The discussion centers on whether a math major that includes courses like calculus, differential equations, and linear algebra can be considered "pure" math, with some arguing that engineering and physics majors are more "applied." It is noted that different universities may offer distinct tracks for math majors, with some focusing on proof-heavy courses. The conversation also touches on the varying rigor of calculus courses available in high schools across the US, with some students having access to advanced classes like honors calculus and real analysis. The importance of elective choices in defining the nature of a math major is emphasized, alongside the relevance of the school's focus on STEM education. Ultimately, the choice of institution and the specific courses taken will significantly influence the classification of the math major.