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[Assistant] And so I was drifting around and I knew lots of people in the department. And there was a post-doc, Chris Robson, who was there working with a different professor.


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[Assistant] Israel Herstein on a different subject, non-commutative rings, but I knew something about that subject, not very much, and I was interested so I began talking to him and we worked together and proved a few nice theorems.


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[Assistant] Then McLean was returning and I remember sitting in a cafeteria.


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[Assistant] Opposite a group of students, a bunch of us went out to dinner chatting about this and the person opposite me said something which


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[Assistant] ...indicated that he thought my thesis was about noncommutative rings. And the light went off in my head that I had written a thesis without worrying.


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[Assistant] And without a thesis neurosis. And I was so pleased by that thought. I went back to McLean and said, you know, are you willing to have this be my thesis?


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[Assistant] He talked to Robson to make sure that Robson thought I had actually done something. And he agreed.


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[Assistant] Very generously read the document and corrected lots of things. His system was that he would begin at the beginning and read until he had marked 25 places where something needed to be improved and he would give it back to me and then he would start again when I re-handed him a fixed copy. Linear editing.


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[Assistant] Well he was famous for having students in lots of different areas.


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[Assistant] He would teach a course on something which he didn't know much about because he wanted to learn something and then one of the students in that class would become his student, work on that subject, become famous.


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[Assistant] And meantime, McLean had moved on. So the most spectacular example of that is a man named John Thompson, who


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[Assistant] Was very central in the program to classify finite simple groups and Thompson was his student at the moment when McLean thought he was teaching a course in group theory. Thompson was an interesting guy in terms of thesis too. He wanted to settle what's called the Burnside problem. Uh, well, nevermind.


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[Assistant] Thompson spent a year working very hard and Thompson was really a hard worker.


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[Assistant] What was your thesis called? My thesis was called Hereditary Nethurian Rings. Was it a good one? It was okay. Meh, it was pretty good.


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[Assistant] I was very close with another math major undergraduate, a man named John Neisendorfer, whom I still know. So he and I were kind of inseparable, bobsy twins as undergraduates, and we took courses together.


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[Assistant] One of the requirements of the department was a logic course.


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[Assistant] And so we took a logic course and it was given in the philosophy department.


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[Assistant] And at least half the class were philosophy majors who didn't know any mathematics.


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[Assistant] And we felt the course was below us. We wanted out. So after a quarter, it was a two quarter thing, we went to the math department and said, look, find us a, please find us a reading.


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[Assistant] Of course, in the subject, then we'll go on. Nobody really wanted to give a reading course to two undergraduates on that subject in the math department, but John Thompson was


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[Assistant] Button hold because he'd once written a paper on recursive functions, which was close.


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[Assistant] And so he agreed mistakenly, I think, to give this reading course. This was a period when he had just had a divorce.


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[Assistant] He was working like crazy on a now very famous paper and


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[Assistant] I think he was sleeping under his desk. He wasn't leaving. It was a mad timeframe. But here are these two undergraduates coming once a week to talk about Gödel's incompleteness theorem, which was not what he was interested in.


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[Assistant] So we would come in and he would sort of put the book down. Clearly he had just opened a chapter where he was supposed to read. And so we would spend the time talking about the first page, so to speak, of each chapter, but it was still a wonderful thing to have worked with him a little bit.


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[Assistant] Interesting question. Different universities are very different.


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[Assistant] So Chicago had a pretty rigid system. Every took the same three first year courses and then went on to other things.


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[Assistant] Berkeley, the faculty is too broad to agree on any three courses, so students are just sort of, do something. It's very different that way.


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[Assistant] But once you settle on a thesis, I think it's very similar.


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[Assistant] And there are the three little clumps of seminars and people working together.


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[Assistant] What's really different though is the job market. When I was ready to graduate, I applied to exactly two places because one of them I knew the person I wanted to work with and the other one.


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[Assistant] Kaplansky told me to apply there and I did. Yale and Brandeis. I got offers from both of them and I went to Brandeis as I had intended.


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[Assistant] That's just unheard of now. What's that like now? Now people apply to a hundred places and it's scattershot and you try to get noticed so that it isn't quite so random. I find the whole process rather unpleasant now.


