Friday, December 11, 2015

Was math invented or discovered?

In our last class of the semester, we were asked two questions: is math a science and was math discovered or invented. We then went on to have a discussion on whether or not it was a science because the class was much more split. For the question of was math discovered or invented, basically everyone in the class said it was discovered except me and like one or two other people. I thought I'd make this blog post to share my thoughts on why I think it was invented.

I think the biggest influence for me is what I attempted to describe in class, and I'll admit didn't do a very good job vocalizing my thoughts. I personally feel that math is extremely similar to something like language. Early civilizations needed a way to communicate with each other and eventually different languages were born. In a similar fashion, I feel like mathematics came about in a way close to this. I will say this is purely my thoughts and for all I know they could be completely wrong. However, I think earlier people needed a way to describe how many of something they had or a way to describe how much they owed another person so they invented certain ways to say these things. As a result mathematics was invented as a tool to get fix certain problems they had.

On the other side, I will have to say that the biggest argument that would sway me into thinking math was discovered is how did people invent all these crazy theorems and find all these interesting patterns, like prime numbers. It seems ridiculous to say someone invented all of these crazy ideas in mathematics.

Even though I say math is invented instead of discovered, I would have to say that I lean more towards the middle of the spectrum. I understand there are valid reasons for both arguments and they both make a lot of sense. Do I think that it really matters if math was invented or discovered? No not really. At least to me, I can appreciate and use mathematics in my life without really caring how it actually came about. Others might be more concerned and have stronger opinions on the matter. If it were to come out tomorrow that math was discovered, in no way would that change my opinion of mathematics, and I'd still continue to enjoy it.

Wednesday, December 9, 2015

Emmy Noether

So this is a pretty late blog post but I still thought I'd share it with you guys. A while back we talked about Sophie Germain and her contributions in mathematics. The biggest thing that stuck with me about her life was how difficult it was for her as a female mathematician. She went so far as signing all her papers as a guy just in case people wouldn't respect her findings if they found out she was a girl. That got me thinking about how many female mathematicians I know about, where I came to the startling realization that I know absolutely no female mathematicians. Because of this, I thought it would be interesting to read up on some and pick one to share with all of you.

Emmy Noether was a German mathematician born in 1882. Growing up, her father was a mathematician at the University of Erlangen where she attended many classes. After finishing at the University, she went on to work at the Mathematical Institute of Erlangen. She worked there for seven years without pay, similar to many other women of the time, then in 1915 she was invited to join the mathematics department at the University of Gottingen. Most historians break down her contributions to mathematics into three different periods of times (Wikipedia).

In this first period (1908-1919), she worked in many different fields of mathematics. One of which is in algebraic invariant theory. Some of her work in this field included expanding off the ideas of Paul Gordon, "the king of invariant theory," by making it possible to study the relationships between different invariants. Also during this first period, she worked a lot in physics. With her work in physics, she proved her Noether's first theorem which solved a problem with general relativity, a geometrical theory of gravity (Wikipedia).

During her next two periods, she made a ton of contributions to abstract algebra. First, she published a paper in which gives one of the first ever formal definitions of a commutative ring. Also in this paper is the Lasker-Noether theorem which basically generalizes the fundamental theorem of arithmetic. She is also credited with the ideas that serve as the foundations for algebraic topology (Wikipedia).

Overall, I found it rather interesting to learn a little more about someone who had seemingly endless contributions to basically every field in mathematics and is yet never even mentioned in any math class I've ever had. I know its hard to recognize every single mathematician, male or female, but I do think classes should at least try to incorporate some of the leading females of the time as well as their male counterparts every once in a while. At least after writing this blog my count of how many female mathematicians I can name has gone from zero to two.