Professor Sacks was the professor for Math 141 (Mathematical
Logic) at Harvard last year. The class was so laid back it sounds
like something out of Hitchhikers. Sacks also provided us with a
few great quotes. It started when he was summing up what we'd
learned about first order logic, and he said, "Now we've seen that
you can take the Peano axioms, and make a standard model for
them... you start with one, then you tack on two, and three, and
four, and..." and as he says this, he moves over one step with each
number, placing them next to each other, until about ten, at which
point he's reached the door. So he walks out the door and turns
the corner, counting faintly... after a few seconds we hear a
"seventeen" wafting down the hallway, and then a door slam shut.
The whole class is cracking up, and about 20 seconds later he walks
back in to the room with "...but we also know that you can
construct a model with numbers bigger than all of those."
Other various quotes from his more inspired lectures:
1. Somehow, the price of clarity is complexity. Wait, are there
any philosophy students in the room?
2. Now this theorem I actually am going to prove. You should
know that not one in a hundred logic professors can prove this
theorem without preparation. Now the interesting thing here
is that I have not prepared... (In all fairness, he did in
fact prove the theorem...)
3. This makes sense. This over here, this does not make sense.
That's why I called it algebra.
4. I brought this book today... a wonderful book. Because I
wrote it. How much do you think this book costs? $60? $70?
Nah. $90. And $130 in Japan.
5. The depth is the significant aspect of the length.
6. By "recursion" I mean "defined by recursion."
7. It goes without saying, but I'm going to say it anyway... I
like to say things that go without saying.
8. I was going to say "topology," but I wasn't sure what I meant
by that.
9. Theorem: I'll attribute this to Myhill; I can't imagine who
else would have proven it.
10. So this element is a smashing witness to the fact that cC is
not We.
11. Set theory. Yaaay, set theory! ...Set theory, as you might
guess, is about sets.
12. [This satisfies] every axiom which I can think of, and a few
more I'll tell you about next time.
13. Existence is a cute proof. I don't know what word to use.
Neat? Cool?... Anyway, existence is not obvious.
14. Of course, we could have introduced recursion theory that way,
by teaching set theory and then restricting ourselves to the
finite ordinals... that would have been insane.
15. Who knows, maybe this will work.
16. I hate rigor.
17. An obscure proof which I managed to present in an obscure way.
18. Mustowski was always annoyed at me that I misspelled various
Polish names -- his was easy, but some of his friends' were
impossible.
19. By induction... No, not by induction... By nothing, we have
that...
20. Absolute. Absolutely absolute. Absolutely positively
definitely absolute!
21. Good question. Why do I want to show they're equal?... I'm
completely confused.
Student: Are we in the middle of a proof?
Sacks: No, this is just another digression.
Sacks: Today we're going to do comprehension. What is
comprehension?
Student: I dunno...