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[Assistant] People from Berkeley get positions, reasonable positions by and large. So it's not that, I mean, I'm talking about Berkeley experience now. Yeah. Different places are different. There are more applicants, but not that many.


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[Assistant] Are there fewer jobs? Maybe then in my year, the balance has changed. I was at the end of the sixties and things were very different in the sixties.


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[Assistant] One of the things that's different is that it's trivial to apply to a hundred places.


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[Assistant] Because of a wonderful institution or a horrible one called math jobs.


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[Assistant] You fill out one application, your people upload their letters and...


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[Assistant] There's so much noise in the system that it's easy to get overlooked. It becomes a different game. And if your thesis advisor is well known, it still matters. It used to matter in a different way, but unfortunately it still matters.


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[Assistant] I was there for 27 years. I was a postdoc with a very temporary position. I guess I was called an instructor postdoc where it wasn't so common. And then I was promoted to an assistant professor, tenure track.


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[Assistant] At Brandeis about a quarter of the tenure track people got tenure. It's different in every place. My first job was in 1970 and I got tenure in 75, I think 74, 75.


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[Assistant] So when I got there, I was still working on non-commutative rings. Which you've done your PhD. Which I've done my PhD on.


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[Assistant] It's become a pretty hot field now, but at that time there was almost nobody in Boston working on non-commutative rings. And I'm a gregarious person as you probably have gathered. And so.


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[Assistant] After a semester, I was unhappy. I went to Buxbaum, who was the person because of whom I'd come. I'd heard him lecture and liked what he did and said, look, I know a little bit about commutative rings. You know a lot about commutative rings, but I have a lot of energy and I'd love to work on a problem with you. And so we began working on a conjecture. It proved to be a false conjecture.


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[Assistant] And that was rather a disappointment. So I've always had a pessimistic view of conjectures. What was it called? It was called the lifting conjecture. And had I known enough algebraic geometry, I would have known that it should be false.


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[Assistant] At that time there was no proper counterexample but there was such a...


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[Assistant] Strong hint of a counter example that it really wasn't in the cards.


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[Assistant] It's more glorious if you prove the theorem than if you find a counter example. Though the counter examples are awfully useful and keep you from trying to prove the theorem.


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[Assistant] So then I, I really worked in commutative algebra with Bookspelm. He was my mentor and we worked together very closely over the next.


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[Assistant] Nearly 10 years was a very, very profitable thing for me. He was my mentor in many senses.


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[Assistant] McLean also had been engaged in the mathematical community. He was a member of the National Academy. He was an editor of the proceedings of the National Academy.


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[Assistant] He was a social mathematician. He had been president of the American


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[Assistant] Mathematical society as I eventually was too. So that was a kind of model, but bookspelm also was.


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[Assistant] Very engaged in department politics and university politics. He brought me along with him in some way. He would tell me about what was going on and so I became aware of those things and aware of it as a legitimate thing to think about.


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[Assistant] I proved some theorem, there was a conjecture, or there was a weak theorem proven, and I thought, gee, it would be nice if that were true more generally, and I proved it. And I put it in my drawer, because I thought, you know, I'm going to run out of ideas sometime.


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[Assistant] And then I'll take this out of my drawer and publish it and I'll at least have a last paper.


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[Assistant] So this was in the first couple of years, I was really worried about the well drying up.


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[Assistant] Genius. Right. I got over it and I finally did publish the paper. There was no fear of being scooped. It could have happened, but it wasn't. It didn't.


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[Assistant] As I've grown older, and this is true of quite a few people, it takes me longer and longer to publish something.


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[Assistant] So I do the work, it sits around, I do a little more work on it a year later, two years later, sometimes five years later.


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[Assistant] And before it becomes mature and goes out. So that could be scooped, sometimes it is. Doesn't bother me so much as it would have then, but I have.


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[Assistant] Retain a sense of competitiveness when I'm working. I want, I want the good result.


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[Assistant] Oh, it's happened more than once, but it's happened recently. I've disproved some of my own conjectures, but other people have disproved some too. Kaplansky always used to say,


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[Assistant] That you should sort of think of the best possible thing that would be true.


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[Assistant] Make a conjecture. It'll get other people to work here. It'll show the way. It's a kind of light, a searchlight ahead of what might be there.


