Prior to the discussion of the knowledge issue, all the terminologies must be clarified. The universal definition of “discovery” is something that has been present before humans found it. However, ‘invention’ is something that did not exist until the humans created it.
Mathematics, a tool that we can utilize to depict our reality or any system based on quantifiable things, can be found everywhere in our lives such as the nature and stock market. Such fact implies that mathematics has existed ever since the creation of earth. Thus, the humans did not invent math, they discovered and substantiated that mathematical concepts reside in the nature. Among the 4 Ways of Knowing, I can employ language, sense perception, and reasoning so as to substantiate to whether mathematics is discovered or invented. Furthermore, referring to the definition of ‘discovery’, the Mother Nature, earth, and universe, which have been present prior to the advent of humans, are the most adequate places to seek the ultimate answer to this knowledge issue.
The ubiquitous numbers, expressed by symbols, were invented apparently; nevertheless, such language is a mere device to convey, delineate, and utilize sophisticated mathematical concepts in our world. For instance, the concept of derivative or differentiation is conveyed through numerous unknown variables, coefficient, transcendental functional, exponential functional, and others. These complex symbols and the concept of derivative are utilized to explicate the theory of immediate rate of change of moving objects and chemical reaction. Therefore, mathematical expression is invented; however, such invention is only utilized to discover and elucidate the concealed mathematical concepts that have been functioning in the world we live.
Thus, what standards decide whether certain mathematical concept is invented or discovered? I believe the correlation between a mathematical concept and reality or physical world determines the answer to this knowledge issue. Our ancestors understood the nature of the positive integers. They could compare and affirm that 9 were more than 6 from simple and daily experience. They could assure that 9 apples were greater that 6 apples in quantity and 9 apples alleviated hungers more than 6 apples. Moreover, the fact that our ancestors or the hunter-gatherers attempted to accumulate the maximum amount of food implies that Therefore, simple calculation and algebra are reveal flawless association with the reality and even pragmatic to our lives. This was the beginning of mathematics. Math evolved into a more sophisticated and abstract form as mathematicians scrutinized and discovered more about the world around them. Such fundamental and conventional logic remains eternally.
The sequence of Fibonacci, for instance, epitomizes a mathematical concept or pattern found in the nature.
1 1 2 3 5 8 13 21 34 55 89 144 …
As plants grow, they seem to grow in a pattern that resembles the sequence of Fibonacci. Majority of the flowers have the number of branches, stems, and petals that resembles the sequence of Fibonacci. This fascinating prevalent tendency then elucidates why four-leaf clovers are seldom found in the nature. Plants do not know this sequence; they just grow in the most efficient way. Adhering to Fibonacci numbers maximizes the space between each leaf, average amount of sunlight falling on each leaf, and thus the growth of the plant.
Therefore, I, as a knower, believe that math is discovered since it has been functioning in our world way before we came to realize math. We simply need to observe the nature and surrounding environment more meticulously so as to ascertain such truth. Nevertheless, the controversy surrounding this knowledge issue will never end since we have a lot more to scrutinize and discover about math, the ultimate truth of the universe.