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,
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.