Regarding “Is Math Real?”
Written as a reflection upon a review in the MAA of what appears to be a lovely book by Eugenia Chang.
To everyone who has ever been made to feel bad at mathematics. You didn’t fail math: math failed you.
Preface ibidem
Hopefully it’s obvious, from the perspective of a hacker, creator, or engineer that math is decisively “not real.” In other words, it’s a system that we created that seems, in many cases, to describe aspects of reality wildly effectively. This should not be controversial; for even Newton and Leibniz’s mathematics of calculus – now treated as gospel – is merely a system that is radically effective at describing empirical physical phenomena, such as the trajectory of a rock launched from a trebuchet.
Lest we forget this, one risks being led to feel subservient to those that came before (whether one is the teacher or student, such a reality in its totality is plain tragedy — which is sadly seemingly non-obvious to most); and of course to discount mathematics entirely is to impoverish oneself of a tremendously useful system, albeit oft understandably. Seen from this perspective, it is not mathematics that poses this challenging paradox for us, but anything systematic yet useful.
Regarding the difficulties so many encounter with mathematics, myself having been on one side and then the other – nearly failing a middle school algebra class and then “getting it” at some point – it is my hope that teachers may find themselves more compassionate; and that we may remember that although there may be something that resembles the truth, there can be multiple ways of expressing it. More concretely, it is my hope that further ways of communicating eexisting known truths of mathematics in not the ways they have been historically present, but in either a kind of synesthetic manner (c.f. Buffon’s needle for pi) or in a translational one (i.e. in the way that the same truth can be communicated in two disparate human languages, say, Greek versus Sanskrit). For we all stand to benefit from a more understanding world by helping others and ourselves to understand.