There is an almost ubiquitous misconception about what mathematics really is, and it’s a misconception that genuinely beckons a correction. I would take a guess that if the average person was asked “What is mathematics?”, they would respond with something along the lines of “well, it’s a bunch of rules that help you find certain numbers”. While this may have been a correct answer long ago, it is far from correct today.
Fortunately, what it actually is can be summarized very succinctly. Mathematics is simply the process of making assumptions and proving what follows. Hence, we all do math on a daily basis—either when talking to one another, or when thinking to oneself: “given what I know, I think that…”. This is math.
This is also why math courses through calculus are terrible—as they are absurdly misleading. Current curriculum is libelous to the discipline of mathematics and its participants, and action needs to be taken to address this.
At this point, high school language arts and composition courses may teach more math than actual math courses. Fundamental to mathematics is logic and its application in the context of sets. Logic was essentially nonexistent when I was in high school. Yet math and language arts classes implicitly assume that students have a solid understanding of it when they are asked to make arguments. Granted, as we are logical entities cognitively, we are trivially masters of logic. But in terms of conveying it communicably, improved training is necessary. I feel the overlooking of this necessity is a grave miscalculation that has hindered scientific thinking (an ability from which every citizen of the world can drastically benefit) for far longer than it should have. This needs to change.
With the termination of the military’s “Don’t Ask Don’t Tell” policy as of yesterday, I am reminded of the fundamental concept at play that delayed this resolution for so long. This fundamental concept is also at the core of many other issues: gender discrimination, racial discrimination, religious discrimination,…, X discrimination. This fundamental concept is at the heart of contemporary political partisan bickering, the wealth gap, and wars altogether. This fundamental concept is the scarcity of resources. When the set of resources available to a population in insufficient for that population, members of the population will inevitably compete for them. The ingroup bias has become the catalyst for nonuniform distribution of resources.
The ingroup bias follows from the ingroup instigation. The heuristic for obtaining resources is cooperative gameplay. We primitively wish to form alliances with people for the sole purpose of overpowering others (or groups of others) in order to ensure the acquisition of resources. This is the biologically intrinsic (and evolutionally reinforced) tendency which I call the ingroup instigation. Given the objective of the ingroup (to work together), the ingroup bias (the tendency to favor individuals in the ingroup and disfavor those in the outgroup) follows. If we assume this to be true, then the function determining which individuals will group is only governed by what best allows them to overpower other groups or individuals. By default this starts with proximity and special cases of it such as family (note also how fundamental physical forces operate). Then, once some groups gather many resources, it may be beneficial for them to team as well. This can be seen in political alliances, corporate mergers, residential segregation with respect to socioeconomic status (i.e. poor towns or rich towns),…,collisions of galaxies, etc.
It then follows that any minority or group of individuals who have less power become targets of the majority, simply because it is easy to take their resources. Whether it be a minority based on gender, race, sexual orientation, or religion, the characteristic of a group being a minority–not being in the ingroup of those with the quantitative or qualitative power–becomes sufficient for hindering their progress and in turn targeting their resources.
Hopefully one day we will realize that “potential knowledge” is a good with no scarcity that can in turn be distributed to everyone without limits. The amount of knowledge in a system will always be finite (but not constant), yet it will also always be an upper bound on usable resources in society (i.e. the amount of consumable resources in the system is dependent upon the amount of knowledge [on how to create such resources from raw resources] in the system at that time).