A major topic of discussion for us this semester has been weather or not mathematics is invented or discovered. At the beginning of the semester I was leaning toward the invented side of this debate. My thoughts were that we invented mathematics in order to explain what was going on in he world around us. However, I now find myself of the discovered side of this question. One of the big topics that converted me was the Continuum Hypothesis. This theory, so far, has not been proved or disproved. My thoughts were that if math was invented, we should be able to invent something to either prove or disprove this hypothesis, but alas we have not. There was also another thing that helped tip me to the side of discovered. When we talked about Gauss, we discussed how he had figured something out but kept it to himself, then years later someone else had figured the same thing out. The fact that two people could "invent" the same type of mathematics years apart and that each of them had no knowledge of the others work is too much of a coincidence for me to believe. It makes more sense to me that they both discovered the same thing at different times, as opposed to inventing it.

Another one of our big questions this semester was "is math a science?" At the beginning of the semester my answer was yes, and it still is. Although depending on how one defines science I see how the answer could go either way. When I think of science, I think of the study of a particular topic in order to explain phenomena we observe. I find myself seeing mathematics in my day to day life, and I'm sure many others do as well. Various mathematical concepts can be seen in nature as well, as ViHart describes in her Doodling in Math youtube video series. She explains how we can find the Fibonacci sequence in various spirals,

Another one of our big questions this semester was "is math a science?" At the beginning of the semester my answer was yes, and it still is. Although depending on how one defines science I see how the answer could go either way. When I think of science, I think of the study of a particular topic in order to explain phenomena we observe. I find myself seeing mathematics in my day to day life, and I'm sure many others do as well. Various mathematical concepts can be seen in nature as well, as ViHart describes in her Doodling in Math youtube video series. She explains how we can find the Fibonacci sequence in various spirals,

So to me math is used to explain the things that we have observed (or at one point was primarily used to explain things that we had observed, though now we are able to abstract math into other higher dimensions that we cannot observe), which makes it a science to me. Also, I think the fact that math can be studied in its own right, now just studied as it applies to other concepts, makes it a science as well.

I know others say that math is not a science because science is used to explain the natural and observable world, and that not everything in math is observable. But honestly, I think that is part of the power of math. It can be used to explain nearly everything that we can see, but it also goes farther than that to explain things we cannot see. I just don't think that that reason is enough to make math somehow not a science.

The other big question this semester was "what is math?" And, honestly, I still don't have a formal definition set in my head. However, I do know that math isn't just about using formulas to solve equations, or using numbers to figure something out. I think that one of the most important parts of mathematics is having a mathematical thinking mindset. By this I mean that you have to have good problem solving skills, and be flexible enough to approach a problem in more than one way-because that way you try it the first time might not work the way you thought it would.

I know others say that math is not a science because science is used to explain the natural and observable world, and that not everything in math is observable. But honestly, I think that is part of the power of math. It can be used to explain nearly everything that we can see, but it also goes farther than that to explain things we cannot see. I just don't think that that reason is enough to make math somehow not a science.

The other big question this semester was "what is math?" And, honestly, I still don't have a formal definition set in my head. However, I do know that math isn't just about using formulas to solve equations, or using numbers to figure something out. I think that one of the most important parts of mathematics is having a mathematical thinking mindset. By this I mean that you have to have good problem solving skills, and be flexible enough to approach a problem in more than one way-because that way you try it the first time might not work the way you thought it would.