Mathematics and Civilization

Throughout human history, mathematics has been a driving force behind intellectual development and the advancement of civilization. The axiomatic system of geometry established by Euclid in ancient Greece formed the foundation of Western thought, while Newton and Leibniz's calculus became the basis of modern science and technology. The computers invented by Turing and von Neumann have even changed the way modern people live. Mathematics is one of the most fundamental and oldest sciences, applied as the foundational theory across all fields. Natural sciences such as physics, chemistry, life sciences, and astronomy, as well as applied sciences such as engineering, electronics, chemical engineering, computer science, medicine, and economics, cannot progress properly without mathematics. Mathematicians develop new mathematical theories and use mathematical knowledge to solve problems in areas like economics, science, engineering, medicine, and business. The era when only mathematics majors studied mathematics has come to an end.

Mathematical work can be divided into two main fields: theoretical mathematics and applied mathematics. However, these categories are not always clearly distinct and often overlap. Theoretical mathematicians advance mathematics by developing new theories and exploring the relationships between existing mathematical concepts. They focus on increasing foundational knowledge without considering its practical use, yet this pure, abstract knowledge forms the foundation for the advancement of civilization. On the other hand, applied mathematicians use mathematical modeling and techniques such as computer applications to solve and formalize practical problems in fields like management, engineering, medicine, and social sciences. Applied mathematicians working in industrial research and development face complex issues and develop and refine mathematical methods to address them.

Mathematics: The Foundation of All Disciplines

Mathematics serves as the foundation for all disciplines and plays the role of a language in natural sciences, engineering, and social sciences like economics and management. Mathematics is the pinnacle of human intellect and civilization, and a broad understanding of it is essential for becoming a well-rounded and cultured individual.
As we have learned earlier, mathematics forms an organic relationship with other disciplines. The process of finding motifs through observation and representing them through images is connected to the field of biology. Identifying patterns in these images and how they form natural structures, such as fractals, is applied in chemistry. When the concept of time is introduced, it reveals phenomena where patterns are created and then collapse. This phenomenon falls within the realm of physics, where invisible forces and laws are at work. When patterns collapse and the world of chaos unfolds, phenomena that defy common sense occur. To understand this, one must observe from a higher-dimensional perspective. Developing such higher-level thinking requires a foundation in the humanities. Mathematics uncovers how nature operates within these invisible forces and laws and creates predictive programs to forecast how it will evolve.