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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