Math - language or art or science, or neither?

Our group has spent the better part of the past three weeks untangling the role of Mathematics as an Area of Knowledge. As in true TOK fashion, we have spent a good deal of time wrestling with key issues regarding Math's nature as an academic discipline, and as such, its role in our lives as students/thinkers/tax payers. For the most part, the debate over the history of how Math came to be - as a system of knowledge - has been along the lines of the invented/discovered trajectory, with students looking at this dichotomy as rather redundant, so to speak. Namely, our group - those who see Math as a tool as well as those who see no personal value in it - tend to examine its history from the perspective of a system that could only be invented since there was a need (larger, conceptual, pragmatic) while this invention - perhaps similar to how language came to be - was deeply rooted in an existing capacity human society possessed, thus a sort of a discovery. Its beauty - aesthetic appeal - tends to remain mostly vague, perhaps as most conversations about externalities tend to end up as. 

What continues to strike me as a good puzzle to have is how strong opinions are by students who plan to join the pathway of math-infused disciplines at the undergraduate level when it comes to the role Math could serve society, yet with little causality addressed. In other words, whether we are good or not that great at Maths as a school subject seems to be linked with whether we see Math as something of a logics game - hence, quite performative and dependent on how the political North/South global divide views its role in education; in other words, the better we seem to be at it, the less we can speak about its value, and vice versa. 

Which brings me to another set of questions, mostly about the way we learn and how we see the role of the individual in this process and that of the educational system, i.e., political and social reality. Considering that we have full autonomy, and see ourselves as an almost ideal discourse-producing subject is both sweet and silly, even misguided. And this applies quite a lot to disciplines that are seen as highly specialized, and therefore not for everyone. 

Truth be told, I loved Maths in school - I was good at it; I spent little time thinking about why that was the case, or if the way I was taught to approach it was in fact too definitive, and therefore too confining. I wish otherwise for my students - for I believe there is a lot of relevant reflectiveness we all need to engage in, if indeed Maths takes a more inclusive role in its status as a school subject/foundational discipline.