Mathematical musings

In this post, I mainly want to comment on what interested me in mathematics.

I was pretty good at math (i.e. basic arithmetic) in elementary school.  As best I can recall, I was attracted to it because of its perfection, compared to ordinary physical things which are inevitably imperfect.  I enjoyed the work with fractions.  But when we got into decimal fractions, that was far less attractive.  For, when doing decimal arithmetic, one is usually working with fractions and with rounding answers.  And once you round answers, the perfection is gone.  However, the infinite recurring decimals, as in 0.3333… for 1/3, was something I found very interesting.  Perhaps that was because it allowed perfection once again, or perhaps it was because of a curiosity about the infinite.

When I found out about using the symbol \pi (the greek letter pi in latex notation) that was exciting.  For it allowed me to have perfect (exact) answers, even though they could not be exactly expressed in a numeric form.

I sometimes wonder whether other people saw the same sense of perfection in mathematics.  It is perhaps part of what leads to mathematical platonism.  I may say more about that in future posts.

In mathematics, I rarely found it useful to memorize anything.  Yes, I did practice using multiplication tables, but that was only for efficiency.  I always wanted to know how things worked.  So I made sure that I understood the reasons for the carrying in addition, and the reasons for the multiplication rules.  It had to make sense to me, before I could use it.

When, in later life, I came upon the philosophers’ definition of knowledge as justified true belief, that just seemed wrong.  For me, mastering mathematics had never been a matter of acquiring beliefs.  And that view of knowledge has carried over to my ideas about knowledge other areas.