A Cognitive and Material Pathway to Recursive Division
This project explores the cognitive origins of the Euclidean algorithm, tracing its development from embodied group-splitting to recursive abstraction. It is intended for students, educators, and researchers in mathematics education, history of math, and cognitive science.
This repository contains the full LaTeX source and compiled PDF of an exploratory paper by Stephen Chong titled:
“Rediscovering the Euclidean Algorithm: From Embodied Group-Splitting to Abstract Recursion”
This paper proposes a speculative but historically grounded narrative for how the Euclidean algorithm may have emerged—not as an abstract mathematical invention, but as a tactile and visual response to the challenge of evenly splitting physical quantities. By framing division as a recursive process rooted in perception, regularity, and reuse of leftovers, the paper explores how ancient builders, stewards, or surveyors may have discovered recursive subdivision long before formalization.
It blends cognitive plausibility with historical context and mathematical structure.
rediscovering_the_euclidean_algorithm.tex— Full LaTeX source coderediscovering_the_euclidean_algorithm.pdf— Compiled PDF of the articleREADME.md— This file
While no definitive records of the discovery process survive, this paper consolidates a set of plausible strategies and intuitions—rooted in manual group-splitting, perceptual imbalance, and recursive reuse—that may have led to the Euclidean algorithm. It is intended not as a strict historical claim, but as a constructive, interdisciplinary narrative that blends:
- Early material practices (e.g., dividing grain, cutting rope)
- Perceptual and cognitive behaviors (e.g., responding to leftovers)
- Mathematical abstraction (e.g., efficient recursive procedures)
- Historians of mathematics interested in cognitive or material origins
- Educators exploring intuitive ways to introduce GCD and division
- Mathematically curious readers who enjoy visual and tactile reasoning
- Anyone who, like me, is curious about how ancient algorithms may have emerged from humble beginnings
Chong, S. (2025). Rediscovering the Euclidean Algorithm: From Embodied Group-Splitting to Abstract Recursion. GitHub Repository. https://github.com/chevestong/rediscovering-euclidean-algorithm
(This is an informal citation; arXiv or DOI links may be added in the future.)
This is an evolving exploration. If you are a teacher, researcher, or student with comments, questions, or suggestions for revision—or if you'd like to collaborate on improving or extending the model—please feel free to open an issue or start a discussion.
This work is shared under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License.
Please contact the author before citing or referencing this work in a formal publication. Informal discussion and personal sharing are welcome.
This project is part of an ongoing personal interest in the history of mathematics, the emergence of formal systems, and the embodied cognition underlying early discovery.