“Do you prefer geometry or algebra? You can tell a lot about someone based on whether they prefer geometry or algebra.” ... He had noticed that there was a difference between people who work backward from the answer and people who seek the unknown.
I don't think he was right. High-school algebra was a set of tools for manipulating unknowns to try to learn their values. Geometry was a different set of tools, coupled with some disciplines for proving that statements you think are true actually are true--in this case about geometry, but the same disciplines appear repeatedly through the rest of math.
In math quite a bit of progress happens when someone is noodling around on a set of problems, finds something that looks like a useful pattern, and then sets out to try to prove the relationship.
Problem is, it might not be as universal a relationship as he thought. He winds up "proving it" in the old sense--testing it. Unknowns abound.
FWIW, both courses were straightforward and fun.
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