The Meaning of Abstraction in Modern Mathematics: An Epistemological Study of Structure and Formalism

Muhammad Hasanuddin; Daniel Nyberg; Esther Nalubega; Amina Kodjo

Authors

Muhammad Hasanuddin Institut Teknologi Bandung Author
Daniel Nyberg Norwegian University of Life Sciences Author
Esther Nalubega Mbarara University of Science and Technology Author
Amina Kodjo University of Lomé Faculty of Sciences Author

Keywords:

Epistemology, Formalism, Mathematical Abstraction

Abstract

This article explores the significance of abstraction in the development of modern mathematics from an epistemological perspective and how formalism plays a role in the formation of mathematical knowledge. Abstraction in mathematics not only serves as a cognitive strategy for simplifying concrete objects into general structures, but also serves as a conceptual principle underlying the understanding of mathematical objects that are increasingly distant from direct experience. Using a qualitative approach based on literature-based research, this article conducts a critical reading and comparative philosophical analysis of classical and contemporary literature in the philosophy of mathematics. The analysis shows that abstraction plays a central role in enabling the generalization of theories and the formation of consistent formal systems, while also influencing the understanding of mathematical truth as the internal coherence within formal axiomatic systems. Furthermore, formalism provides a methodological framework that allows the manipulation of symbols and formal structures without relying on intuitive meaning, thus maintaining consistency as the primary criterion of truth. These findings confirm the symbiotic relationship between abstraction and formalism in the epistemology of modern mathematics and open a dialogue about the challenges and tensions between abstraction, intuition, and structural practice in contemporary mathematics. Thus, abstraction is not simply a technique but an epistemic principle that shapes how mathematics is understood and developed today.

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