- .. 68 references and counting,

which means i've reading reviews, checking up on facts,

and occasionally hunting down and browsing through articles.

there's a lot i never learned.

i'm not a very well-read mathematician .. not by my own standards, at least. sometimes i wish i were born earlier, when the analysιs of metric spaces was in its true nascence or before.

this field follows a long history, from many traditions.

when i was a graduate student, it had already begun to take shape. subsequently one can now train a student in purely metric ways and avoid classical formulations altogether .. not that one*should*. - for example, in heιnonen's
__lectures on analysιs on metric spaces__, the first discussion of capacιty (chapter 7) doesn't really do justice to the history. by this i mean that the "mod=cap" theorem feels tautological. the definitions make it so.

in contrast, at the time it required nontrivial efforts by gehrιng and zιemer to prove the "mod=cap" theorem in the classical setting. the point is that one had to construct a function with the right*gradιent*, not just an upper gradιent ..

.. never mind the rich geometry one can do with capacities. in some sense, they are the analytιc cousins of hausd0rff measures; you can even study rectifiabilιty of sets in terms of capacitιes. - i've been feeling the same way about many other topics, which puts me at an impasse:
- there's no time for me to re-learn the past. there's two more years of postdoc left, and one more year before i fill out the job applications.
- without some awareness of the past, and how some constructions came to be, i have that much less intuition with how to proceed, much less pose well-motivated problems.

if you learn only axiomatic definitions, then how do you escape pseudo-problems arising from the continual manipulation of axioms?

oddly enough, i had meant to write this not to as an uneasy invective, but as something positive. what i really wanted to say was this:*the more i read about them,*

the more i am impressed with euclιdean spaces.**(-:** - there's no time for me to re-learn the past. there's two more years of postdoc left, and one more year before i fill out the job applications.

## Wednesday, September 30, 2009

### in which, not being well-read, i am sidetracked by reading.

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