Is Mathematics Always There, Independent of Human Existence?

Mathematics, a fundamental system of numbers and relationships, has always existed long before the invention of humans. It permeates every point in time and space, and thus, is beyond the constraint of the time-space continuum. This article delves into the age-old question of whether mathematics is inherently present and immutable, or if it is, indeed, a human invention.

The Unchanging Nature of Mathematics

Mathematics is not a creation of human minds. It is an immutable system of numbers and formulas that exist independently of time and space. The famous mathematical constant (pi), for instance, is an unchangeable entity. It answers questions about the circumference of a circle relative to its radius and has been known for centuries. Even before mathematicians provided a name for it, its value was inherent and absolutely present. Similarly, other mathematical constants and relationships were present long before humans recognized them.

The Semiotics of Mathematics

Discovering new mathematical concepts is not the same as inventing them. We merely uncover, through research or exploration, the knowledge that is already there. Complex numbers, for example, obey the same relationships they do today even though they were not recognized by humans until much later. These numbers were always out there, even if we did not name or use them.

Mathematics, being a system of absolute truths, serves as the foundation for any form of knowledge. It is a core component of the vast array of fields that humans have conceived and continue to explore. From the simplest addition to the most complex calculus, mathematics remains a constant and a key to understanding the universe around us.

Mathematical Axioms and Their Universality

The axioms of mathematics, such as the property of equality stating that anything is equivalent to itself at any given moment (a a), are not invented but discovered. These axioms are foundational and cannot be proven or disproven. This principle is crucial as it forms the bedrock of any mathematical system. Without this basic tenet, we would lack a meaningful way of identifying and understanding the world around us.

For instance, if we deny the axiom that x is the same as x, then we face a significant challenge in constructing any kind of knowledge or system. Without a consistent identification system, every object would change its identity continuously, rendering any form of memory, language, or conceptual understanding impossible. In a more extreme scenario, if we cannot agree that a second is a second, then the very fabric of our understanding of time and cause-and-effect would unravel.

The Cosmic Significance of Mathematics

If you consider the vast scale of the universe and the concept of infinity, mathematics becomes an even more intriguing topic. Infinity defies logic in many ways and is not bounded by it. Beyond the time-space continuum, classical logic fails, as the principle of sufficient reason (one of the principles of causality) also collapses. In such a scenario, every cause and its effect would coincide (T 0), leading to an endless loop where every cause is also the effect.

The question then arises: what truly lies at the heart of mathematics if not a human creation? Many believe that only an Infinite Being, such as a god, can create something that transcends the limitations of time and space. Mathematics, with its infinite and unbounded nature, fits this description perfectly. From the smallest subatomic particles to the largest structures in the universe, mathematics provides a framework that is consistent and applicable everywhere.

Conclusion

In conclusion, mathematics, as a system of numbers and relationships, has always existed and is not something invented by humans. It is a part of an existential landscape that is independent of human presence. Whether we express it in Greek, English, or any other language, the fundamental truths of mathematics remain unchanging and universal.

The role of mathematics as the foundation of knowledge and its potential for universal communication make it a fascinating subject of philosophical and scientific inquiry, bridging the gap between human understanding and the vast cosmos.