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One amusing feature of math classes at the master's level or above is that they almost take pride in not motivating the subject in external terms. For example, here's a page from a canonical textbook in algebraic geometry.
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This does a good job of reminding me of how Lecture 1 in such classes often felt, which is roughly, "The motivation for this class is fuck you. Let k be an arbitrary algebraically closed field. Now..."
Which was not a problem when I had my own motivations!
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Which was not a problem when I had my own motivations!
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At some point it stopped being enough. Incidentally, I don't think my economics courses were much better in the way of giving some great external motivation: I just found a cycle of self-reinforcing curiosity that kept me happily studying that subject.
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This may even have some efficiency rationale if the purpose of the courses is NOT attracting the marginal student - as it probably shouldn't be in research mathematics, for example. It leaves more time for the hard stuff, and selects for students who have their own reasons
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It obviously has big implications in terms of WHO you get - people with a lot of "cultural resources" independent of their academic program. And in less dramatic ways, that seems true in all research subjects, not just math.
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(Math blogs improved the situation a lot in math - I found them only later, but it felt like they unlocked a secret code. It felt shocking that the information in them wasn't somehow part of the curriculum, but I guess that's just another way of saying what's above!)
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I am idly curious whether research subjects that are growing, whose main challenge is recruitment rather than sorting, are different at the front end. There also doesn't need to be any great economic reason for a subject to be this way - could be just culture!
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Anyway, in reminiscing I was struck by the intensity of this quality of math.
It also helps me understand how advanced students in my own subject probably feel when they lose motivation - it's much easier to connect with recalling my "outsider's" experience of math.
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It also helps me understand how advanced students in my own subject probably feel when they lose motivation - it's much easier to connect with recalling my "outsider's" experience of math.
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PS/ In defense of alegebraic geometry, it seems like Hartshorne is agreed to be an uninspiring prose stylist? A lapsed algebraic geometer says, "even though I no longer find algebraic geometry particularly interesting, it's more interesting than THAT."
