"I have no problem with the Axiom of Choice. This is not what keeps me awake at night." - Constantine Dafermos, 21 January 2009
"This is the kind of book where you feel that the author is your friend. It's not the kind where he says 'it can be seen that' and then he deletes the last page of his calculations." - Brian Cole, 21 January 2009
"In Russia, there is a tradition that the professor never follows the book. Even if it is his own book, if he follows it he will get no respect. When I got here, the students thought, 'this guy is an idiot; he cannot even follow the book.'" - Sergei Treil, 21 January 2009
"When I was a student we had a saying, if something is forbidden but you really want it, you can do it." - Sergei Treil, 21 January 2009
"One of the rules is, never do computations on the blackboard." - Sergei Treil, 21 January 2009
"I knew that one of the problems on the exam was explicitly from the book, but I didn't realize that several others would turn out to be from the book. It just shows that I should have read the book more recently." - Tom Goodwillie, 22 January 2009
"You may find some books where they don't like to waste ideas so much." - Tom Goodwillie, 22 January 2009
"It's easy for me to recycle that diagram... or maybe cocycle that diagram." - Tom Goodwillie, 22 January 2009
"I should have called it I_j. I_i sounds silly." - Stephen Lichtenbaum, 22 January 2009
"If you have a space that is not complete, how do you complete it? By completion." - Constantine Dafermos, 23 January 2009
"There are serious people in Chicago and Princeton doing pages and pages of estimates, but this is complex analysis and a miracle happens." - Sergei Treil, 23 January 2009
"I remember when I taught undergraduate complex analysis, a girl thought I was a crook, kind of a used car salesman, using tricks instead of hard mathematics." - Sergei Treil, 23 January 2009
"Unfortunately -- or fortunately, depending on if you like challenges or hate challenges -- the following theorem is true." - Constantine Dafermos, 26 January 2009
"We'd better stop before the barbarians come bursting through the door." - Brian Cole, 28 January 2009
"Limits have a nice habit of not existing." - Sergei Treil, 28 January 2009
"This is a simple homework exercise for you. Let's see what the answer is. Actually, I know the answer." - Constantine Dafermos, 30 January 2009
"When you do math at a research level, you do not have to compute all of the derivatives. But if someone asks you, you have to be ready to explain." - Sergei Treil, 30 January 2009
"It seems my mind has stopped. This is something obvious. I can see it, but I cannot do it." - Constantine Dafermos, 2 February 2009
"Each of these has only a finite number of terms, so there's nothing scary about this." - Brian Cole, 4 February 2009
"We know that this converges in every single case, so I can write this down without fear." - Brian Cole, 4 February 2009
"Let me show you how you can get this formula if you don't have a book, you don't have access to the Internet, your computer died on you..." - Sergei Treil, 4 February 2009
"Every capital letter I'm using, except perhaps the one at the beginning of a sentence, is an R-module." - Tom Goodwillie, 5 February 2009
"It's not like anyone agonized over this for years. It's trivial." - Stephen Lichtenbaum, 5 February 2009
"Undergraduates are not supposed to be exposed to these constructions." - Stephen Lichtenbaum, 5 February 2009
"Maybe it's pretentious to say this, but when you compose this, you get nothing more than you would get with the product." - Brian Cole, 6 February 2009
"Now the question is, if this space was invented by Bergman, why is it called A?" - Sergei Treil, 6 February 2009
"That's not obvious. Well, it is obvious, actually; it's not as hard as I thought it was when I started saying the sentence." - Stephen Lichtenbaum, 10 February 2009
"So you use curly braces for that? I use random symbols." - Stephen Lichtenbaum, 10 February 2009
"Sorry for missing the class on Monday, but my back again completely killed me." - Constantine Dafermos, 11 February 2009
"I will reveal a secret, perhaps ahead of time." - Constantine Dafermos, 11 February 2009
"Somehow, by a miracle, we have constructed an m-tilde." - Brian Cole, 11 February 2009
"For any red-blooded mathematician, this oughta be really exciting." - Brian Cole, 11 February 2009
"I'm a little embarrassed to call this a theorem." - Sergei Treil, 11 February 2009
"I have some homework for you to hand in. Someday you may get it back; I make no promises." - Stephen Lichtenbaum, 12 February 2009
