MATHEMATICS AND BEING: THE LANGUAGE OF THE UNIVERSE OR A HUMAN ABSTRACTION?

ABSTRACT

This article examines the fundamental connection between mathematics and reality, analyzing two key positions: mathematics as an objective structure of the universe and mathematics as a subjective construct of the human mind. Philosophical concepts, scientific examples, and contemporary hypotheses are also considered. Mathematics is analyzed from different perspectives, serving as a universal language of being and an effective tool for its description. The article combines philosophical depth with scientific specificity.

Keywords: mathematics, being, Platonism, nominalism, ontology, philosophy of science, Tegmark, Einstein.

Mathematics is not just a science of numbers and formulas. It is a fundamental way of describing reality that permeates all levels of being, from the movement of planets to the structure of human thought [1, p. 15]. But is mathematics an objective truth that exists independently of us, or is it a product of the human mind?

Mathematics as the Language of the Universe

Mathematics is the fundamental language of the universe, tracing back to antiquity. Pythagoras said, "Everything is number" [2, p. 48], and Plato considered mathematical objects to be part of the world of ideas, that is, eternal and unchanging entities [3, p. 112], which are merely discovered by the human mind. This tendency is known as mathematical Platonism, which is reflected in the works of both scientists and philosophers. Considering mathematics in physics, Galileo Galilei asserted: "The book of nature is written in the language of mathematics" [4, p. 32], which is confirmed by the entire history of science: Newtonian mechanics was able to express the motion of planets using differential equations [5, p. 89]; Einstein's general theory of relativity was able to describe gravity as the curvature of space-time [6, p. 154] through tensor calculus. It can also be found that many mathematical theories, such as Lobachevsky's non-Euclidean geometry, were initially developed as abstractions but later found applications in physics [7, p. 203]. If we delve into the mathematical universe hypothesis by M. Tegmark [8], which develops the idea of reality as a pure mathematical structure, then according to his hypothesis, all physical objects (from atoms to black holes) are mathematical abstractions, and other universes with different physical laws may exist as alternative mathematical models [9, p. 71]. Tegmark's view blurs the line between mathematics and ontology, suggesting that we consider reality itself as "materialized mathematics" [10, p. 118].

Mathematics as a Human Construct

There is an opposing view to mathematical Platonism, namely that mathematics is not a discovery but merely an invention of humanity, shaped by the process of evolution, cultural development, and needs. Mathematical systems have existed in different civilizations, such as Babylonian mathematics, which used a sexagesimal system but did not have a concept of zero, or Maya mathematics, which included a positional system with zero but was closely tied to astrology and rituals. Such differences in development show that mathematics was formed not as a single "truth," but as a toolkit adapted to specific human needs. Constructivist philosophers argue that mathematical objects do not exist until constructed by the mind; an example of this is the imaginary unit "i," which was long considered nonexistent until it became fundamental in quantum mechanics. However, one cannot assert that it existed before human discovery. Contemporary research suggests that "mathematical abilities are a byproduct of evolution," meaning that spatial thinking developed for navigation, and arithmetic for assessing resource quantities. It can be said that mathematics is a dynamic system, limited by human cognition and logic.

Mathematics and Its Boundaries

Modern philosophy of science and mathematics offers more complex models of the interaction between mathematical structures and being, exploring how mathematics shapes the possibility of understanding reality. I. Kant argued that mathematical truths are a priori synthetic judgments that structure human perception. Space and time are forms of sensibility that organize experience, rather than objective entities. Thus, non-Euclidean geometry was able to change not only mathematics but also the understanding of philosophy. Quantum theory questions the classical understanding of the relationship between mathematics and being, leading to certain philosophical conclusions that mathematics not only describes reality but dictates the conditions of its possibilities, limiting the range of permissible physical models. Thus, mathematics is not just a language or a tool, but a conduit through which being manifests its structure.

Conclusion

Mathematics is a balance between discovery and invention. It reveals the structure of the universe [8] and is a tool created by humanity for understanding. However, the connection between mathematics and being remains a mystery of knowledge.

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