Words of Wisdom from Maciej Zworski (in Math 279, UC Berkeley, Spring 2003) [For those who care: I audited this class on (mathematical) semiclassical analysis when I was in residence at MSRI for their program of the same name. Thankfully, the program included lots of quantum chaos stuff as well...] 1/22/03: "This is a traditional example of semiclassics in 'physics'." (phrased as "quote unquote 'physics'") 1/24/03: "One of the primary purposes of calculus is to learn the Greek alphabet." "It's a formal calculation, so it doesn't matter." "When I'm at the blackboard, I find this all very confusing." "Historically, it goes back to Lagrange, so there are certainly no problems here." "Sorry. What am I doing here?" (with a variant of this later in the lecture) "This result is due to Jacobi, so it's old." 1/27/03 "Either you're used to this stuff... or you have to get used to it." (Zworski on symplectic geometry...this quote is slightly paraphrased, as I couldn't remember the exact conjunctions [etc] he used) "It's not hard, but it's one of those things that just what else could be true." (on a fact he stated but didn't prove) (Note: The following five quotes [in order of appearance] come from Zworki's derivation of the same identity.) "Simply... I am confused." (Zworski) "There's a quick way to see it if one just stares at it for a moment." (Zworski, on an identity that appeared during the derivation) "This is just the definition that used to be here [indicates a section of the blackboard that by then contained something else]." (Zworski) "Is this supposed to follow from what I wrote over there?" (Zworski) "I withdraw my request to prove this." (the prof auditing the course [L. Craig Evans] who asked that Zworski prove the identity rather than just state it) 1/29/03: "Now I want to prove something which is actually, you know, pertinent to this course." 1/31/03: "This is an easy exercise... Well, it's an exercise. I haven't actually done it, so I don't know if it's easy." (on an omitted proof) "It was meant as a generic derivative." (on putting a prime rather than specifying what he meant) "I'm not a numerical analyst. I'm an armchair numerical analyst." 2/3/03-2/7/03: I was out of town, so quotes were not tabulated. 2/10/03: "This convention is not just purely to confuse oneself." "If there is one thing on which people agree, it's this." (on the correspondence between commutators in quantum mechanics and Poisson brackets in classical mechanics) 2/12/03: "My signs are not working as well as I was hoping." (in the middle of a calculation) "I can't find my sign mistake." (at the end of a calculation and a minute or so of pondering) "It could be worse. There could be an odd number of sign mistakes." (Craig Evans) "Oh well. Let's just destroy the evidence." (Zworski, after a couple more minutes of pondering and just before erasing the board of everything but the answer) "I fear that if I started with the simpler way than I could never convince you to sit through the difficult way." "I will do it and then I will worry... I will worry at home." (on a factor of h that same to have switched from the denominator to the numerator) "Somewhere along the way it switches sides." (on the same factor...this reminds me of stuff that occasionally occurred on my old hw assignments) 2/19/03: "I know! I know! [brief pause] No, I don't know." 2/26/03: "We start the proof by saying 'indeed'." "In an ideal world... I guess it wouldn't be an ideal world because it would cut some of us out of the profession. In some sort of world..." "We use the a_\alpha, which somehow mysteriously disappeared from the board." "That's obvious... Why is that obvious? [mutters a bit and then pauses] Well, anyway, it's a fact from outside my area of expertise." "Who is fascinated by this lemma and couldn't imagine life without proving it?" "My hand can't go through this wall because it's exponentially small." 2/28/03: "In case you get bored with today's lecture, you can look at the coming attractions." "The thing is so elementary that I could not solve one of the problems I wanted to explain, so I'll assign it as an exercise." "I've actually done this, so I hope it will come out right." "I can do it. I just don't know what's going to happen. [brief pause] Oh, this is fine! What am I saying!" "I don't want to prove it, but it's easy to believe it. The physicists have been doing it for a long time." "I'm worried about my constants, but they must somehow work out at the end." "Now I can return to something more advanced. I'm more comfortable with that." "I can add an imaginary part to \chi, and then I could have avoided my sign problem." 3/3/03: "I proved it by inspection." "This is a nontransitive equality sign." "I want to get as close to writing this as I can get." "We'll use the time-honored method of adding and subtracting." "I'm out of time [brief pause] conveniently." 