"We really want to do this for commutative rings; it isn't just a joke." - Stephen Lichtenbaum, 12 February 2009
"In honor of Riesz, I will not try to squeeze the proof into five minutes." - Constantine Dafermos, 13 February 2009
"The proof is elementary, but kind of exhausting." - Brian Cole, 13 February 2009
"A Russian mathematician asked an American at a conference, 'do you know Gilbert?' He said no, and the Russian said, 'you are not a mathematician if you don't know Gilbert.' It turned out he meant Hilbert." - Sergei Treil, 16 February 2009
"Life is quite nice on a Lie group." - Brian Cole, 18 February 2009
"I'll just say this -- you won't know what it means, but I'll say it." - Stephen Lichtenbaum, 19 February 2009
"There are just gobs of terminology here." - Brian Cole, 20 February 2009
"I know this seems sort of dreadful because it seems sort of ad hoc and not very interesting." - Brian Cole, 20 February 2009
"In calculus we have exterior derivatives and we luxuriate in their properties." - Brian Cole, 20 February 2009
"You may have noticed that I do not number my theorems, because if you are talking to someone who knows the material but has not taken the same course, you cannot say 'by Theorem 14 in my lecture notes...'" - Sergei Treil, 20 February 2009
"This is because of the Banach theorem. Oh yes, the Hahn-Banach theorem; let's not forget Hahn." - Constantine Dafermos, 23 February 2009
"For magical reasons, there is no such obstruction." - Brian Cole, 23 February 2009
"We have to pay the piper at some point." - Brian Cole, 23 February 2009
"Let me remind you magical formula." - Sergei Treil, 23 February 2009
"To prove the statements are equivalent, you have to construct a connected oriented graph of statements." - Sergei Treil, 23 February 2009
"It's not true, but it's true enough for this." - Stephen Lichtenbaum, 24 February 2009
"I don't like to change variables in public." - Jill Pipher, 24 February 2009
"We have to depart before the next class comes bursting in the door." - Brian Cole, 25 February 2009
Maybe in more prosaic language, that's all our assumption amounts to." - Brian Cole, 27 February 2009
"Gee, why didn't they come bursting through the door?" - Brian Cole, 12:03 PM 27 February 2009
"It's kind of tedious to go through the Inverse Mapping Theorem on the fly every time. - Brian Cole, 27 February 2009
"If you are in a sadistic mood, you can write this down in x's and y's and give it to your students in Math 9 to compute that the Laplacian is nonnegative." - Sergei Treil, 27 February 2009
"If I don't give a damn about the constant, then we are already done." - Sergei Treil, 27 February 2009
"You have to integrate; you have to do work. You cannot just estimate and wave hands." - Sergei Treil, 27 February 2009
"I apologize for the bad weather." - Constantine Dafermos, 2 March 2009
"This seems uninspiring but I hope it's true." - Brian Cole, 2 March 2009
"I realize the notation is about to kill us here." - Brian Cole, 2 March 2009
"The walls are about to come crashing in here... let me do one more thing." - Brian Cole, 2 March 2009
"I don't want to do lots of computations on the blackboard. It's not fun." - Sergei Treil, 2 March 2009
"Watch out for my dots and stars; they migrate from top to bottom." - Stephen Lichtenbaum, 3 March 2009
"I am sorry for saying adjoint adjoint, because I am stuck in the Hilbert space case." - Constantine Dafermos, 4 March 2009
"I thought the author's proof was not particularly transparent, but you're welcome to fight with it yourself." - Brian Cole, 4 March 2009
"This is obviously a useless concept." - Brian Cole, 4 March 2009
"Okay, we have a couple more minutes." - Brian Cole, 11:53 AM 4 March 2009
"We want to sink our teeth into what is J_1 going to be here." - Brian Cole, 6 March 2009
"When you can get a more fruitful homomorphism is a somewhat serious question." - Brian Cole, 9 March 2009
"We end up with C sub g star, which is a magical thing." - Brian Cole, 9 March 2009
"I don't give a damn about anything that happens outside my neighborhood."- Sergei Treil, 9 March 2009
"Flatness is not so exciting in this situation." - Stephen Lichtenbaum, 10 March 2009
"Now we start playing funny games." - Stephen Lichtenbaum, 10 March 2009
"In old age, you forget your spelling with e. Resolvant? Resolvent?" - Constantine Dafermos, 11 March 2009
"If H isn't closed, we're dead." - Brian Cole, 11 March 2009
"This is like the Grassmannian on steroids." - Brian Cole, 11 March 2009
"Great, so you found one more mistake."- Sergei Treil, 11 March 2009
"We used the left leg rule for integration."- Sergei Treil, 11 March 2009