Monday, April 21, 2014

Mathematics: Invented or discovered?

Is mathematics invented or discovered? In order to answer this question, we must examine the relationship between math and reality. To what extent does math describe the reality we live in? Did mathematical equations exist prior to their discovery, or did Pythagoras and Einstein invent their own equations? If these mathematical concepts were discovered, then how did they exist and in what form? 
We live in a mathematical macrocosm, where math describes the reality we see, the reality we cannot see, and the reality we imply to be true. Mathematical models are used to depict everything from the orbital path of each planet in our solar system to the parabola of a basketball flying through air, from the geometric patterns formed in a sunflower to the expansion of the universe. However, why should mathematics describe reality? Why should there be an equation relating energy and mass, or one linking the three sides of a right triangle? We take these mathematical concepts for granted, and yet these questions lead us to one underlying question: is math a manmade invention created to understand the universe around us, or did we merely discover the equations of mathematics, which were present in particular aspects of our reality? 
Newton’s Second Law of Motion which relates force, mass and acceleration, works just as well on the surface of Mars as it does on Earth. Einstein’s equations explaining the warping of space time by gravity apply in galaxies light years away from ours. Boyle’s Gas Law stating the relationship between pressure and volume when temperature is held constant, also applies to Newton’s law of motion in a molecular level. Ohm’s law which links current and voltage in a circuit, drawn by Georg Ohm in 1827, can be applied to any electronic device containing an electrical circuit. When such mathematical laws are discovered they do not simply depict reality from a human perspective, but a more fundamental, objective reality is exposed.
One can argue how math is the only subject that is exact and there will always be a right answer, unlike literature where the text is subject to our own interpretation and perspective. History is also an ambiguous subject, as we can only know so much about what happened centuries ago. In reality, math is used to measure quantifiable things in the real world, and many consider it to be concrete and definite, although, as we dig deeper in mathematics, we realize how uncertain and subjective it can be. For example, in basic arithmetic, we can all agree that 1+1=2, however, in binary numbers, 1+1=0 and in base 2, 1+1=10. This merely shows how math can exist in numerous forms; And how it can be perceived in different ways depending on our culture and schema. Individual cultures can have their own ways of counting and depicting their reality through their own mathematical system. 

As mankind evolved, we tried even harder to describe the reality that surrounds us by discovering and substantiating mathematical concepts that reside in nature. To certain extent, one can conclude that math was discovered, but as we tried to further comprehend and analyze the universe around us, we began creating our own way of expressing mathematics. For example, symbols such as e, i and π were created to represent irrational numbers that have always existed in nature. On the other hand, as we closely examine and scrutinize nature, we start to notice mathematical sequences that have been functioning in our world long before we realized it. The Fibonacci sequence, for instance, can be applied to the coiled shape of a shell or maybe even the growth of a plant. There are of course, other remaining factors that must be taken into account to answer the question whether math was invented or discovered, mainly due to the fact mathematics has its own flaws and uncertainties.

1 comment:

  1. What's really good about your answer, Andre, is the specifics you use to make your points. Referring to specific mathematical concepts in your exploration gives evidence to your claims. Nice work. I get the sense, though, that your counterclaims (that math is invented) are mostly for decoration, and that those sections don't do a lot of work in your response. Since you don't really dig into the other side, there's not much to synthesize in the conclusion. Don't worry. I don't expect you to show mastery of this process yet, but this is the direction we're moving in: give just as much thought to the perspectives you don't immediately gravitate to as you do to the perspective you naturally fall into. Then see what changes.

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