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[Assistant] I'll put a link in the notes for this show for people who want to try their luck. So that's, that's one. The three things I guess I'm best known for the early work with bookspelm and that theorem and the things that came out of it.


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[Assistant] And then my work with Joe Harris on modular space of curves and something called limit linear series, which cleaned up a large number of conjectures in the theory of curves.


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[Assistant] Not so much. There are people who really spend many, many years chasing a particular thing.


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[Assistant] In my very earliest time with Books of Album, we chased this conjecture quite hard and it got away because it turned out not to have been there to begin with.


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[Assistant] Willow the Wisp, but I tend to work on things that I can do rather than things that are the shining glory of a problem. You know, there was this recent film about Hardy and Ramanujan and in the film Hardy is declaiming that the important thing is to achieve immortality by proving the great theorem. That was never my idea.


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[Assistant] Yes, indeed there are. Many people keep their thesis problem for all their lives.


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[Assistant] Or things related to it. And sometimes it's such a good problem that that's a really good thing to do. And sometimes it's a terrible problem and there's just stuck on it.


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[Assistant] It's quite tragic, yes. There's luck involved and taste and who your thesis advisor was.


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[Assistant] I once was talking to a young student at some conference, and I asked,


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[Assistant] Her it was, you know, what are you working on? And she told me her problem and we discussed a little bit and it became clear.


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[Assistant] That it was really her thesis advisor's problem, which he hadn't solved.


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[Assistant] And it wasn't a very good problem and I thought, oh, I wish I could do something for her. But of course you can't at that point.


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[Assistant] Brandeis, I'm sorry to say, lost its ideal of being a real strong research university. A number of bad things happened that were not Brandeis' fault. They over-invested in some building project.


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[Assistant] The chancellor who had been so connected to the Jewish community and such a wonderful fundraiser, retired finally, does happen to people, and was replaced with someone who was not a good fundraiser. Actually, there was a funny story about this guy.


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[Assistant] Which I think is worth telling. It was told to me by one of the fundraisers.


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[Assistant] There's one word you've got to be able to pronounce correctly, and that's Brandeis. But when so-and-so says it, it comes out Princeton.


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[Assistant] Right. So anyway, that was a problem. It was also a problem that Harvard dropped its anti-Semitic quotas and so that rich Jews felt comfortable about giving money to Harvard instead of Brandeis. So there was a whole complex of things that happened. The seven day war in Israel also diverted


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[Assistant] Resources to that. And so Brandeis began to lose resources, tried to fix it by recruiting more undergraduates. The grade point averages of the incoming students, the SAT scores went down. It became less of a prestige place to go. This spiraled a bit.


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[Assistant] And the glory days of funding of science in the 60s also passed, and so the whole institution became


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[Assistant] Math department was cut to a fraction of its size. I was chair a couple of times during this.


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[Assistant] Period. And I was mad as hell at the administration. And so I was easy bait. And when I heard about this job in Berkeley, I can tell a story about that too. I was eager.


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[Assistant] You're ready to jump. I was ready to jump. I had been visiting Bernd Stromfels in Berkeley when he was a new faculty member here.


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[Assistant] And we were chatting very idly about retirement. This was infinitely far in the future for both of us. But a friend of mine had said,


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[Assistant] That she would really like to retire in Berkeley when she retired. So I repeated this story, and we joked about it a bit. And so,


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[Assistant] At the time when the job in Berkeley became available, Barron sent me a...


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[Assistant] An email with a subject line, which I still remember, which was retire in Berkeley, question mark. That was the lure.


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[Assistant] It was quite a bumpy road before I was hired, but never mind.


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[Assistant] I would have come to be a professor had they invited me, but I was more attractive I think as a director of MSRI than as professor, though they were willing to hire me fortunately.


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[Assistant] I would not have come without having a tenure job at Berkley either.


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[Assistant] Well, not much actually. To be perfectly honest, I did not have the required experience. I was a bit of a dark horse in every sense. I had been a year, a visitor for a year at MSRI.


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[Assistant] But how shall I say, the other candidates were less suitable.


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[Assistant] One of them was perhaps more suitable, but there were other political problems that occurred and kept it from happening.


