Wednesday, June 1, 2016

Blog Post 3: What is Math?

Mathematics is something unique. It cannot be define specifically, rather it should be a set of ideas. You could say mathematics is problem solving or abstract thinking. Or you could take a very different approach and say it is completely something else. In my opinion there is not one definition, it depends on how one views it. Mathematics is a system put in place to better understand numerical facts about the universe. Now I know that this could be argued by many, and I would like to hear everyone's argument. For my personal purposes however, mathematics' purpose for me, is to serve as a system that puts complex ideas and numbers into a more observable, practical, sense.

Math is something incredible, it can be an infinite amount of things. It can be theories, equations, ratios, and even games. It falls under a realm of problem solving. Math is not one specific thing, rather it is very difficult to define because it is considered to be many different acts. The most specific definition of math that I can create is: Mathematics is an abstract way to explain quantity and space. It is an art  involved in almost every aspect of our lives. It keeps time, helps us calculate movements, create technology, and many other every day tasks. Without math, we would have no clues to why and how we exist. Math helps us predict simple things such as when we should leave for work, how much we need to pay the cashier, and other minuscule things we take for granted. Simple tasks such as these are basic arithmetic. For example, to pay the cashier, we need to add the dollar amounts in our pockets to be as close to, without going whole dollar bills over. For calculating when we need to leave, we take what time we want to be at our destination, and subtract how much the drive time takes to get to our destination to determine when we need to leave by. 

To do mathematics could mean many things. Examples from above are calculating when to leave for work or paying the correct amount of money. However, fundamental mathematics is what we teach to younger children to help aid them to be able to do every day activities. Teaching numbers, solving simple arithmetic, identifying shapes, and many other simplistic math we teach to students is doing math. However, there is also very complex reasoning as well. Applied mathematics however can be interpreted completely differently. Applied mathematics, for example, is what engineers of physicists do to calculate formulas. They apply math to help them determine forces and many other things linked to their work. 

Famous mathematicians and even high school aged students do mathematics. For example, high school students are taught theorems based on work from mathematicians. Students are only adding their own knowledge to the proofs and are also adding evidence that the proof works. Finding theories, applying theories, and generating proof or reasoning behind problem solving is mathematics. Discovering how and why the world ticks the way it does is mathematics. Math and science are so closely related to one another that they both feed off of one another. Doing math is a very hard question to answer.

My definition of math is not the only one. Leopold Kronecker said "The integers came from God and all else was man-made." In my opinion, it sounds like the tools we work with were given, but to what we do with them is considered mathematics. So a broad definition from Kronecker might be that mathematics is what we do with integers. According to Elaine J. Hom from livescience,com, "Mathematics is the science that deals with the logic of shape, quantity, and arrangement." She goes on to say similar ideas to mine that, "math is all around us." She explains that it is a part of our every day life and that it includes the technology we use, buildings we create, other art such as tessellations, money, applied mathematics such as engineering, and even sports. Hom has a very similar outlook of mathematics as I do.

Because I am planning on going into education, I wanted a definition from a person with similar interests. Therefore I found informal writing from Wendy Petti, a 4th grad math teacher on She asked students and teachers of all ages to reflect on what math is. An elementary school volunteer she interviewed said "math is more than a subject we learn in school."
A first grade student said "Math is you. Math is me. Math is everything we see!" A 13 year old student replied with "Math is the entire world simplified on a piece of paper... Math is ingeniousness morphed into a tiny simple forumula so we can harness its fantastic powers."  Lastly a 12 year old stated, "math is the universal language of the world,." According to just about anyone who is surveyed about what mathematics is, math is more than just something we study in a classroom, it is what the world is made out of, it's what makes the world turn. Other experts have various answers as well. Professor Dave Moursund, states that mathematics can be broken into 3 overlapping areas. 1. Mathematics is a human endeavor. 2. Mathematics as an academic discipline. 3. Mathematics as an interdisciplinary language and tool.

To sum up what mathematics is, mathematics is something that can be studied, created, used as a tool or language, used in our everyday lives, and how the world works. Mathematics is very difficult to define because it can be used in many ways. The best way to define mathematics is to say that it is complex body that requires logic and reasoning to describe the world around us.


  1. Hmmm - this is a deep question, but I'm not sure you gave it a full assault.

    To be complete you would want to show more time - maybe in researching others' answers to this?

    Content: if math can be anything, isn't it a useless term? What makes doing those things you list math. Numbers? I feel like when I figure out change, that's not really doing math for me. Although I'm fond of asking people - especially kids - how they did it. Then I think we're both doing math. I encourage you to dig deeper.

    Or maybe you want to argue that it doesn't matter if we have no specific meaning for what math is? How could famous mathematicians and high school students be doing the same thing?

    C's: 3/5
    clear, coherent, consolidated: +

  2. I thought this was a very thought out blog post! I like the examples you gave in the beginning, and I especially agree with the quotes in the second to last paragraph. However, I agree math can be described as many different things, I do think that a little more research could have been done to back up why you think math is what it is. If you need references, the book I read for class "A Mathematician's Lament," or even Michelle's book have great examples of what math is and how it can be described!

  3. Anthony,
    I was very impressed with your approach to this post. You seem be attempting to define math by providing multiple definitions, which for such a complex idea, I think is very helpful. Yet, it leaves me wondering if perhaps math is really just a collection of many complex concepts all put together under one category because they seem to deal with numbers. Perhaps math has grown so much that it can no longer be contained under one category?

    I found two of your thoughts very interesting and was wondering if you could shed some more light on them. The first is, “Without math, we would have no clues to why and how we exist.” That seems to be an incredible claim, what do you mean by this?

    The other is, “For example, to pay the cashier, we need to add the dollar amounts in our pockets to be as close to, without going over, how much we owe.” This brings two things to mind. First, a friend of mine told me the other day that cashiers seem to be losing the ability to count back change. If the cash register doesn’t tell what to give back, they are lost.

    The other is in regards to the part where you say, “without going over.” That seems to imply that the amount we give to the cashier should be less than or equal to what we owe. However, shouldn’t it be greater than or equal to what we owe? Perhaps I am reading it wrong. It has been a long weekend and I am dragging.

    Thank you for your post,