Monday, October 19, 2015

The Joy of X

For class, the book I chose to read was The Joy of X by Steven Strogatz. Strogatz opens his book by stating that his goal of writing this book is to have "a guided tour of math, from one to infinity." He realizes that many people are off-put by mathematics early in their lives for some reason or another, and hopes that through his book, them (or anyone) can once again come to enjoy or at least not despise math.

Honestly, I struggled to get through the first few chapters of this book. As someone who enjoys mathematics, I found the beginning to be rather dull as it just went through basic ideas about numbers and counting which almost everyone already knows. Because of this, my hopes were not high for the remainder of the book, however I was pleasantly surprised with how much I enjoyed the rest of it. In chapter 4, he talks about how counter intuitive the commutative property of multiplication is and how it breaks down in nature, i.e. the Heisenberg Uncertainty Principle. I had never really given this much thought and it sparked my interest and helped make me want to actually read more. Throughout the chapters from this point forward, there were quite a few more moments like this. For example, in chapter 15, he talks about sine waves and how they show up almost everywhere in nature, and in chapter 24 he talks about linear algebra and how its the basis for google's web search. All these little examples of mathematics occurring in everyday life really made me appreciate this book much more than when I started out assuming it was going to be wall after wall of boring text.

One thing I noticed about the book that I thought was kind of interesting was that the order in which he presents his topics is pretty much identical to how we have been learning about mathematics in our class. The first few chapters are almost parallels of the few first days of class we had in regards to the subjects that we discussed. Another aspect of the book I thought was kind of cool was that Eugenia Cheng and Strogratz both used the example of mattress flipping when talking about group theory and bagels with mobius strips.

Overall, I ended up really enjoying this book and would definitely recommend it to anyone interested. The amount of real life examples he uses to show the importance of math really hooked me. The fact that its a book about mathematics written in a style that allows anyone to be able to understand what is being said is also really appealing and this may have been the biggest thing that drew me to it. The fact that you can just casually read the book and understand what is going on or have an active approach to look at investigate some of the notes he has on further proving some topics was really nice. There were days where I didn't really feel like thinking too much so I could just read it like any other book and then there were moments where something he said was super interesting so you could go to the notes part and there might be further discussion or proofs on it. In the end, I have nothing but praise for this book and would probably be tempted to read any other book similar to this.

Sunday, October 11, 2015

Is math a science?

The question of is math a science was posed in our last class. My initial thoughts on this question is that yes it I would say it is a science. Before really looking in to this question, I would define science as tools used to describe what occurs around us, which I believe math does. Also, math is present in many of the natural sciences like chemistry and physics, so based off this I would also say math is a science. However, after doing some more digging, I'm inclined to disagree with my initial thoughts and say math is not a science.

First, after reading the conveniently named article "Is mathematics a science," one of the reasons the author thought it shouldn't be considered one really stuck out to me. He explains that when determining if something is true, the natural sciences use the scientific method. More specifically they look at tons of observations and then make assumptions off that. For example, say a scientist wants to determine if our climate is slowly getting warmer. He may gather data on temperatures from many different months in the last 20 years. However, if we want to say something is true in math, we use proofs. It is not enough to just believe something is true based solely off observations in mathematics. For example, if we wanted to say that an odd number plus an odd number is even, it is not enough to just look at 1+1, 1+3, 1+5, etc. We use the observations to make a guess, but we need more than this to come to an actual conclusion. As mathematicians we would want a proof that shows this is true for any two numbers x and y, not just all of the ones we looked at in our observations. In this sense math definitely doesn't act like a natural science.

Furthermore, my opinion on this question changed when simply looking at the definition of what science is. Science, defined by, is systematic knowledge of the physical or material world gained through observation and experimentation. Another way of saying this is science is based on empirical reasoning (making sense of all the data you've gathered). Let me first say this is only my opinion, and it may not be correct, but I believe math is not based on empirical reasoning. This is not to say that it isn't commonly used in mathematics like when finding patterns of numbers, but I don't need to make observations and do experiments to be able to do algebra. If I was asked to solve some equation for x, I don't need any background on the numbers, observations, or experiments to be able to do this.

Overall, this is simply how I my take on the question after digging a little deeper into the question. I can understand why some people would say math is a science since it is pretty much used in every natural science in some way, shape, or form. Because of this fact, there is inherently a ton of grey area in the question and thus many ways to interpret it. I don't think one answer is right and one is wrong, which you can see by the fact that I changed my mind from yes to no, and I'd love to hear someone's argument for why it should be considered one.