This is a graph... no, this is just chalk on a chalkboard, but it represents a graph. (Fall 1993, on algorithms)
This is trivial, but not obvious. (Rabin in 224r, Fall 1996)
Maybe if one of you falls off the high path and goes to law school... (1997-09-16)
(introducing probability theory) I apologize to those people who know everything, but... (1997-09-27)
It's a trivial proof, even if some of you think that you're lost.(1997-09-29)
So that's f of u. (1997-09-23)
... b_1 ... b_12. That's not a vitamin; it's the name I give to this coefficient, so don't eat it. (1997-09-23)
And now if I have an enormous p... (1997-10-14)
... and n is correct so I'm always correct. (1997-10-16)
There are many methods -- none of them as good as the randomized primality test. (1997-10-16)
That was studied by [Rabin stumbles over some name hard to pronounce and even harder to transcribe]... somebody and myself. (1997-10-16)
The probability of an error is smaller than the probability that none of us is awake and we are all dreaming this. (1997-10-16)
One plus one equals zero. We have to get used to this fact of life. (1997-10-30)
[paraphrase] Quantum mechanics is very difficult to understand, but once you understand it, it's really quite simple. (1997-11-04)
Don't write this in your notebook -- write it somewhere else because this is all complete and perfect. (1997-11-13)
I'm sure that when people were reading the hieroglyphs, they had whole theories that resulted from reading a tilde like that as a squared. (1997-12-04)
One of those moments in math which leave us mere mortals with our mouths open in astonishment. (Fall 1997, on what he was about to do)
These are not disposable diapers. (Fall 1997, on algorithms)
You'll recall from last time -- Even if you don't recall, you have no choice. I'll tell you. (1998-01-08)
Teaching this course for an entire term and I still don't understand how to move around these blackboards. (1998-01-08)
The reason I use stars [rather than numbers for equations] is that I used numbers in the last lecture and now we're getting to really essential things. (1998-01-08)
A weight is always going to be positive, even in extreme cases of anorexia. (1998-09-22)
Wow. Some people really lead an interesting life. (1998-09-24, uncovering a beautiful geometric drawing from a previous class)
You should be in a situation where you can just be woken in the middle of the night and be asked about finite fields and be able to recite everything out of your head. That's real knowledge. (1998-10-22)
Consequently, without a proof, I mean just proof by example, that holds true. (1998-11-10)
So it could be, or could it be? Well, no. (1998-11-10)
Three Indians! I don't see anything funny in that! (1998-11-10)
Now I'm becoming completely irresponsible. (1998-11-12, introducing mutual reducibility)
The theorem, I don't know exactly the genealogy, but let's say Karp, he's a friend of mine. (1998-11-12, attributing the NP-completeness of Knapsack)
It's a real riot! (1998-11-12, on solving NP-complete problems in poly-time)
1970 in computer science is not classical; it's sort of ancient. Classical is 1990. (1998-11-17)
[If P = NP,] then all of modern cryptography collapses. On this happy thought... (1998-11-24)
I'm one of those people who is just never wrong. I mean, not one of those people. I'm like everybody else. Nobody is ever wrong. (1998-12-08)
After all I said, put here the word "obvious". (1998-12-15)
I am going to show that in one round the probability of not reaching agreement is less or equal to 2. ... Yeah, we're establishing new ground in probability theory. (1998-12-17)
It's more than 10 years old. It's either classical or incorrect. (Fall 1998)
1 x M, even without Euler, is M. Lecture 5, Spring 2002, Cryptography at Columbia University
And now the cat is out of the hat... (Spring 2002)
[Of scheduling an extra class] We can never have a fit. Well, I could have a fit trying... (Spring 2002)
[Of the sliding blackboards] Sooner or later you will see me break a finger. It will be worth staying around for that. (Spring 2002)
Blah, blah, blah (Spring 2002)
[After snapping everyone who came late that they should have been on time] Don't take it seriously when I seem angry - that's just for show. (Lecture 1, Spring 2002)
Gauss could multiply two numbers in his head of, I don't know, something like 20 digits, or some other really depressing number. (Spring 2002)
So, even if Euclid had been sitting here, he would have learned something. (Lecture 3, Spring 2002)
Zero plus zero is still zero, even in this advanced class, (Lecture 3, Spring 2002)
And now I present you this theorem, which is both shocking and satisfying. (CS 226r, fall 2004)
[95% quote, 5% paraphrase, relating to Cryptographic One Time Pads] You should never re-use a pad. It's like toilet paper; if you re-use it, things get messy. (CS 220r, fall 2005)
It is customary for a student and teacher to be on first name basis once the student gets his Ph.D. Personally I found it difficult to address A. Church as "Alonzo", but I managed. So let us do it. (Email to Christopher Thorpe, spring 2008)
As the Lehman Brothers say, "Trust me." What I'm trying to say is that your future is not in financial engineering but in computer science. (CS 226r, fall 2008)
Berlekamp Massey... It's going to be messy. Not really. (CS 226r, fall 2008)