lessons learned, advice given.

on two separate occasions today i gave advice to fellow math grads about thesis advisors and meetings with advisors. it likely means that they don't follow this blog at all, otherwise they'd realise how little i know about these matters, and ask someone wiser. (;

so i did the best i could: i told them what not to do, and why it might be a bad idea, such as

if you have to, read less material in order to understand it better, because

1. inevitably you'll be discussing it with (inserted advisor's name here) and the details will matter. mathematics may be intuitive ideas, but it is also details and rigor.
   
   
2. if (s)he asked you to read it, it's probably instructive and will be useful for your later work. glossing over it now will probably mean that you'll have to learn it properly later;
   
   
3. you might as well read what you can comfortably handle, because with random exceptions, nobody ever reads as much as they expect to read.

as you can imagine, i learned all of these reasons the hard way.