The Perspectives on Discovering in Mathematics

Mathematics is full of unanswered questions. Arguably the most important and famous question, maybe this one. People continuously argue that mathematics is something that, as a society, we created it, or mathematics has always been there, and we only ever could have discovered it. The creation of math would be that humanity invented mathematics. The discovery of mathematics would be based on the ideology that mathematics occurs naturally. In what follows, I claim that mathematics has always been there and that humanity has only ever discovered mathematics.

This will be demonstrated through the analysis of biological and physical sciences.

One of the most convincing pieces of evidence that mathematics is discovered is found in biological sciences, plants, and animals. When plants and animals are free to adapt to nature, they build patterns to maintain efficiency and safety. My friend, Destenee, says, 'if there is a pattern involved, there is math involved, especially in nature.' One case of plants and animals using mathematical patterns is voronoi tessellations.

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Voronoi tessellations are the dividing of a plane based on the distance of the points that never cross paths (D'Agostino,2019). In nature, this phenomenon occurs in honeycombs and trees. In the case of honeycombs, the Voronoi tessellations occur in a consistent pattern. The shape of the honeycomb is built to provide efficiency and safety for bees. The hexagonal design is significant to a bee's efficiency as the form avoids gaps and uses the least amount of beeswax to make but can withstand the most considerable amount of weight (Rcwebber, 2018).

In trees, the formation of Voronoi tessellations occurs as a form of protective behavior. This tendency is called crown shyness, and it occurs when trees have evolved in a way where their leaves never cross paths with another tree. This evolution is believed to occur as a way for trees to protect themselves from larvae that eat leaves (MacDonald, 2018). Another example of mathematics occurring in nature is in the case of Fibonacci's sequence and the golden ratio. In dolphins and starfish, the golden ratio occurs in their body proportions (Haelle,2014). In plants, such as succulents and sunflowers, follow Fibonacci's sequence naturally. It is believed the golden spiral evolved in specific plants as it is the most efficient way for some plants to obtain the nutrients they may need to survive (Steph, 2012). The spiral is the best way to gather water and ensure each leaf captures the sunlight it needs (Steph, 2012). The examples listed show how specific patterns are spread across nature. The same mathematical phenomenon occurs in different plants and animals in different species that never cross paths. We did not create nature; nature has always done its own thing, and that regularly consisted of evolving to survive. Just as biological studies demonstrate how mathematics was already in existence, chemical and physical sciences also have evidence of mathematics being discovered.

Physical sciences, such as chemistry and physics, demonstrate that mathematics was discovered. In my geology class, my professor broke a piece of halite repeatedly. Each time the mineral broke, it would maintain its cubic atomic structure. Due to the sodium and chloride being close to one another molecularly, the breakage causes a 90° angle causes the mineral to maintain its cubic molecular structure. The chemical elements bonded in a way that a 90° angle occurs no matter how small the mineral gets. When studying physics, we learn that gravity’s effect occurs at a rate of 9.81 meters per second squared. The pull of gravity has always been in effect; the scientists that discovered the constant speed of gravity on earth was 9.81 m/s2 did so through experimentation. Gravity’s effect was never created; we only gave the natural occurrence a value that, as a society, we would understand. In the study of space physics, it is seen that certain galaxies have a specific shape based around the concept of the logarithmic spiral. For any point, the tangent line and the radius will form an angle; if the angle is constant, then the spiral has a logarithmic spiral (Wyatt, 2011). The spirals of these galaxies can be expressed in a mathematical polar formula. Humanity cannot alter these galaxies. The mathematical phenomenon occurs on its own. Nature did the work; we create the values to understand nature.

I will always view mathematics as humanity’s most significant discovery. But, the debate of mathematical creation or discovery will never see an end. If the universe could have a language, it would be mathematics. We barely understand the phenomena that is mathematics, let alone deem ourselves the creators of such a concept. We can only ever keep pushing ourselves to uncover more of the secrets that mathematics may hide. We study mathematics to understand it, but we do not bring mathematics into existence.