I enjoy my Math classes. I know, this is probably tantamount to a coming out of sorts, but about my feelings towards the Humble Art of Numbers (as opposed to any romantic feelings towards other members of the same gender).
I enjoy the feeling of successfully performing long division on Nth degree polynomials. I revel in finding the general solutions to trigonometric equations in terms of 2k * Pi. There’s something magically fulfilling about defining domains and ranges, all the while remembering to exclude values of x which make y undefined.
Tangents, slopes, reflections, even and odd functions, vertical, horizontal, and even the oddball oblique asymptotes… Intervals, inequalities, upper and lower bounds… Sets, sub-sets, intersections and unions… Right, obese, and cute angles (oh self-image problems), bisectors, perpendparticularity… And I have now somehow deviated from the Pureness of Mathematics.
There are all these things to learn about and use in Math, and yet, it is a hollow pursuit. At the end of the day, numbers and symbols and large operators like limit and sigma notations are nothing more than scratchings (on paper or heads). Math is about many things, and you can learn a lot from Math, like using the right tool for the job, or making sure all possibilities are considered. Math can be used to model complex situations, but can it be used to describe something as real as a single person’s entirety, wants, needs, and dreams? For that, you’re going to need a different tool.
The Math I have come to know is based on abstract examples, proofs and theorems. Sure there are corollaries and lemmas, which expand on ideas, but at its heart Math must be based on something else, some sort of Base Case, which makes sense of everything else. Just like how one must first define a “y” in terms of an “x”, Math and all its fancy rules must be based on some underlying principle, some unchanging foundation for anything to make sense.
You can talk about everything from basic arithmetic to solving complex implicit differential equations all you like, but if there are no such things as your basic rules of BEDMAS, well, things get hairy and everyone’s got their own interpretation of the situation.
You can try to discuss and graph logarithmic and exponential functions all day and get nowhere if you don’t restrict yourself to values of x and y which make sense.
Consider natural numbers. A natural number, by the binary definition, can be either a 0 (i.e. zero), 2k (i.e. even), or 2k+1 (i.e. odd). What’s k? Well, k is a natural number. Surprisingly, with these three small options, we can generate every natural number in existence. Great. But not without the base case of zero. If zero were not defined as, well… as itself, really, there would be no First K to multiply by 2 and add 1 to. The exact same is true for the definition using 0, and k+1 to generate all natural numbers.
What I’ve been trying to get at with all these examples (albeit stretched thin at times) is that there needs to be a Base Case. A single, self-defined Thing from which all other things are derived, and from which all other things derive their meaning and significance. Math is a practice of abstraction, deduction, and a lot of of other -uctions, but none of it makes much of any difference to anyone if it were all left to swim in the heads of its followers.
Math needs to have a core, some underlying non-contradiction that ensures everything that comes from it makes sense. Math also needs to make a difference in the lives of the common man. If Math wasn’t useful in our day-to-day, what’s the point of playing footsies with this Mystical Mistress if you could do the same, and get way farther, with something more practical, like say… English? And mine fails me now.
What I want to say is, succintly, Math needs to be based on something other than itself, something unchanging, constant, and eternally true, and it needs to make a difference. And so do our lives, wouldn’t you agree?