For example, in linear algebra you might have a feeling about some property of a matrix but then you actually have to show it with math.
I would distinguish between “I have an informal proof sketch, or idea for why a theorem should be true, and now I must convert it to a formal proof” and “I am looking at some piece of reality, and have to create mathematical definitions that capture that aspect of reality”. These might be sufficiently similar that practicing the former helps the latter, but I suspect they aren’t.
Or more relevantly, in Optimal Policies Tend to Seek Power it seems like the definition of ‘power’ came from formalizing what properties we would want this thing called ‘power’ to have.
I agree this is a good example of formalization, but it’s not an example of “studying math”?
if you think there are other useful ways to develop this ‘formalization’ skill.
I don’t really know. Maybe some kinds of economic modeling? Though I haven’t done this myself.
I would distinguish between “I have an informal proof sketch, or idea for why a theorem should be true, and now I must convert it to a formal proof” and “I am looking at some piece of reality, and have to create mathematical definitions that capture that aspect of reality”. These might be sufficiently similar that practicing the former helps the latter, but I suspect they aren’t.
I agree this is a good example of formalization, but it’s not an example of “studying math”?
I don’t really know. Maybe some kinds of economic modeling? Though I haven’t done this myself.