
   Google Scholar
• Hume, D. 1825. Essays and Treatises on Several Subjects: An Inquiry Concerning Human Understanding. A Dissertation on the Passions. An Inquiry Concerning the Principles of Morals. The Natural History of Religion. Edinburgh: Bell & Bradfute.
   Google Scholar
• Iamblichus. 1988. The Theology of Arithmetic. Translated by R. Waterfield. Grand Rapids, MI: Phanes Press.
   Google Scholar
• John of Salisbury. 2009. The Metalogicon: A Twelfth-Century Defense of the Verbal and Logical Arts of the Trivium. Translated by D.D. McGarry. Philadelphia, PA: Paul Dry Books.
   Google Scholar
• Kaku, M. 2021. The God Equation. London: Allen Lane.
   Google Scholar
• Kepler, J. 1963. Johannes Kepler Gesammelte Werke (1937-). 8 vols. Translated by F. Hammer. München: C.H. Beck.
   Google Scholar
• Leibniz, G. W. 1996. Theodicy. Essays on the Goodness of God, the Freedom of Man and the Origin of Evil. Translated by E.M. Huggard. Peru, IL: Open Court.
   Google Scholar
• Maupertuis, P. L. M. 1746. “Les Loix du mouvement et du repos déduites d’un principe métaphysique.” Histoire de l’Académie Royale des Sciences et des Belles Lettres de Berlin, 267–294.
   Google Scholar
• Miller, L. G. 1957. “Descartes, Mathematics, and God.” The Philosophical Review 66 (4): 451–465.
   Web of Science ®Google Scholar
• Miller, C. L. 2015. “God as li Non-Aliud: Nicholas of Cusa's Unique Designation for God.” Journal of Medieval Religious Cultures 41 (1): 24–40.
   Google Scholar
• Murawski, R. 2016. “Between Theology and Mathematics. Nicholas of Cusa’s Philosophy of Mathematics.” Studies in Logic, Grammar and Rhetoric 44 (57): 97–110.
   Google Scholar
• Pagels, H. 1982. The Cosmic Code: Quantum Physics as The Language of Nature. New York: Dover Publications.
   Google Scholar
• Panza, M. 1995. “De la Nature Epargnante aux Forces Générouses: Le Principle de Moindre Action Entre Mathématiques et Métaphysique. Maupertuis e Euler, 1740 -1751.” Revue d’Histoire des Sciences 48 (4): 435–520.
   Google Scholar
• Plato. 1929. Timaeus. Translated by R.G. Bury. Cambridge, MA: Loeb Classic Library.
   Google Scholar
• Polkinghorne, J. 2011. “The Incompleteness of Science: Reflections for Christian Teachers and for Others Interested in the Science-Religion Relationship.” International Studies in Catholic Education 3 (2): 136–144.
   Google Scholar
• Sierksma, G. 1992. “Johann Bernoulli (1667–1748): His Ten Turbulent Years in Groningen.” The Mathematical Intelligencer 14 (4): 22–31.
   Web of Science ®Google Scholar
• Swigon, D. 2009. “The Mathematics of DNA Structure, Mechanics, and Dynamics.” In Mathematics of DNA Structure, Function and Interactions, edited by C. J. Benham, S. Harvey, W. K. Sumners, and D. Swigon, 293–320. New York: Springer-Verlag.
   Google Scholar
• Tegmark, M. 2008. “The Mathematical Universe.” Foundations of Physics 38: 101–150.
   Web of Science ®Google Scholar
• Turnbull, H. W. 1951. Bi-Centenary of the Death of Colin Maclaurin (1695–1746), Mathematician and Philosopher, Professor of Mathematics in Marischal College, Aberdeen (1717–1725). Aberdeen: The University Press.
   Google Scholar
• Wigner, E. 1960. “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” Communications in Pure and Applied Mathematics 13 (1): 1–14.
   Web of Science ®Google Scholar