Discoverd or Invented...or Both?

Having math as the minor to my physics major, I never progressed deep enough into my mathematical studies to get to the meaty philosophical issues we are faced with in this week’s readings. However, I have often pondered on my own whether mathematics was invented or discovered, so I am excited to finally gain some real insight from scholars within the field. As I progress through my Masters studies I am becoming less and less comfortable with the objectivist view that reality is “out there” as an external entity. Consequently I intuitively reject the romantic nature of universal mathematical truths discussed in the first reading. True, we do see evidence of mathematics in physical phenomena such as elliptical orbits and fractal shapes in leaves. But is this really evidence that we are slowly “discovering” a universal truth? Or have we simply “invented” a working conceptualization of such phenomena? I feel the latter is more aligned with my developing philosophy of education.

I found the Reuben Hersh interview, perhaps my favorite of the three readings, to be quite fascinating. I definitely had an “Aha!” moment when he declares that things don’t necessarily have to be either internal or external, but can exist as social beings, or as he states, “part of human consciousness.” Here I am struggling with this discovery vs. invention issue, all the while never considering the possibility of it being both somehow. It’s a strange concept to wrap your head around, but I find the easiest way is to use the parallel of money, an example used by Hersh. Money is only real because we as humans say it is real. We can look at mathematics in the same way as only being useful because we say it is useful. The whole issue is still kind of fuzzy, but one thing I think I can commit to is that mathematics is a human activity, and would not exist without us. I also found his conception of good math teaching very valuable and in alignment with my currently held ideals. A teaching style based around interaction and communication sounds appealing. Starting with examples, a question instead of an answer, is a very practical piece of advice as well.

Brent Davis offers up some rich food for thought in our final reading for the week. What if we “are not converging onto a totalized knowledge of the universe?” What if mathematics is a tool that allows us to perceive the tiny percentage of possibilities that make it to consciousness? Mathematics has allowed us to conceptualize so much more than our ancestors of two hundred years ago. But whether these conceptualizations are snippets of universal truth depends on your philosophy. I am reminded of the example given in ED 6100 to illustrate the point that a theory need not be real. No one has ever seen an electron, but it is widely accepted that they exist. The theory serves its purpose until a better theory comes along. Tomorrow we may uncover evidence that the whole idea of electrons is no longer accurate. That said, can everything we perceive as scientific and mathematical truth potentially change at the drop of a hat?