Had a quick discussion on App.net about studying higher mathematics and what the point was. I got a lot out of studying mathematics. Now, when I talk about higher mathematics I’m talking about things like multi-variable calculus, matrix algebra, and advanced statistics. You real math folks would scoff at those being “advanced” but they are just a bit more than most undergrads study I think. In any case, this is how and why I studied those thing. Oh, and what I got out of them.
I think the first actual mathematics I did was in 9th grade. What I mean is that it was the first time I had to think mathematically instead of just following an algorithm. It was an intro to geometry class. We started with basic logic, truth tables, basic proofs. I loved the entire course. The rest of high school slowly drained me of any interest I had in mathematics. By the time I limped through my analysis class in 11th grade I was done. It had stopped making sense to me. Like most kids my overwhelming question was, “Why in the world do I need to know this stuff? I’ll never add an infinite sequence or find out what the limit of something is.”
I proceeded to major in film and photogtraphy in college. Was not required to take any mathematics and I didin’t take any. Why would I? One thing I did take as part of my religon/philosophy minor was logic. It was an intro to symbolic logic course and it brought back all of the warm feelings I had in my geometry course. I did really well in it and have made good use of it all through the rest of my life. It was there that the then arbitrary sounding rules of association that were covered in 8th grade made sense to me.
I got my BFA in ’94 and proceeded to join the working world. The most complicated thing I did mathematically was to calculate sales tax. 4 or 5 years out of school I began to read voraciously again. Mostly nonfiction. Read several books on the history of mathematics. I have no idea what prompted that. There could have been a very good reason for it but it was probably just a whim. In any case, I really enjoyed them. There wasn’t actually any mathematics in them, they were really histories of thought. How thinking about things like the Arabic number system, zero, negative numbers, and imaginary numbers came about and how folks tried to make sense of them.
My next purchase was volume 1 of a three volume set entitled Mathematics; Its Form, Content, and Meaning. Why in the world would I buy that? I read the introduction while sitting in Barnes and Nobles. Those 30 pages were able to make sense of my three years of high school math courses. All it took was 30 pages. I’m still a little bitter about this. Who knows what I might have done if I managed to understand and enjoy mathematics in high school… I was never really able to connect the dots between algebra and geometry and into mathematical analysis. 30 pages was all it took.
That was the last thing I did with mathematics for 7 or 8 years. When I decided to go back to grad school for architecture I knew that I would need calculus. When I decided to go for an economics PhD instead I knew that I would need a lot more math than just a calculus course. I took pre calc, calculus 1 and 2 (8 credits worth all told), matrix algerbra, and statistics 1 and 2. I eventually took an intro to econometrics course (basically a little more advanced and applied statistics course) and I learned multi variable calculus on the fly in a graduate econ course.
I did pretty well in all of them. Well, that last course where I had to learn multivariable calculus and the course’s content at the same time almost killed me but the rest were fine. I can honestly say that I have never had to use any of the mathematics I learned since I got out of school. I’m still really glad I took those courses though. Why? What changed between high school and grad school?
One of my guiding principles in life is that the more you know, the more you can know. True to form, it really wasn’t possible to learn the economics I did without knowing the math as well. So there’s that. Mathematics can open up new fields of knowledge for you. On top of that, mathematics can open your mind to things that you wouldn’t have thought were related.
For example, studying infinities made some spiritual and philosophical concepts easier to grapple with. Learning that some infinities are constrained while others aren’t, learning that there are some infinities larger than others, and learning that anything divided by infinity was equal to zero all blew my mind. More importantly those lessons loosened up some mental blocks I had when it came to understanding eternity, quantum mechanics, and some other tricky philosophical issues.
My econometrics course was the culmination of my statistical studies. We spent a lot of time agonizing over the importance of truly random samples, how safe your assumption over how the underlying data fell across a normal distribution was, and how to minimize likely errors in estimating the central tendency of a data set. All great statistical knowledge to be sure but it also taught me so much about assumptions we make when making decisions, the value of realizing that things may not be the way they look at a casual glance, and the importance of starting with good data.
There are tons more but basically it was very easy for me to generalize the lessons I got from my mathematics courses to many other aspects of life. Usually it wasn’t the minutia of the problem solving that were important but rather the underlying principles that made all of the mathematics possible. Turns out they make other kinds of thinking possible too. Mathematics has really enriched my life in ways that nothing else could. While I’ve never had to find the second derivative of anything in real life, and I doubt I could do it now, I’m so very glad I know what it means.