I studied commutative algebra in graduate school which is an adjacent subject to algebraic geometry. People capable of understanding Hartshorne have number sense.
Re:I am starting an AI+Education company
by aleph_minus_one on Tuesday July 16, 2024 @08:40PM
(#40981621)
I just wrote down how I feel about this topic.
Textbooks about particular areas, in particular specific topics in physics (including mathematical physics), teach me a lot about number sense (and let me feel that mine is not really good or perhaps badly trained). On the other hand, these very abstract topics feel like a quite different activity to me that is only barely related to number sense.
> People capable of understanding Hartshorne have number sense.
This can also be explained by the hypothesis that people with a strong number sense love to feel themselves challenged - thus they attempt to understand this nontrivial textbook (even though understanding it may in particular require different skills).
On the other hand, textbooks about, say, analysis and mathematical physics (both in a broader sense) - which can also be very complicated - have a tendency to demand a lot of (also long, tedious) "routine" calculations from the reader (often to do by his own). For these areas of mathematics your argument surely makes sense.