by Brian Katz
A few days ago, Jo posted the following question (or anguished cry) under “To Post or Not to Post” below: “Is it normal to be in second year graduate school and about 30% of the time be utterly confused?”
In short, yes it is normal to be confused a fair amount as a graduate student. At the end of approximately 5 years the strongest claim you’ll really be able to make is that you’re the expert in a very narrow question and that you’re likely to understand nearby questions. The faculty with whom you interact have been doing this for much longer, and in that time they have learned far more than content. They have learned coping mechanisms for confusion, they have learned unrelated facts that support an entirely different kind of intuition, and they have changed their standards for what is appropriate to expect of themselves in terms of understanding others’ presentations.
I see two main reasons to expect graduate students to be confused.
(1) Mathematics is much like a language. Would you expect to immerse yourself in a culture that spoke a new language without there being a period of discomfort? Moreover, would you feel comfortable claiming that you were fluent if you hadn’t been immersed? So what I suggest, and what I have suggested to my mentees for years, is to go to seminars and classes that you may not understand. Try hard to understand, but when that breaks down, simply try to understand how the experts are using the terms, what value they are attaching to certain goals or processes, and something basic about how they fit together.
(2) Although you have taken “Math” classes since you were in elementary school, you have only recently been introduced to Mathematics as is is known to practitioners. The material you have learned is complete revisionist history. It was neither created in the form in which it is currently taught to young people (0-22 years old), nor is it created in the order in which it is taught. There are hundreds of thousands of people who have devoted their lives to structuring basic mathematical ideas in a way that all citizens can learn and use it. But now you are hoping to answer a new question (or heck, find a new question), and the old skill set is close to inapplicable. In short, sometimes I miss tests: straight-forward goals set by someone who is sure that I have exactly the skills needed to succeed (and has primed me to chose those skills instead of others).
I’m in no position to tell anyone if grad school is right for him/her, but I hope it helps you to realize that you are functionally entering a new discipline that uses a language only slightly familiar to you, and as such you should adjust the standards that you have set for yourself.