The Wisdom of Hendrik W. Lenstra, Jr.

   One of the best lecturers in Berkeley was Prof. Hendrik W. Lenstra, Jr. He was also one of the funniest. Here's a collection of some of the funny remarks he has made when I've been there. I hope to add to this list as more funny things of his come my way.

As heard during the Department Colloquium, Fall 1994

• "So, Cebotarev had to carry water and cabbages from the lower part of Odessa to the higher part of Odessa. Which is, of course, the most difficult direction."
• "The next important date in Cebotarev's mathematical career came in 1927, when he did not prove Artin's Reciprocity Theorem. [...long pause...] Perhaps I should explain."

As heard in Math 274, Fall 1995

• "So... I'm competing with the Office Draw now. I better say something interesting then."
• "Who doesn't know what a local ring is? Don't be shy... [Student raises his hand] Learn it!"
• "Separated, which means something you find out in Hartshorne."
• "A discrete valuation ring, sometimes abbreviated dvr by people who are lazy... [long pause] or who want to save chalk, like me."
• "You take Z, and you choose your favorite prime number, which is 37."
• "So h(x) must be the inverse of zero. This is a very big problem for x, which decides to solve this problem by ceasing to exist."
• "So our prime ideal p is maximal. We change its name to m, which is important, as [the] Theorem [we want to apply] only works when we have maximal ideals which are called m."
• "Expansion in Zp is just like decimal expansion in Z, except that 10 is not prime and the expansion goes the wrong way."
• "You pick your favorite real number bigger than 1, and that number is 2."
• "`Spec' is pronounced `spectrum', with a small `s'."
• "Proving this requires so much notation that you don't want to be seen doing it in public."
• "The textbooks on Galois Theory that you will write will explain it in this way, which I'm just now going to explain."
• "Later we shall see... I don't know exactly how late, maybe just as soon as the course is over."
• "I do not guarantee that what I'm about to say is true, but it should be helpful to those of you who have, amazingly enough, learned something outside of this class."
• "Two means one plus one."
• "That would be an interesting problem to think about. Of course, the first thing to do is to turn the library upside down and see if something falls out."
• "They are not like negative numbers, which as you know don't really exist."
• "Adèles. You put the accent there if you want people to know you speak French."
• "Anybody can define his own hat."
• "Isn't that clear from the syntax of my sentence?"
• "Take a very negative D. Very negative means negative and that makes my proof work."
• "I cannot help this [bad notation]. I did not create this part of the world."
• "There is one very convenient property of the number zero, and that is that non-negative integers cannot be smaller than zero."
• "If you believe this... and you should believe it, since you did not protest when I proved it in the first place."
• "If you do not complete then this [theorem] is just completely wrong. Sorry about that."
• "If you want to distinguish an Algebraic Geometer from a non-Algebraic Geometer, just look at the ease with which he talks about line bundles. I'm not an Algebraic Geometer, but I've been practicing in front of a mirror for the last two weeks so I can pretend I'm at ease talking about them."

As heard in the Graduate Student Colloquium, October 15 1996

• "Any arithmetician from the street could do that."
• "The proof is natural in the sense that after seeing it you'll say you could have invented it yourself."
• "Archimedes, in a Letter to the King - that's what papers were called back then..."
• "That's difficult: it is four times three plus one; let's say it's 13, at least for today."
• "The problem with wrong proofs to correct statements is that it is hard to give a counterexample."
• "The art of doing mathematics is forgetting about the superfluous information."
• "Most square free numbers are non squares, except for 1; and 1 does not tend to infinity."

As heard in the Number Theory Seminar, December 4 1996

• "If G is trivial, then this talk collapses."
• "Suppose the Martians defined the complex numbers by adjoining a root of -1 they called j. And when the Earth and Martians start talking, they have to translate i to be either j or -j. So we take i to j because I think that's what the scientists will decide."
• "But it was later discovered that most martians are left handed, so the philosophers decide its better to send i to -j instead."

As heard in the SIMS Colloquium, July 17 1997

• "If you solve a problem that has been around for a couple of centuries, you should replace it by another problem to give other people something to do for posterity."
• "I think Andrew Wiles is working on a problem he can claim he solved, but lost the solution in a computer crash."
• "I'll show you how to discover all of this by yourself, assuming that you are Fermat."

As widely reported in the Berkeley Math Department, c. 1997.

• [Seminar speaker has stated a theorem incorrectly; he is trying to remember what the hypothesis should be to make the statement true, and muses, 'What do I need to do to make this statement true?'] "Well, you could always put a Not in front of it."

As heard in the AMS-MAA Invited Address, Harmonic numbers and the ABC Conjecture, San Diego, January 8, 2002

• "Nowadays, when a Number Theorist applies for a grant, he says that Number Theory is used in cryptography, and so doing Number Theory is good for National Security. Back then, since it was before the discovery of America, they said Number Theory is used in music. But I won't comment on the progress of civilization since then."
• "The name of the ABC Conjecture is derived from the equation a+b=c. If Masser and Oesterlé had started somewhere else in the alphabet, it might have been known as the XYZ Conjecture. And if my trip to San Diego had been sponsored by the Royal Dutch Airlines..."
• "Recreational Number Theory is that branch of Number Theory which is too difficult for serious study."
• "A mathematics lecture without a proof is like a movie without a love scene... This is already my third proof, make of that what you will."

As heard in the Invited Lecture, Pi in de Pieterskerk, AMS Banquet, San Diego, January 9 2002

• "Since this is an after dinner speech, there won't be more mathematics than there is 'pi' in 'de Pieterskerk.'"
• "This date [1616] is wrong, since van Ceulen died in 1610, and we may assume he did it [calculated several digits of pi] during his lifetime."
• "If there are experts in prime numbers, then there certainly must exist experts in English travelers to Leiden in the 17th century."
• "Everyone had to be there at 19:45 and wait 15 minutes so the Prince could make an entrance. Well, that is the way it works in our democracy."
• "We needed to figure out how to unveil a monument. First we thought we could go to the bookstore and buy a book 'How to unveil your own monument', but no such book existed. So we then thought we would consult Holland's leading experts on unveiling monuments, namely the Royal Family."

As heard in the AMS Colloquium Lectures, Joint Mathematics Meetings, San Antonio, January 12-14 2006

• "Being an uncountable field, we cannot hope to represent all of C, so we should consider it as having some sort of dim existence far off in the distance."
• "If I had prepared my talk on a laptop, my last statement would have been printed in red and would now be flashing at you."
• "[The symbols K(\/K*), K{\/K*}, K[\/K*]] all have different meanings; they are not merely flowery variations in my mathematical writing. I sincerely hope that you are not bracket-blind."
• "[New archief voor Wiskunde] is like the Notices of the AMS, only it is in Dutch and therefore much better."
• "Two to the zeroth power is 1; two to the first power is 2; two to the second power is 4; two to the fourth power is 16; two to the sixteenth power is 65536. The next value is two to the 65536th power, and it would probably take me the whole hour to pronounce. I do not want to spend my time that way, so I decided not to memorize it."
• "We will finish [the series of lectures] tomorrow. So, same topic, same room, same time, same speaker, different transparencies."
• "I figure that before I give this problem to a grad student, I will think a little bit about it."