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Is Math A Science?

To compare math to a science we need to first clearly define what a science is. An interesting definition I found online was from Explorable which defined science as "the observation, identification, description, experimental investigation, and theoretical explanation of phenomena." It is in particular used in activities applied to an object of inquiry or study. Looking at that definition we can see that math does have some of these traits that define a science for example before we come up with any kind of conjecture in math we first observe and experiment to identify patterns so that we can formulate the most accurate conjecture. I think math perfectly fits the part in the definition about science being a theoretical explanation of phenomena which is why I would argue for math being a science. My best example for math being a theoretical explanation of phenomena would be discrete dynamical systems, in my independent study on discrete dynamical systems we looked at how different factors affected population numbers. The University of Texas has a cool article talking about a professor using discrete dynamical systems to model natural phenomena. So if we define science the way that Explorable does I would say math is indeed a science.
Although using other definitions for science such as Webster's definition which is that science is "the knowledge about or study of the natural world based on facts learned through experiments and observation." I would disagree that math is a science with this definition because math may study the natural world in some cases but the facts are not based on experiments and observation but rather on proof. We may use empirical evidence to help with formulating conjunctures and disproving them but for us to accept them as fact we need to generalize them and prove they still hold. Another important difference between math and this definition is that math is not just knowledge about the natural world one easy example would be in linear algebra when we would have vectors that were in the 4th dimension and higher. In math mathematicians can create strange worlds using many different areas of math and since the definition we are using here limits the knowledge to just about the natural world I would say math is not science if we define science in this way.
So it really depends on how you define science for whether or not math is a science. Personally the definition of science I like the best is comes from Dictionary.com which defined science as " a branch of knowledge or study dealing with a body of facts or truth systematically arranged and showing the operation of general laws" coming from the online dictionary. I think that this definition really captures the essence of what science is which is basically an ordered collection of information showing how things work. So to me math is a science because it is a system of knowledge about numbers, shapes, and abstract ideas which are built off sets of axioms, which can be thought of as basic rules or general laws something must follow. I believe the question of whether math is a science is a tough question because there exist many different definitions for what a science is, and depending on what definition you pick can affect your answer.
You build a solid case. Maybe a different organization would strengthen it - introduce your key definition before the end and then describe why it fits, etc. it would also strengthen it to include some of the arguments on why math is not a science and deal with them. (Complete.)

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