Can we know if mathematics is invented or discovered?

            To answer this, many other questions show up. What does the term “mathematics” encompass? How could we know it is one or the other? Mathematics is defined as the “abstract science of number, quantity and space” (Oxford Dictionary). There are two major fields within it: pure and applied mathematics. Applied mathematics allows people to use concepts learned in that area in other subjects (physics, engineering, etc.), whereas pure mathematics is studied “alone” solely using it for its own field. Defining the term is important since we need to know what it means to reach a conclusion about it. It is especially significant in this case because, quantum physics is a part of the answer and it uses applied mathematics. Since the definition of mathematics includes the word “abstract” (at least the definition I am using to answer the question) an important part of reaching a conclusion will be accepting that the answer might not be concrete.

            Having defined the term, quantum physics is another subject area that is crucial to look at. Humans categorize things, we are the ones that make up measurements and these are only there because we are making observations. If we were to remove all humans from Earth, would there still be patterns and quantities? Since we are the ones that classify and group what we see and determine whether something is bigger or smaller, if we were removed from Earth these attributions would no longer exist. The size of an object might not change but the idea of it being bigger than another one will no longer be present. This is due to the fact that there will be no one making an observation and that is a great part of quantum physics. Quantum physics/mechanics says it is possible for something to be in multiple places at the same time. This can be exemplified with an experiment with light, when light is reflected through two small openings, that light, even though it is a microscopic beam, will pass through both openings, not only one, which is similar to the process of photosynthesis (How Long is a Piece of String). In the documentary where this information is presented, another example is presented later, with a cat. The professor shows a stuffed cat and asks whether it is dead or alive, the obvious answer would be dead but he says it is both. Supposing it was killed by poison in its milk, since the particles of that poison could be in different places at the same time, it could be in the milk and could be elsewhere, leading to the cat being both alive and dead. The professor followed to state the only reason we conclude it is dead is because we are there to make that observation. Thus, if there were no humans to say that the cat is dead, it would be both alive and dead.

            What we notice in these examples is that we create categories as we make observations, therefore seemingly “inventing” mathematics. However, both experiments show that without the observations there is still the principle of quantum physics, thus supposedly showing it is there without our presence. Since quantum physics uses applied mathematics, this could suggest that the latter was discovered. The experiments allow us to create a paradigm, how is math discovered and invented? What we can see is that certain aspects of math might have been created since they wouldn’t exist without the presence of a human being, on the other hand, there are aspects that are found, since they would exist if we didn’t. These ideas go back to the definition of mathematics, the fact that it is abstract.

            Having taken all of that into consideration, we should go back to the initial question. Can we know if mathematics is invented or discovered? The question does not ask which one it is, instead it asks whether it is possible to determine that or not. There are many experiments that might lead to one direction or another, but to know whether it was invented or discovered, it seems like the best way is imagining how the world would be without our interference. However, there is a downfall, to what extent can we imagine it how it would really be. All we can do is think that it would stay the same, because that is all we know, but the world might be different without living things in it. Thus, we can try to reach conclusions based on some assumptions we make but we cannot really determine whether mathematics is invented or discovered since to know that we would have to be inexistent. It could be a mixture of both, as it seems with the experiments, but that conclusion is based on certain assumptions we make to be able to create a theory. Thus, I don’t think we can know for sure.

Works Cited

BBC. "How Long Is a Piece of String? - Full Documentary." YouTube. YouTube, 13 Apr. 2013. Web. 15 Apr. 2014. <https://www.youtube.com/watch?v=231AKaNr1AY>.

"Definition of Mathematics in English." Oxford Dictionaries. Oxford University Press, n.d. Web. 15 Apr. 2014. <http://www.oxforddictionaries.com/us/definition/american_english/mathematics>.

Keim, Brandon. Plantburst. Digital image. Wired. Wired Science, 07 July 2010. Web. 16 Apr. 2014. <http://www.wired.com/2010/07/leafy-green-physics/>.