May 17 2011
Despite its importance in everyday life, I’ve never been the biggest fan of arithmetical work. I remember muttering curses of the Arab scholars who invented algebra in 10th grade, constantly commenting, rather morbidly, that Arabs were responsible for 9/11 and algebra. Despite my rather tumultuous relationship with the subject, however, I’ve never been one to deny it’s absoluteness in providing answers. After all, I’ve always merely viewed math as being either a futile exercise in number crunching on a piece of paper to find another number to provide a solution to a question, or as being the way in which I’d have to calculate the number of days I’d have left before I had to beg my parents for more money. However, following Mr. Chao’s talk on mathematics this past week, I’ve come to realise that math is so much more than my previous perceptions of the subject, as I’ve come to see that it’s definitely more intricate than I previously thought. One particular question that stuck with me following the talk was the question on whether math was a human invention or a human discovery, invoked through the memories I had of placing (undeserved) poxes upon the households of these scholars out of spite, which in turn inspired me to conduct a small investigation.
I find it appropriate, however, to firstly define what exactly I mean by “invention” and “discovery”. The online dictionary definitions didn’t really provide a sufficient definition for “discovery” in particular, with “discovery” being defined by “The Free Dictionary” as being “the act or instance of discovering”, leading me to personally define an “invention” and a “discovery”. It goes like so. During the talk, I came to, following the opinions of others, define an “invention” as being “the creation of an object or an idea that had previously not existed”, while “discovery” came to be defined as being an “observation of a naturally occurring phenomenon whose existence had not previously been acknowledged by humanity”. To give a further example, a “lightbulb” would be an invention, as it had not previously existed prior to its creation, while the antibiotic properties of penicillin would be a discovery.
Now that the definitions are out of the way, here’s what I think. I feel that math is simultaneously both an invention and a discovery, in the sense that numbers and mathematical symbols, the medium of communicating mathematical ideas, were an entirely human invention, created to express the observed, naturally occurring patterns or relationships seen in objects in everyday life. After all, the numerical glyphs we use to express modern day mathematical patterns were invented in India sometime between 400BC and 400AD, and were passed on to Europe by mathematical works created by Arab scholars which utilised them sometime during the 10th century (hence why the numbers are known as Arabic numerals). Even before the advent of Arabic numerals as the main method of communicating expressions of quantity worldwide, however, we’ve seen other cultures invent their own means of expressing quantity, such as that of the Roman numeral system (I = 1, V = 5, for example) or even the Chinese characters expressing numbers, shown here below:
From the widespread invention of numerous (no pun intended) methods of expressing quantity across cultures, it is easy to deduce that the invention of numbers arose as a result of early humans needing to develop some method of expressing quantity to fellow members of their respective civilisations.
Another notable example of math as an invention would be the invention of formulas used in the hard sciences such as chemistry and physics that would provide a sufficient, quantifiable means to their discoverers of expressing their discoveries and observations. It is notable that entire fields of mathematics have been created in an attempt to create a system that provides a sufficient explanation for naturally observed phenomenon in the hard sciences, with Newton and Leibniz’s invention of calculus to help express physics concepts being particularly notable. This to me is the most telling piece of evidence with relation to math as either an invention or discovery, as it shows to me how mathematical structures can be derived to help quantify the observations made by scientists in their work, which is reflected by the vast array of formulas used in all fields of science.
Thus, I can thereby conclude that math is both an invention and a discovery, as naturally occurring mathematical patterns and observations, such as that of the idea of quantity, have been expressed through means of human invention, as shown by the wide array of symbols and formulas we use to provide explanations for the naturally occurring mathematical concepts we observed.
Chao, Michael. “Mathematics and the Theory of Knowledge.” Theory of Knowledge Class. Shanghai American School, Shanghai. 10 May 2011. Lecture.
“Discovery.” Def. 1. Discovery – Definition of Discovery by the Free Online Dictionary. 2009. Web. 17 May 2011. <http://www.thefreedictionary.com/discovery>.
O’Connor, J.J., and E.F. Robertson. “Indian numerals.” History Topics. N.p., Nov. 2000. Web. 15 May 2011. <http://www-history.mcs.st-and.ac.uk/HistTopics/Indian_numerals.html>.
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