A Cultural overview on the concept of infinity

Keywords: infinity, mathematics, culture, education, school, research, mystery.


Abstract: The human being meets the idea of infinity very early, still a child, when he  realises that he can go on counting using  natural numbers until it is impossible to continue to count. The idea of infinity attracts and rejects, sometimes becomes an  object of desire and sometimes of study and systematic research. Infinity is the testimony that intellect, even starting from experience, can overcome limits and boundaries. Our own limited experience on the Earth suggests the existence of something beyond it. Scientists, artists, philosophers, musicians, writers, mathematicians have often assumed towards this concept positions and opinions sensitively different. Infinity would be, by its etymology and nature, what escapes all possible classification and measurement, while mathematics tends to classify and measure every object it examines, and  has been able to measure it. Infinity follows us from primary school until university, but often remains a misunderstood concept in the mathematical sense.

Author Biography

Paolo Di Sia, University of Padova, Via 8 Febbraio 1848, 2, 35122 Padova PD, Italy

Paolo Di Sia is currently adjunct professor by the University of Padova (Italy) and by the Free University of Bozen-Bolzano (Italy). Scientific interests: transdisciplinary physics, nanophysics, theories of everything, metaphysics, foundations of physics, history and philosophy of science. He is author of 274 works to date, is reviewer of some academic books, editor of 3 international academic books, reviewer of 14 international journals. He obtained many international awards, is member of 10 scientific societies and of 39 International Advisory/Editorial Boards, recently selected for the awards of Doctor of Science (D.Sc) and Doctor of Mathematics (D.Math) as legitimate honors by the International American Council for Research and Development, California Public University, USA.


Adorno, F. (2005). Introduzione a Platone [Introduction to Plato].

Roma-Bari: Laterza.

Alighieri, D. (2013). The divine comedy. Oxford: Oxford University Press.

Ault, D. (1987). Narrative Unbound: Re-Visioning William Blake’s The Four Zoas. Barrytown, NY: Station Hill Press.

Bell, E. T. (1986). Men of Mathematics. New York: Simon and Schuster.

Bellatalla, L., Genovesi, G. (2018). Il De docta ignorantia di Niccolò Cusano. «Sub specie educationis». Roma: Anicia.

Bentley Jr., G. E. (2001). The Stranger From Paradise: A Biography of William Blake. Yale: Yale University Press.

Berti, E. (1997). Guida ad Aristotele [Guide to Aristotle].

Roma-Bari: Laterza.

Bolzano, B. (2003). I paradossi dell’infinito [The paradoxes of the infinity], Torino: Bollati Boringhieri.

Borges, J. L. (1976). Otras inquisiciones [Other inquisitions].

Madrid: Alianza.

Cantor, G. (1955, 1915). Contributions to the Founding of the Theory of Transfinite Numbers. New York: Dover.

Cellucci, C. (2007). La filosofia della matematica del Novecento [The philosophy of mathematics of the twentieth century]. Roma: Biblioteca Essenziale Laterza.

Dauben, J. W. (1979). Georg Cantor: his mathematics and philosophy of the infinite. Boston: Harvard University Press.

del Giudice, G. (Ed.). (2009). Il dio dei Geometri - quattro dialoghi [The god of Geometry - four dialogues]. Roma: Di Renzo Editore.

Di Sia, P. (2005). Un intervento sull’evoluzione dei concetti di spazio e tempo [An intervention on the evolution of the concepts of space and time],

Periodico di Matematiche (Mathesis), VIII, 5(3), 55-68.

Di Sia, P. (2015). Approaching youngs to unified theories: the charm of string theories. Procedia - Social and Behavioral Sciences Journal (Elsevier), 174C, 10-16.

Di Sia, P. (2016). A Historical-Teaching Introduction to Algebra. International Letters of Social and Humanistic Sciences (ILSHS), 66, 154-161. DOI: 10.18052/www.scipress.com/ILSHS.66.154.

Di Sia, P. (2018). Fisica moderna, coscienza, multiverso, azione divina. Problemi, dubbi, convergenze [Modern physics, consciousness, multiverse, divine action. Problems, doubts, convergences]. Roma: Stamen.

Di Sia, P. (2019). On new technologies for studying and learning mathematics. E-methodology (review process).

Di Siaa, P. (2013). Fondamenti di Matematica e Didattica I [Foundations of Mathematics and Didactics I]. Roma: Aracne.

Di Siaa, P. (2014). Describing the concept of “infinity” among art, literature, philosophy and science: a pedagogical-didactic overview. Journal of Education, Culture and Society, 1, 9-19, DOI: 10.15503/jecs20141-9-19.

Di Siaa, P. (2017). A Hystorical-Didactic Introduction To The Key Concepts Of Mathematical Analysis. TOJET (The Online Journal of Educational Technology), 60-68.

