Entretien avec Nick Katz (Princeton University)
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Katz, Nick
 I'm Nick Katz. I teach mathematics at Princeton University. I'm interested in number theory and algebraic geometry and have been ever since I learned that these subjects existed. I came by boat in 1968, in June of 1968, so I had just missed the, I was Evan Mondemay, and it was very exciting to be here. Well, so I first came in 1968, stayed for a year, and over the next 20 years, I think with one exception, I spent every summer here, and every once every four years I had a sabbatical and I would spend the entire year here. So in this 20-year period, I think something like 40% of my life was physically spent here. There's so many fond memories. So my first year here was, turned out to be the last year that Grottendijk was fully engaged in mathematics, and he asked me to give some lectures in the SGA seminar, and a very young, one year younger than I, and that remains the case. Deline was also here, and he was terrifically helpful to me in preparing these lectures that I was going to give. And so this forming a close relationship with Deline in that very early time was sort of a very important experience. So this combination of Deline and Grottendijk, both, so to speak, at the height of their powers in this one year, I mean it completely changed my mathematical life, the way I thought about mathematics. It was amazing. Grottendijk, after the academic year 1968-69, basically stopped being very mathematically active because his interest shifted to, he founded a movement called Survivre, which was concerned with problems of nuclear disarmament or the absence of that disarmament. And so Deline became the person for some time, who was the main reason that people wanted to come here. But starting, I would say around 1980 or 82, Ofer Gauber became the other important reason to come here. And Deline left here to go to the Institute in Princeton in 1983, I think, 1984. And after that, Ofer became, for me, the reason to want to come here. And so it's completely appropriate that there's a conference honoring him because, well, he had tremendous impact on my own work. And as we've heard from the other people giving lectures, far from the only person on whom Ofer had a terrific impact. So it really starts with Descartes, who understood really for the first time that, on the one hand, people had, if you like, drawn pictures of things. And a completely different set of people had written down equations. And Descartes saw that the pictures were pictures of equations. And that's algebraic geometry, this interaction between the pictures and the equations. Ayesha was founded in 1958, largely under the, so to speak, scientific influence of Dio D'Ane, who understood that Grottendijk was this tremendous talent, and that he, Dio D'Ane, who was a very fine mathematician in his own right, he decided that the best thing he could do for mathematics would be to basically stop his own work and become Grottendijk's scribe, which is already a terrifically selfless thing to have done. And he convinced Mochan, who was the administrative founder of the institution, that what they had to do was hire Grottendijk immediately as a permanent member. So I believe at the beginning, the two permanent members were Dio D'Ane and Grottendijk. And that put IHES on the map as the world center of algebraic geometry. And it remained that way for the 11 years that Grottendijk was both here and completely active in algebraic geometry. Well, I first met him, it must have been 1981 or 82. I actually looked at some old papers of mine to find the earliest one where I explicitly thank Ophir Gaba for telling me something. And that was a paper, if I look carefully enough, I think the earliest one was a paper that was published in 1982. And since it typically takes a year or a year and a half between when you write a paper and when it actually is published, that would say that already starting in 1980 or 81, I was, we were both here at the same time, and I was already able to benefit from his tremendous insight into all sorts of aspects of mathematics. No, I mean, he's made a number of contributions. The ones that have had the most impact on me, he gave a proof that for projective smooth varieties over, well, over finite fields, but projective smooth varieties over algebraically closed fields, the Z-Elatic homology is torsion free for all but finitely many L. It sounds like a very technical thing, but for lots of applications, it's a very important thing to know. But if you ask 100 different people the same question, what was the most important thing that Ophir Gaba did as it related to your own work, you get 100 different answers in almost 100 different subjects. It started when I was an undergraduate and I stumbled across a book in the library at Johns Hopkins by Segre, which had a title, something like Arithmetic Questions in Algebraic Geometry, or I don't remember the exact title, I should have looked this up for you, but already this concatenation of the words arithmetic and algebraic geometry just seemed fascinating to me. What motivated me to pursue my interest, well, I think it's a general fact that people start off doing something they find interesting and if it turns out by luck that they're good at it, they can keep doing it, they keep enjoying it, they can be employed to do it, which is sort of miraculously wonderful thing. People pay you to do something you want to do anyway. I don't know that it's what I'm going to say is special to mathematics, but you've been thinking about a problem trying to figure something out and assuming that you eventually do, when you do, when you realize how it all works, typically this realization, the actual realization, the awareness takes place in a matter of minutes or seconds. Of course, you've been thinking about it for a long time, but this actual realization is a tremendously powerfully pleasant experience. There's a famous essay by Poincare where he talks about how he discovered the concept of automorphic functions stepping off a bus on his way to do compulsory military service. I'm not comparing myself to Poincare, but this experience of suddenly realizing something, it's very powerful. I spent the academic year 1968-69 here, that was my first year here, and Luke was one of a few of Grottendijk students who I would physically see every Tuesday afternoon at Grottendijk's Tuesday afternoon seminar. I didn't really get to know him, but then I think it was two years later, Luke spent one semester as a visitor at MIT. In the course of that visit, we invited him to Princeton to give a lecture. After this lecture, there was a dinner for the lecture where the attendees were myself, Luke, and Bill Messing. It was a long and pleasant evening, several hours, although it certainly wasn't a restaurant worthy of several hours from a gastronomical point of view. That's when I think I would say I first really got to know Luke. Then subsequently, the academic year 1971-72, I was again back for the entire year. I think it was in the course of that year that I met Luke's family. I would say I've known him well for 46 years.
