Upon arriving at this topic, I had previously been asked a simple opinionated question, is math is a science, an art, or a philosophy. I thought to myself, well of course all three. Mathematics is for the most part (at least what people see) is a science; adding, subtracting, multiplying, dividing, differentiating, integrating, etc. These are all very well defined operations which, for the most part, have very algorithmic solution methods. The art comes in the proofs. Typically, when formulating a proof you're not given anywhere to start and so, just like in art, practice makes perfect. Also, when writing theorems this process is completely in reverse and the amount of creativity required is staggering. Just try drawing a conclusion from a set of fragmented, typically unrelated information (this doesn't even have to be math related). The philosophy comes from concepts of infinity and most of set theory. A lot of early mathematics (after the Dark Age) were, for the most part, philosophers. They were fascinated by how something so simple as mathematics could model something so abstract and complicated as nature, and yet could itself become as abstract as to not be visualize-able by humans (infinite, dimensions greater than 3, etc.) So it is all three, although rarely is it simultaneously all three. One of these usually dominates while working with math at any one time. But there have been points in history where all three of coincided and it is some of the most mind-boggling and beautiful work you'll ever see.
But it had got me thinking after taking this course that is math really a science, an art, or a philosophy, though for more thought out reasons. Having an art background and studying art history front and back, I came to the idea that mathematics and art go hand in hand. (And now knowing this, I have a stronger connection as to why math would be considered an art compared to a chemical engineer who would be more likely to lean towards a more scientifical...
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