Abstract / Synopsis
How you think about a phenomenon certainly influences how you create a program to model it. The main point of this essay is that the influence goes both ways: creating programs influences how you think. The programs we are talking about are not just the ones we write for a computer. Programs can be implemented on a computer or with physical devices or in your mind. The implementation can bring your ideas to life. Often, though, the implementation and the ideas develop in tandem, each acting as a mirror on the other. We describe an example of how programming and mathematics come together to inform and shape our interpretation of a classical result in mathematics: Euclid's algorithm that finds the greatest common divisor of two integers.
Cuoco, A. and Goldenberg, E. "Computational Thinking in Mathematics and Computer Science: What Programming Does to Your Head," Journal of Humanistic Mathematics, Volume 11 Issue 1 (January 2021), pages 346-363. DOI: 10.5642/jhummath.202101.17 . Available at: https://scholarship.claremont.edu/jhm/vol11/iss1/17