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mathwonk
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happy birthday Gib Z! I first read Lincoln Barnett's "The universe and Doctor Einstein" at about 15, but knew nothing at all of calculus, so you are way ahead of me.
You haven't learned differentials yet. :tongue: (And the chain rule is even more obvious in differential geometry!)Gib Z said:Well then its nice to know I have a small chance of one day becoming as knowledgeable as yourself :D
Ahh feels a little lonely to be on a physics forum on the morning of my birthday, no one at home...but o well, andytoh, i know all of those fundamentals, however I am not 100% sure I have the formal definiton of a limit in my head...and also, somethings that worries me, I understand, but don't like, using the formal limit approach to differentials, I prefer viewing them as infintesimal quantites, helps me understand, rather than just calculate. I find it more intuitive, and makes the chain rule a breeze :D.
mathwonk said:i also have worked in a somewhat narrow specialty most of my career ...also sometimes you get bored being specialized .
Tom1992 said:so what does a specialist mathematician do when after several years he gets bored in his specialized area? can an abelian varietist suddenly become a number theorist like you suggested?
Gib Z said:Study mathematics for the beauty of it. ...take the time to appreciate it.
mathwonk said:i certainly don't know all that stuff, especially not the pde...
mathwonk said:i have used the heat equation in my research.
mathwonk said:i do get bored sometimes with my speciality. it does seem possible however to switch to number theory, from abelian varieties, since those subjects are closely related.
also algebraic geometry is so broad, that moving to many other fields, like diff geom, diff top, several complex variables, commutative algebra, number theory, maybe algebraic topology, or even mathematical physics such as string theory or quantum field theory, is quite feasible.
i have friends who have done such a transition.