Math is strange. I was good in math, but did not like it much. Other members of my family saw math in completely different ways and could envision things mathematically in very advanced ways. I met an acquaintance of mine at a college visit, so we went around together. We were both on the academic track at high school and took what was called ‘12th grade math’, but not in the same class. So I knew what was taught.

The school did a math placement test, and I qualified for Math 1. (Admitted students who did not qualify took an easier Math 64, but had to pass Math 1 to graduate.). Half of M1 was what I took in HS, but I knew many students did not take that.

My now friend qualified for Math 3, which was a requirement for engineers and architects, which was where he was going. Since I knew what was taught in HS, I knew for sure we only got half of 1 and none of 2, “so how did you qualify for 3?” He taught himself calculus.

Boggled my mind. We had a very good library in the neighborhood, his math teacher told him which books to start with, and he taught himself calculus.

The range of people’s math abilities is great indeed. Some can’t get simple algebra, others invent, or discover, The Calculus.