I have always felt that the best way to stay current with something is to be required to teach it.
I suppose part of my job is to teach the younger staff about issues in their work, but the reality is that in instrumental chemical analysis, all calculations are carried out by sophisticated software usually featuring and audit trail. Thus the conversation is general more about molecular biology and organic chemistry than it is about the theoretical underpinnings of either the instrumental set up..
As for "looking it up" that's easier than ever before. There are many reference books that I could throw away were it not for nostalgia. Does anyone ever open a table of integrals anymore?
Surprisingly, my son did take course in Mathematica from the guy who ended up being his advisor. (Nobody really uses it at his institution. ) The tenor f the course was "Everything is there somewhere if you want to find it." As it happens, my knowledge of statistics was embedded in other courses part of a formal course. Thus when I am confronting with a concept like false discovery rate in proteomic software spitting out the location of post translational modifications, I have to dig down deeper to be sure of the results.
I'm encouraging my son to TA, irrespective of his intense time constraints. Teaching is good for learning and knowing I think.