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[Assistant] But I mean, you'd been chairing a math department. I'd twice chaired a math department. I'd run big meetings.


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[Assistant] I had been very much involved in organizing things in the community.


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[Assistant] In small ways, I've been involved with the American Math Society.


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[Assistant] So you're quite a network guy. I was quite networked, but not particularly with people at MSRI or brick.


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[Assistant] Elwin Berlekamp was the chair of the board at the time and he took hiring a director very personally and very seriously. He even came to visit me at home.


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[Assistant] In newton mass to see whether I lived right. Unannounced or? No, unannounced. So I was nervous about this, of course, and I invited book spam to come over and join us for the talk. Wingman. Which he did.


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[Assistant] Yes, right. Anyway, apparently he liked what he saw. Yep. So eventually I got this offer. Yeah. Burley Camp also taught me about fundraising. I had really not done any fundraising though I was interested. Yeah. And I went, I spent endless time with.


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[Assistant] With Brilicamp in the car going to visit his friends and him telling these stories of MSRI and of.


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[Assistant] Play this card pretty consciously that I could go to someone and say, look, I'm young and I have lots of energy and you actually know something about this field, let's work together. Then really plunge into their problem.


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[Assistant] And that stopped working at a certain point because I grew up. But then it sort of has worked in the other direction. Former students of mine and I have collaborated very, very happily.


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[Assistant] Well, it's actually a little different than I, at least I perceive it a little differently than that. I've been really quite productive in these years. So I see myself now as doing both.


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[Assistant] With some frustrations, of course, I surely would have proved more theorems if I weren't directing.


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[Assistant] But that I'm very happy with the trade-off. I feel I've done a lot of good for, for mathematics in this way. Probably more than those theorems would have done. I'm very proud of MSRI and the changes I've been able to make there too.


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[Assistant] So I wandered. I worked in algebra early on.


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[Assistant] Sort of category theory, then algebra. I was interested in algebraic number theory. I was interested in operator algebras.


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[Assistant] Then moved into singularity theory and moved into algebraic geometry.


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[Assistant] At one time I thought I'll move from area to area. I'll know a lot of things.


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[Assistant] Of course that has dried up a bit because I don't have the time to both be productive and learn a lot of brand new areas. I have to choose.


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[Assistant] When I came to MSI, I had the fantasy that every semester there would be a new program.


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[Assistant] And I would really learn something about a new area every semester.


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[Assistant] But it's been too busy a job for that and I've been, the process of staying productive mathematically has ruled that out to some extent.


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[Assistant] Well, I've often said and I think it's true that MSRI is the world's greatest collaborative math research institute.


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[Assistant] So it's primarily a math research institute where people come from all over the world because they want to talk to each other about their favorite problems. And we host programs, we don't create them, but we host extremely good people and people who are just developing.


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[Assistant] So that's one of the things MSRI does. Another is to cultivate talent in lots of areas, lots of different levels of people, undergraduates, graduate students, postdocs and others.


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[Assistant] And the third really is public understanding of mathematics and math education, which are related but different areas.


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[Assistant] And you're my finest achievement in public understanding of mathematics.


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[Assistant] People who run the show have term appointments or like me or like a land servant pleasure, but, um, presumably fairly long term. I've been there pretty long too by now. It's 20, 21 years since I came. I did take off six years in the middle, but it's been 20 years.


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[Assistant] Maverick. People tell me I need a better name for MSRI. MSRI is hard to remember. Hard to say.


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[Assistant] Yeah. Well, emissary, shall I tell you that story? Go on then.


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[Assistant] So at the end of the eighties, people had gotten into the habit of calling MSRI misery, which is a terrible thing if you're also trying to be important in the world and raise money and things like that. Jokingly like to be derogatory. Jokingly, no, completely, you know, it's such a wonderful place to be. Right. Haha, we call it misery.


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[Assistant] And the first laser printer that they had was called the miserable laser writer, right? So that was all too catchy, I'm sorry to say. And Bill Thurston, one of the things he decided to do was try to fix that. And so


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[Assistant] He was a very clever guy and he said, well, if you'll pronounce...


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[Assistant] The letters rather quickly and with a French accent, M S R E.


