Mathematics as isolation of logical difficulties of learning
Mathematics (especially pure mathematics at the non-research level) provides a kind of "lab environment" for analyzing the logical difficulties that arise during learning. Many other subjects besides mathematics have other difficulties that make learning difficult, including:
- Dealing with nonsense (post-modernism, literary analysis)
- Grappling with counterintuitive empirical (natural and social) phenomena (physics, economics, evolutionary biology (see section 2, "Anthropomorphic Bias"))
- Dealing with subtleties of measurement, the scientific method, etc. (the sciences)
- Dealing with models of phenomena that might be wrong or simplistic (economics, social sciences)
Pure mathematics (at the undergraduate and beginning graduate levels) generally does not deal with the difficulties mentioned above. Instead, it is all about the "logical difficulties" of dealing with things like abstractions, rigorous argumentation, and the surprising connections one can find in a purely deductive environment.