Filters make it easy to keep track of new questions within favorite tags. However, they do not offer a way to follow new answers. I suggest adding a tab for them:
Rationale:
The activity tab is a poor way to track new answers. It contains edited questions, new questions, and even questions bumped by Community. Most importantly, what it shows -- the beginning of text and its author -- pertains to a question, not to an answer. This is not a list of answers.
Following new answers within one's tags of expertise is the best way I know to refute misguided answers before they get accepted by the clueless OP. (In more abstract subjects like Math it's easy to be fooled by a wrong answer.) The site should make it easy for experts to correct such situations.
While it is easy to search for
is:answer [tag1] or [tag2], the search becomes awkward with a large number of tags. The search box is limited to 240 characters, which is enough for 6-8 tags in practice. With 52 favorite tags, I had to create a 1597-character search URL in a text editor.
This one:
http://math.stackexchange.com/search?tab=newest&q=is%3aanswer%20%5bcomplex-analysis%5d%20or%20%5bfunctional-analysis%5d%20or%20%5bdifferential-equations%5d%20or%20%5bdifferential-geometry%5d%20or%20%5bpde%5d%20or%20%5bplane-curves%5d%20or%20%5bdifferential-topology%5d%20or%20%5bmanifolds%5d%20or%20%5bdifferential-forms%5d%20or%20%5bcomplex-geometry%5d%20or%20%5bdifferential-operators%5d%20or%20%5boptimization%5d%20or%20%5bconvex-analysis%5d%20or%20%5bconvex-optimization%5d%20or%20%5bsubgradient%5d%20or%20%5bnonlinear-optimization%5d%20or%20%5bharmonic-analysis%5d%20or%20%5bfourier-analysis%5d%20or%20%5bfourier-series%5d%20or%20%5bwavelets%5d%20or%20%5bmetric-spaces%5d%20or%20%5bbanach-spaces%5d%20or%20%5bhilbert-spaces%5d%20or%20%5bweak-convergence%5d%20or%20%5blp-spaces%5d%20or%20%5bnorm%5d%20or%20%5bintegral-inequality%5d%20or%20%5btopological-vector-spaces%5d%20or%20%5bnormed-spaces%5d%20or%20%5bsobolev-spaces%5d%20or%20%5bholder-spaces%5d%20or%20%5bgromov-hyperbolic-spaces%5d%20or%20%5bhardy-spaces%5d%20or%20%5bcalculus-of-variations%5d%20or%20%5bapproximation-theory%5d%20or%20%5bapproximation%5d%20or%20%5bconformal-geometry%5d%20or%20%5briemannian-geometry%5d%20or%20%5bhyperbolic-geometry%5d%20or%20%5bcomputational-geometry%5d%20or%20%5bdistribution-theory%5d%20or%20%5briemann-surfaces%5d%20or%20%5bmetric-geometry%5d%20or%20%5bbounded-variation%5d%20or%20%5bclassical-analysis%5d%20or%20%5bdata-analysis%5d%20or%20%5bgeometric-measure-theory%5d%20or%20%5bmaple%5d%20or%20%5bsage%5d%20or%20%5bmatlab%5d%20or%20%5bgeometric-group-theory%5d%20or%20%5bgeometric-topology%5d
It works. But I'm not sure that experts on Christianity or Cooking would find this way to interact with the site easy and intuitive. Having it built in a filter, which already syncs with the user's favorite tags, would make this functionality more accessible.