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[Assistant] It sounds like emissary. So let's call it emissary. That's at least a word it's pronounceable. Not bad. He didn't make friends with this idea because he would say at the beginning of every workshop, now we're changing the name to emissary. So please repeat after me emissary.


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[Assistant] And of course the mathematicians don't like to repeat after me at all. So this was kind of a negative.


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[Assistant] For the name. There are still people walking around who call it emissary, but not very many. And so I abandoned that attempt when I came and just used MSRI.


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[Assistant] So the decision is made by the so-called Scientific Advisory Committee, which is advisory in name only. It's a committee with the power to make those decisions.


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[Assistant] The ten top mathematicians who serve four year non-renewable terms and they work hard. They come in person to MSRI for two days at a time, twice a year, and they work in between as well.


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[Assistant] And they donate their services to the institute because they believe in this thing.


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[Assistant] Yes, so they receive proposals from the outside and they also instigate proposals. So every meeting, one, the largest agenda item is consideration of the proposals on hand and thinking about how to pair them. We also have this shtick, which


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[Assistant] Is that we run two programs at a time typically and we try to choose them


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[Assistant] So they have some interesting relationship to each other. And sometimes that's been very successful. Sometimes it's not successful. Matchmaking is always perilous, but it can be very good. And so the committee spends a lot of time on pairings and things like that.


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[Assistant] People work hard as organizers, so it's a little more muted celebration, I think.


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[Assistant] But it is very good for the field and people are eager to do it for their field or to have someone else do it for their field preferably.


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[Assistant] So the first thing is that a program is chosen with a set of organizers. The organizers have proposed that every program comes as a proposal, whether it was instigated purely from the outside or sort of seeded by the committee. It comes as a proposal and it's judged on that basis.


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[Assistant] Brady makes the proposal to work on, you know, number file mathematics and is accepted. And then that's three years before the program. So we choose almost exactly three years in advance.


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[Assistant] And of course it's been a consideration before that. So the proposal was submitted probably four years in advance or something like that. Three years in advance, you get the green light and then you begin advertising in your community.


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[Assistant] Who wants to come? Boy, we really need these three people. I'm going to tell them to apply.


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[Assistant] But every person who comes has to make an application. And that's actually something which is controversial.


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[Assistant] We feel it strongly because it levels the playing field.


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[Assistant] You have to put in an application. You know, there are ways of making it easy for you and the organizers can write the recommendation letter, but there has to be such a letter.


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[Assistant] And people get quite mad at this. I'm a Fields Medalist or I'm a whatever. Actually, the Fields Medalists don't mind.


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[Assistant] Mantra seriously. Anyway, so people apply and they apply in different categories. There are research professors, members and post-docs and some graduate students come with their mentors too. But there's a long list of applications. The.


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[Assistant] Organizers submit their recommendations to the SAC, which has the power to decide the scientific advisory committee.


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[Assistant] And the human resources committee also combs the applications to make sure nobody, no women, no minorities are being missed.


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[Assistant] And so all that information gets to the SAC and they make a final decision.


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[Assistant] And then they call in one of the organizers and say, you know, we are thinking of changing your recommendations in the following way. Tell us why we're being stupid.


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[Assistant] Then there's a negotiation and then there's a final list.


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[Assistant] Not as draconian as that, but there's still.


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[Assistant] Lots of very good mathematicians whom I would have loved to have, who we just didn't have room for.


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[Assistant] So that's an interesting question and it's a subtle question too because success is almost never we solve the Riemann hypothesis.


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[Assistant] There are lots of breakthroughs made. We have lists of them on the website. You can find it, but we're really an incubator. Mathematical theorems take a long time.


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[Assistant] Somebody comes, they haven't had an idea, they want to prove this, they have a reason why it's possible.


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[Assistant] They have 17 conversations. It's advanced this way and that way. And then.


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[Assistant] Probably, if it's going to be proved by them, they go home and prove it. Rather than on, on site. So.


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[Assistant] It's a very complicated process and complicated to measure. I personally measure it by the sort of excitement in the field that's been generated by it. And there are programs where the senior people don't come in sufficient numbers and it's kind of quiet and at the end of the


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[Assistant] But certainly there are times when it's just everybody is ecstatic at the end of the program, and other times when it's just like, eh, time to go home.