3/5/03: "A certain fraction of them are crazy and can't teach anything." (just before class; Craig Evans on the Berkeley math faculty) "Let me say some cliches about quantum versus classical pictures." "I'll maybe discuss more about its history when I learn more about it." "Steve... I'll cite you for contempt." (Zworski trying to get Steve Zelditch to stop talking during class...he admitted watching "Law And Order" the night before) "I'd use Beals' lemma, but we voted against it." "It's obvious... I didn't even bother to write it, so it must be really obvious." "I was trying to finish, you see, and that's always a problem." 3/7/03: "Since there's no homework in this course, we might as well have a friendly discussion." "Well, let's hope it will work out somehow." 3/10/03: "Things are going to get worse... Or better, depending on your point of view." 3/12/03 (seminar talk): "If there is no other verification, then the method is clearly successful." 3/12/03 (class): "Again, if there's a mistake... this is coffeehouse mathematics." 3/14/03: "That is just straightforward in principle." 3/17/03: "I don't want to give lectures on non-optimal estimates. We have our standards in Berkeley after all." "It's going to get worse. You'll see. I'm going to hit you with something really nasty in a moment." "This is an exciting--if almost impossible--area of research." "Maybe this goes away. I didn't really do the computation. It must go away." (Zworski then erases a phase factor from the board.) "There's no need to do any finger tricks because it's evident that these measures are different." (This caused me to wonder what a 'finger trick' was, but I didn't express my thoughts aloud.) 3/19/03: "Then I got confused and decided not to bother." "It's a nothing assumption and a sort of nothing result." "Why do you bother with this?" (Steve Zelditch [a prof sitting in on the class], on something other than what's in the quote above) "Well, I bother because I'm in charge here." (Zworski, answering Zelditch) "As confirmed by local experts, any way you do it will give you this [indicates something on the board] and if you do it my way will (sic) give you this [indicates something else on the board]." (continuing the above debate) 3/21/03: "The relationship between these two operators is obvious, whatever it is." "It's a theorem that you only need three quantifiers ever, and I always have at least five." "Is everybody convinced by this hand-waving?" 3/31/03: "How should I do this in a more intelligent way?" 4/2/03: "Steven wants to lecture. He's a professor." (Zworski's comment after Steve Zelditch persists in having a private [mathematical] conversation with a nearby graduate student) "This is not a linear algebra course." (Zworski) "Well, this is linear algebra." (Zelditch, answering quietly) 4/4/03: "Steven has something to say?" (Zworski, on seeing the expression on Zelditch's face.) Zelditch's frown becomes deeper, so Zworski says "No? That's unusual..." 4/14/03: "Steve, you can't control yourself." "I'll do it Steve's way, since he will not be pacified any other way." "I don't want to repeat the question. I want to finish the proof of Lemma 1." "Maybe there are some problems, but if nobody is going to notice, I'll avoid them." 4/18/03: "I don't want to get into theological affairs on Good Friday." "Back then I was trying to be very careful and wrote down all the details." 4/21/03: "I will probably not finish, so I'm fine." 4/23/03: "I thought it was some sort of supervision." "This was left as an exercise for the truly enthusiastic student." "This is a very fluid way of thinking." "At some point, analysis breaks away from algebra, and--to become algebra--requires a sort of fluid way of thinking." 4/25/03: "Who can guess my mind here?" "This is terrible notation. What can I do about this? Let me not write it at all." "That's the point of this theorem. It's trivializing linear PDEs." 4/28/03: "I'm somewhat short of letters here." "Life is a system...apparently." (said in a scornful tone) "I'll present an example rather than discuss it precisely." 4/30/03: "I proved it in class, so I did it of course." "It's not a problem. It's a fact of life." "Since it's the last few lectures, one can sort of digress freely." "It's not so obvious. I got tenure at MIT for proving that." (said by Melrose [Zworski's thesis advisor] when Zworski mentioned a result that was seemingly simple that he couldn't prove) "An exponentially small error is, you know, really very small." 5/02/03 (last day of lecture): "This is more like a community service on the part of the authors." "I betrayed my statement. G is now a function. [pause] But this is for illustrative purposes only." "In this discussion, I certainly don't need it. Maybe I never need it. We'll see in a moment." Note: Later that night, there was a wine & cheese party. I didn't end up showing up---that stuff is way too upper class for me---but I imagine there may have been some nice witty remarks from there as well. 5/13/03 (from a talk given by Zworski at MSRI) "If they know any, they know more than I do." "It's only for talks that I'm allowing myself such lapses as the use of distributions." "If I knew, I wouldn't be giving talks on this. I would be doing it." "I already erased it, so I don't need to make any apologies." "I think even the constants are correct, so it's a real proof." 2/20/07 (from a seminar Zworski gave at Caltech) "It is a theorem from algebraic geometry that all log-log plots look like a straight line."