Some final life lessons from grad school
I learned a lot of cool things in grad school, including life lessons. These life lessons are equally as important and as valuable as the knowledge and problem solving and technical skills I gained in my graduate program. They are as follows:
1) Be careful not to conflate academic credentials or level of education with intelligence. Some of the smartest people and people with the most integrity you will ever meet did not even go to college. The brightest students at the “less prestigious” schools are just as smart as the brightest ones at Harvard or any other top tier university.
An advanced degree is a testament to one’s persistence and hard work, not intelligence. Moreover, respect has to be earned, and a degree by itself is not a cachet. I don’t care if you have a PhD in physics; this does not mean that I should automatically respect you or your opinions (for example, this whack job has a PhD in physics). Nothing is more annoying or idiotic than someone brandishing academic credentials as if it lends more credibility to their arguments or their image.
2) Ask dumb questions. It’s totally fine. No one is scrutinizing you, waiting to pounce on you or call you out the second that you ask something that’s “dumb” or “obvious.” Sure, a lot of times, you might feel totally foolish for not seeing something that should have been immediately apparent, but this happens to everyone. No one is going to think less of you, and you won’t fully know what you’re doing wrong if you don’t clarify points of confusion, so ask away!
3) Be patient. A lot of answers will not come to you overnight. You could spend hours (or even days) working on a single problem. And after all that effort, you might still not be totally correct. It’s just the way it is.
4) I don’t know anything. I mean, I do know things, but grad school has definitely made me realize the extent of how little I know. The amount of mathematics in existence is really endless — there is a reason why some mathematicians can spend their entire lives researching one obscure subfield of math. It’s because there is still so much to be discovered about it. No one can really ever know that much, so it does not make sense to be arrogant. People who are the most arrogant generally are hiding the most insecurities.
5) Raw talent can only get you so far. Success in graduate school (and life in general) is proportionate to how much effort you want to put into it. You can be the most “naturally” smart person, but it will not matter if you only put in minimal effort. You will probably still fail. Even those who are not the most talented can succeed at something if they are willing to put in enough effort. I have taught students who were not able to grasp mathematical concepts as quickly as other students, but they worked hard and ultimately performed better in the class than those who showed more math aptitude but who slacked off.
6) Don’t try to be better than anyone else. Try to be the best that you can be, to your own satisfaction. When it comes to math, there’s always someone who is faster, more competent, more experienced, and better at it than you are. Always. I am positive there are many talented students who are better at math than I am. But I just need to do my best, and as long as I do well at it by my own standards, then it doesn’t matter a whole lot if others are better or worse at it. After all, math is not a competitive sport (though it is a grueling but fun and rewarding mental exercise!)
Some of the things above were inspired by reading Terence Tao’s blog.