As we go through grad school, we all spend years learning new things but, if you’re anything like me, you don’t really feel any “smarter” (whatever that means). I have been taking classes, studying for and taking prelim exams (see Shelby’s post here for some stellar study tips!) but I still don’t feel smarter.
Gaining knowledge is difficult to quantify. If I solve a homework problem, I have learned something but there is always another problem waiting for my attention so these small victories are rarely, if ever, celebrated.
So how can we remember that we are getting smarter? For me, the most satisfying way is by helping other people.
When a newer-than-you graduate student asks you a math question and you can provide some insight, it feels awesome! There was a time you didn’t know the answer and now you do and you can pass that knowledge on to someone else. If that’s not evidence that you are getting smarter, then I don’t know what is.
Next time you need an academic pick-me-up, see if there is someone around that you can help get unstuck. You might gain a new friend and some self-confidence!
If you have other ideas for noticing your mathematical progress, post them in a comment!