Sophomore. Currently reading the manual to this very big machine.
"It is a deeper subject than I appreciated and, I begin to suspect, deeper than anyone yet appreciates. To see it whole is certainly a daunting, for the moment even impossible, task." (Robert Langlands, writing about the theory of automorphic forms.)
"Understanding what a theorem means is a prerequisite to understanding its proof." (Contemporary Abstract Algebra, pp. 82, Theorem 4.3.)
"Better known for other work." (Lara Pudwell, after referencing a result due to Ted Kaczynski.)
And from this Quora Q&A that was one day randomly recommended to me:
Q: As a professor, has there been a student you instantly recognized as a genius in the first week of knowing them?
A: Certainly. I have been doing part-time university teaching since 1977. Some symptoms of success:
- Student is in class on time.
- Student sits in front row if at all possible.
- Student arrives to class prepared with textbook, notepad, pen or pencil, anything else required.
- Student asks questions like “I don’t understand the third paragraph on page 34. Could you explain it please?” (Very likely there’s a slip of paper in student’s textbook at page 34.)
- Student does not ask questions like “Do we have to know this for the test?”
- Student comes to office hours and/or asks questions by email on the course website.
- Student does not address me as “Professor Edwards”.