We can use mathematics to successfully model real world processes. Is this because we create mathematics to mirror the world or because the world is intrinsically mathematical?

Mathematics is defined as the organization of reason and ideas. In the prompt, the expression “real world” incorporates the universe rather than the physical world. Due to this, “real world processes” refers to all of the processes in the universe, not solely processes that are commonplace in the physical realm. Mathematics assists in organizing the logic behind these real-world processes and can be employed to better our understanding of these processes. Mathematics are able to be successful in modeling real world processes because the world is intrinsically mathematical.

               Before the prompt can be answered, it is necessary to explore how applicable these mathematical concepts are in real life situations. To what extent can knowledge that is not directly pertinent to real life processes be utilized to further relevant knowledge? The question insinuates that mathematics are directly pertinent to real world processes. This means that mathematics can be applied to processes that already exist in the real world. Since there are so many patterns that reveal themselves in real world processes, it is common for mathematical processes to have numerous applications within the world. While most mathematical knowledge has a direct application to processes in the real world, some knowledge does not. However, this does not mean that this knowledge is not just as vital. This knowledge can be employed to help further our understanding of the limitless nature that mathematics has in the real world. In order to understand such abstract mathematical concepts, imagination is essential. One example of such a mathematical process is complex numbers. Complex numbers can be expressed in the equation a+bi where a and b are real numbers and i is the complex number. In order to conceptualize this, a person must be able to visualize deriving a two-dimensional complex plane from a basic one-dimensional number line. In the process of visualizing this, imagination and sense perception are necessary. For example, complex numbers have a real application in the realm of physics. In quantum mechanics, it is impossible to say with complete accuracy where a particle lies, it is merely possible to give an approximation in terms of the position in space. In this situation, complex numbers are the only way to compute these distributions.

Although the majority of mathematical knowledge has a direct significance to processes in the real world, some knowledge does not. While this type of knowledge does not provide an answer to a specific question, it is a steppingstone that leads us to knowledge that can later be implemented. For example, Andrew Wiles dedicated years of his life to solving Fermat’s Last Theorem. Fermat’s Last Theorem is an example of certain ma