In math, we prove everything we say. Similar to the Matrix, mathematics is a constructed system, where, in order to claim something exists, we first must prove it.
I think vision is a good analogy for describing the general population’s ability to do mathematics.
33% of Americans are legally required to wear corrective lenses to operate a motor vehicle. Another 40% wear corrective lenses some of the time. As with driving, to properly do mathematics, you need to see both “up close” and “far away”, that is, you need to 1) know the right equation, but also 2) understand its significance. Furthermore, I would claim that most STEM (Science, Technology, Engineering, and Mathematics) majors are “near-sighted” in that our education system focuses far more on “what” and largely disregards “why”.