How We Understand Mathematics pp 1-5 | Cite as

# Introduction

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## Abstract

On July 20, 1969, the lunar module of Apollo 11 landed on the moon. The trajectory of this historic space flight has been calculated by hand by a group of the so-called human computers. It is just an example of the effectiveness of mathematics in modeling (and changing) the world around us. Mathematics continues to be productively applied in engineering, medicine, chemistry, biology, physics, social sciences, communication, and computer science, to name but a few. As Hohol (2011: 143) points out, this fact is often treated by philosophers as an argument for mathematical realism of the Platonian or Aristotelian variety. It is from this perspective that Quine-Putnam’s “indispensability argument,” Heller’s “hypothesis of the mathematical rationality of the world,” and Tegmark’s “mathematical universe hypothesis” have been discussed. Eugene Wigner, a physicist, often quoted in this context, finished his paper titled

*The Unreasonable Effectiveness of Mathematics in the Natural Sciences*in the following way:The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning. (1960: 14)

## Keywords

Mathematical Universe Hypothesis Space Flight History Indispensability Argument Unreasonable Effectiveness Lunar Module
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## Bibliography

- Alexander, J. (2011). “Blending in mathematics”.
*Semiotica*, Issue 187. Pages 1–48.CrossRefGoogle Scholar - Bernays, P. (1935). “Platonism in Mathematics”. Lecture delivered June 18, 1934, in the cycle of
*Conferences internationales des Sciences mathematiques*organized by the University of Geneva. Translated from French by C. D. Parsons. http://www.phil.cmu.edu/projects/bernays/Pdf/platonism.pdf, accessed 2017-11-07. - Danesi, M. (2016).
*Language and Mathematics: An Interdisciplinary Guide*. New York: Mouton de Gruyter.CrossRefGoogle Scholar - Evans, V. & M. Green. (2006).
*Cognitive Linguistics: An Introduction*. Edinburgh: Edinburgh University Press.Google Scholar - Fauconnier, M. & M. Turner. (2002)
*. The Way We Think: Conceptual Blending And The Mind’s Hidden Complexities*. New York: Basic Books.Google Scholar - Herstein, I. (1975).
*Topics in Algebra*. New York: John Wiley & Sons.zbMATHGoogle Scholar - Hohol, M. (2011). “Matematyczność ucieleśniona”. In B. Brożek, J. Mączka, W.P. Grygiel, M. Hohol (eds.),
*Oblicza racjonalności: Wokół myśli Michała Hellera.*Pages 143–166. Kraków: Copernicus Center Press.Google Scholar - Lakoff, G. & R. Núñez. (2000).
*Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being*. New York: Basic Books.zbMATHGoogle Scholar - Núñez, R. (2006). “Do Real Numbers Really Move?”. In R. Hersh (ed.),
*18 Unconventional Essays on the Nature of Mathematics*. Pages 160–181. New York: Springer.CrossRefGoogle Scholar - Stockwell, P. (2002). Cognitive Poetics: An Introduction. London: Routledge.Google Scholar
- Turner, M. (2005). “Mathematics and Narrative”. Paper presented at the International Conference on Mathematics and Narrative, Mykonos, Greece, 12-15 July 2005. http://thalesandfriends.org/wp-content/uploads/2012/03/turner_paper.pdf, accessed Nov. 11, 2016.
- Turner, M. (2012). “Mental Packing and Unpacking in Mathematics”. In Mariana Bockarova, Marcel Danesi, and Rafael Núñez (eds.),
*Semiotic and Cognitive Science Articles on the Nature of Mathematics*. Pages 248–267. Munich: Lincom Europa.Google Scholar - Wigner, E. (1960). “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”.
*Communications in Pure and Applied Mathematics*, Issue 13(I). Pages 1–14.CrossRefGoogle Scholar

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