 I'm Nick Katz. I teach mathematics at Princeton University. I'm interested in number theory  and algebraic geometry and have been ever since I learned that these subjects existed.  I came by boat in 1968, in June of 1968, so I had just missed the, I was Evan Mondemay,  and it was very exciting to be here. Well, so I first came in 1968, stayed for a year,  and over the next 20 years, I think with one exception, I spent every summer here,  and every once every four years I had a sabbatical and I would spend the entire year here.  So in this 20-year period, I think something like 40% of my life was physically spent here.  There's so many fond memories. So my first year here was, turned out to be the last year  that Grottendijk was fully engaged in mathematics, and he asked me to give some lectures in the  SGA seminar, and a very young, one year younger than I, and that remains the case.  Deline was also here, and he was terrifically helpful to me in preparing these lectures  that I was going to give. And so this forming a close relationship with Deline in that very  early time was sort of a very important experience. So this combination of Deline and Grottendijk,  both, so to speak, at the height of their powers in this one year, I mean it completely changed  my mathematical life, the way I thought about mathematics. It was amazing.  Grottendijk, after the academic year 1968-69, basically stopped being very mathematically  active because his interest shifted to, he founded a movement called Survivre, which  was concerned with problems of nuclear disarmament or the absence of that disarmament. And so  Deline became the person for some time, who was the main reason that people wanted to  come here. But starting, I would say around 1980 or 82, Ofer Gauber became the other important  reason to come here. And Deline left here to go to the Institute in Princeton in 1983,  I think, 1984. And after that, Ofer became, for me, the reason to want to come here. And  so it's completely appropriate that there's a conference honoring him because, well, he  had tremendous impact on my own work. And as we've heard from the other people giving  lectures, far from the only person on whom Ofer had a terrific impact.  So it really starts with Descartes, who understood really for the first time that, on the one  hand, people had, if you like, drawn pictures of things. And a completely different set  of people had written down equations. And Descartes saw that the pictures were pictures  of equations. And that's algebraic geometry, this interaction between the pictures and  the equations. Ayesha was founded in 1958, largely under the,  so to speak, scientific influence of Dio D'Ane, who understood that Grottendijk was  this tremendous talent, and that he, Dio D'Ane, who was a very fine mathematician in  his own right, he decided that the best thing he could do for mathematics would be to basically  stop his own work and become Grottendijk's scribe, which is already a terrifically selfless  thing to have done. And he convinced Mochan, who was the administrative founder of the  institution, that what they had to do was hire Grottendijk immediately as a permanent  member. So I believe at the beginning, the two permanent members were Dio D'Ane and  Grottendijk. And that put IHES on the map as the world center of algebraic geometry.  And it remained that way for the 11 years that Grottendijk was both here and completely  active in algebraic geometry. Well, I first met him, it must have been 1981  or 82. I actually looked at some old papers of mine to find the earliest one where I explicitly  thank Ophir Gaba for telling me something. And that was a paper, if I look carefully  enough, I think the earliest one was a paper that was published in 1982. And since it typically  takes a year or a year and a half between when you write a paper and when it actually  is published, that would say that already starting in 1980 or 81, I was, we were both  here at the same time, and I was already able to benefit from his tremendous insight into  all sorts of aspects of mathematics. No, I mean, he's made a number of contributions.  The ones that have had the most impact on me, he gave a proof that for projective smooth  varieties over, well, over finite fields, but projective smooth varieties over algebraically  closed fields, the Z-Elatic homology is torsion free for all but finitely many L. It sounds  like a very technical thing, but for lots of applications, it's a very important thing  to know. But if you ask 100 different people the same question, what was the most important  thing that Ophir Gaba did as it related to your own work, you get 100 different answers  in almost 100 different subjects.  It started when I was an undergraduate and I stumbled across a book in the library at  Johns Hopkins by Segre, which had a title, something like Arithmetic Questions in Algebraic  Geometry, or I don't remember the exact title, I should have looked this up for you, but  already this concatenation of the words arithmetic and algebraic geometry just seemed fascinating  to me.  What motivated me to pursue my interest, well, I think it's a general fact that people start  off doing something they find interesting and if it turns out by luck that they're  good at it, they can keep doing it, they keep enjoying it, they can be employed to do it,  which is sort of miraculously wonderful thing. People pay you to do something you want to  do anyway.  I don't know that it's what I'm going to say is special to mathematics, but you've  been thinking about a problem trying to figure something out and assuming that you eventually  do, when you do, when you realize how it all works, typically this realization, the actual  realization, the awareness takes place in a matter of minutes or seconds. Of course,  you've been thinking about it for a long time, but this actual realization is a tremendously  powerfully pleasant experience. There's a famous essay by Poincare where he talks about  how he discovered the concept of automorphic functions stepping off a bus on his way to  do compulsory military service. I'm not comparing myself to Poincare, but this experience of  suddenly realizing something, it's very powerful.  I spent the academic year 1968-69 here, that was my first year here, and Luke was one of  a few of Grottendijk students who I would physically see every Tuesday afternoon at Grottendijk's  Tuesday afternoon seminar. I didn't really get to know him, but then I think it was two  years later, Luke spent one semester as a visitor at MIT. In the course of that visit,  we invited him to Princeton to give a lecture. After this lecture, there was a dinner for  the lecture where the attendees were myself, Luke, and Bill Messing. It was a long and  pleasant evening, several hours, although it certainly wasn't a restaurant worthy of  several hours from a gastronomical point of view. That's when I think I would say I first  really got to know Luke. Then subsequently, the academic year 1971-72, I was again back  for the entire year. I think it was in the course of that year that I met Luke's family.  I would say I've known him well for 46 years.
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