This is certainly not the definitive collection of all that has been said by our professors, but then, as Loic Dubois pointed out, that’s life.
Not all of these are first hand.
1) If there is any justice in the world, then this should be the derivative!
2) I don’t know why I am doing this. (on the theorem he was proving)
(Vemuri, during his course on functions in several variables)
3) Ignorance is not a crime, ignorance of ignorance is.
(Ramanan, in the Global Calculus course, when the students failed to reply clearly whether or not they knew some particular theorem)
4) Here is a similar one I found when I was googling to see if Ramanan was just quoting somebody -
To be ignorant of one’s ignorance is the malady of ignorance.
(A. Bronson Alcott)
5) This corollary is proved by staring hard at the blackboard.
(Nagrajan, humouring us when we failed to prove a relatively simple corollary in the classroom and sought refuse in staring vaccantly at the blackboard as if we were going to come up with the solution any moment)
6) But what can we do? It’s a theorem, it is true! That’s Life.
(Loic Dubois, to Anirbit, when he insisted that the inverse function theorem (or was it the implicit function theorem? I wasn’t there.) could not be true because some jacobian somewhere was not symmetric.)
7) The purpose of mathematics is data collection.
(By P. J., apparently in a workshop in the AMS-India conference.)
8) Pi meson is a recognized and a perfectly respectable particle.
(Prof. R Parthasarthy in a quantum mech class when Anirbit said that there is debate going on over pi meson being a particle.)