Di Siab, P. (2013). Elementi di Didattica della Matematica I - Laboratorio [Elements of Didactics of Mathematics I – Laboratory]. Roma: Aracne.

Di Siab, P. (2014). Fondamenti di Matematica e Didattica II [Foundations of Mathematics and Didactics II]. Roma: Aracne.

Di Siab, P. (2017). Learning mathematics through games in primary school: an applicative path. Edutainment 1(1), 127-133. https://jecs.pl/index.php/EDUT/article/view/10.15503.edut.2016.1.127.133.

Fabro, C. (1997). Introduzione a San Tommaso. La metafisica tomista e il pensiero moderno [Introduction to St. Thomas. Thomist metaphysics and modern thought]. Milano: Ares.

Fano, V. (2012). I paradossi di Zenone [The paradoxes of Zeno].

Roma: Carocci.

Galluzzi, F. (2002). Picasso. Firenze: Giunti Editore.

Giannantoni, G. (Ed.). (1973). Opere [Works]. Bari: Laterza (4 vols.).

Gödel, K. (1986-2006). Collected Works. New York: Oxford University Press (5 volumes, texts in German with English translation in front).

Hamilton, J. (Ed.). (2008). Turner e l’Italia [Turner and Italy].

Ferrara: Ferrara Arte.

Heilbron, J. L. (2013). Galileo. Scienziato e umanista [Galileo. Scientist and humanist]. Torino: Einaudi.

Hilbert, D. (1970). Fondamenti della geometria [Foundations of geometry]. Torino: Feltrinelli.

Kahn, C. H. (1994). Anaximander and the Origins of Greek Cosmology (3rd ed.). Indianapolis: Hackett.

Kojève, A. (2005). Kandinsky. Macerata: Quodlibet.

Laerzio, D. (2005). Vite e dottrine dei più celebri filosofi [Lives and doctrines of the most famous philosophers]. Milano: Bompiani.

Marchi, C. (2006). Dante. Milano: RCS.

Migliorato, R., Gentile, G. (2005). Euclid and the scientific thought in the third century BC. Ratio Mathematica, 15, 37-64.

Moore, G. H. (2012). Zermelo’s Axiom of Choice: Its Origins, Development, and Influence. Berlin: Springer Science & Business Media.

Nicosia, F. (2003): Munch. Firenze: Giunti Editore.

Ockham, W. (Gál G. et alii (Eds)) (1967-1988). Opera philosophica et theologica. New York: The Saint Bonaventure University Press.

Parente, M. I. (2002). Introduzione a Plotino [Introduction to Plotinus].

Roma-Bari: Laterza.

Pascal, B. (Vozza, C. (Ed.)) (1995). Pensieri [Thoughts]. Rimini: Guaraldi.

Pelloux, L. (1994). L’assoluto nella dottrina di Plotino [The absolute in Plotino’s doctrine]. Milano: Vita e Pensiero.

Plato. (1982-1984) (Giannantoni G. (Ed.)). Opere complete [Complete Works]. Laterza, Roma-Bari (9 vols.).

Prini, P. (1993). Plotino e la fondazione dell'umanesimo interiore [Plotinus and the foundation of inner humanism]. Milano: Vita e Pensiero.

Ratzinger, J. (1978). Popolo e casa di Dio in Sant’Agostino [People and the house of God in St. Augustine]. Milano: Jaca Book.

Schimdt, R. (1966). The Domain of Logic According to Saint Thomas Aquinas. L’Aia: Martinus Nijhoff.

Vaughan, W. (2004). Friedrich. Oxford: Phaidon Press.

Weil, A. (Argentieri, N. (Ed.)) (2014). La fredda bellezza. Dalla metafisica alla matematica (Cold beauty. From metaphysics to mathematics). Roma: Castelvecchi.

Weil, A., & Weil, S. (Chenavier, R., Devaux, A. A., Sala, M. C. (Eds)) (2018). L’arte della matematica [The art of mathematics]. Milano: Adelphi.

Wolf, N. (2003). Caspar David Friedrich. Colonia: Taschen.

Yarnelle, J. E. (1966). An Introduction to Transfinite Mathematics. Lexington, Massachusetts: DC Heath.

Available online12 (January 30, 2019): https://www.digizeitschriften.de/dms/toc/?PID=PPN37721857X_0008.

Available online13 (January 30, 2019): https://eudml.org/doc/158776.

Available online14 (January 31, 2019): http://bauhaus77.blogspot.com/2012/02/kurt-godel-my-philosophical-viewpoint.html.

How to Cite
Di Sia, P. (2019). A Cultural overview on the concept of infinity. Journal of Education Culture and Society, 10(1), 17-38. https://doi.org/10.15503/jecs20191.17.38