Graduate Program
Mathematics
Degree Name
Master of Arts (MA)
Semester of Degree Completion
2011
Thesis Director
Keith Wolcott
Thesis Committee Member
Patrick Coulton
Thesis Committee Member
Yevgeniy Gordon
Abstract
The purpose of my study was to answer the philosophical question of whether mathematics is invented or discovered. This question is an age-old and important one with many implications regarding the understanding of mathematics, logic, science, and truth. Answering this question correctly can inform us not only about the nature of what is known, but even what is possible to know. In the field of mathematics itself, the answer to this question could change the way that mathematics is taught, learned, and implemented in the future. The problem was addressed through research, comparison, and analysis of books and articles where the question of whether math is created or discovered was either dealt with explicitly or implicitly. The answer to this question was found to be that mathematics is invented. Proof of this result is shown through debunking the myth of the objective world, and showing instead, how perception and thought give us a world of objects through creative use of metaphors. Mathematics is dependent on metaphorical, and not truly objective, thinking. The conclusions suggest that reality is not ultimately made of mathematics, and as such, there is a growing dissonance between the highly mathematical human-made world and much more fluid natural world. The world, not being the sum ( or algorithm) of its parts, should be encountered in new ways (that are sometimes actually quite old), if one wants to gain fresh perspectives on the nature of reality and the meaning of truth. With these results in mind, subjective domains such as dreaming, creating art, and perceiving have much more truth to tell than could probably be imagined under the old taken for granted paradigm that science and math are the primary and most important tools that humans use in understanding the world and universe correctly.
Recommended Citation
Leach, Gregory A., "Of music, mathematics, and magic: Why math is all made up and why it works so well" (2011). Masters Theses. 493.
https://thekeep.eiu.edu/theses/493