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[Assistant] Well they work really hard and they have tremendous passion. Motivation counts for a lot in mathematics and people drift away from


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[Assistant] Research is hard. Research is frustrating for pretty much everybody. And the rewards are very rare.


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[Assistant] There are big rewards if you really get something you're excited about. Oh, that's super exciting.


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[Assistant] And it can be frustrating and the really good mathematicians, maybe they have enough rewards so that they keep on or maybe they keep on and therefore have enough rewards.


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[Assistant] Talent certainly plays a role. People who say there's no such thing as talent, I think are talking nonsense. I do think everybody can learn mathematics and enjoy mathematics with good teaching. You know, there's no, no such thing as not being able to understand fractions. But talent at the highest level you see and you just, it's jaw dropping.


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[Assistant] Describe, but here, well, here's a personal experience. So I was a visitor at an institute in Paris when I was pretty young. So I was five years beyond my degree. I went to this institute. I walk in.


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[Assistant] There's one of the most famous mathematicians in the world standing there, Pierre Deligne. And, ah, Pierre Deligne, oh my god. But he's very friendly.


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[Assistant] He takes me out in a bicycle in the French forest and we have, I'm still in awe.


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[Assistant] But if you ask Pierre a question, I've always felt, and I've found this over the years, you get back an answer, which first of all is absolutely penetrating, but it's at your level. So he's seen through the problem, he's understood it at a very deep level, and so he can explain it, what you need to know. And he's not pretentious about it, he's willing to explain it to you.


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[Assistant] And the rapidity with which it happens is astonishing.


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[Assistant] Now, it has to be said that there are quick mathematicians and slow mathematicians, and some of the best ones are not quick.


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[Assistant] So that kind of instant response and instant ability to solve any problem, some of the best ones have it and some of them don't.


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[Assistant] Uh, von Neumann was very famous for speed, for rapidity. There's a sort of silly mathematical problem. Two trains start


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[Assistant] 20 miles apart, facing each other on a track and they go towards each other at 40 miles an hour.


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[Assistant] And a bee starts from the nose of one and flies to the nose of the other and flies back and flies back until finally the trains meet and something happens to the bee. How far did the bee fly? There are two good ways of solving the problem. There's an infinite series there. You can sum the infinite series. It takes you a little while, or you can notice that the trains took


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[Assistant] If they started 20 miles apart, they were traveling 40 miles an hour, 80 mile relative speed. It took them 40th of an hour or whatever it was to. Yeah. Right.


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[Assistant] Oh, the speed of the bee is known as well, I forgot to say. So the speed, that's how far the bee flew. And the joke was,


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[Assistant] We thought you would have solved it as a mathematician solving something the infinite series.


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[Assistant] Just don't feel like working on a problem that somebody else sets, or feel that they're inadequate at it or something, but just don't get grabbed by it.


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[Assistant] So, there's a great range of styles. Some people are...


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[Assistant] Really genuinely slow seeming, but boy do they get to the goal by deep thoughts somehow.


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[Assistant] Certainly there are. There are people who have incredible ability to work with complicated formulas and other people who just...


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[Assistant] Never touch a formula and see a geometric picture. Thurston was incredibly geometric, for example, and just had that insight, which was astounding to everybody around him. And there are people who work all their lives on one problem and go deeper and deeper and there are people who.


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[Assistant] Glad when somebody else pitches in, you're glad to have them as a collaborator. You're proud to be their collaborator then.


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[Assistant] There's a famous mathematician whom I won't name, who


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[Assistant] Tells his students they must not talk about their problem with anybody else.


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[Assistant] It's a secret, and I think that's very bad for students. My students work with each other all the time. So there are a lot of personality things.


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[Assistant] There's a kind of intensity about mathematicians which is not universal, but very characteristic, I think.


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[Assistant] Some people think that very good mathematicians are usually on the autism spectrum somewhere. I think that's overdrawn. But here's another story about how mathematicians are. You know, I studied voice for many years. I'm a singer. I once had a voice teacher.


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[Assistant] With whom I studied for a while and one day he said, you know, I'm really sorry to tell you this, but you'll never be able to be a professional singer. I didn't want to be a professional singer. I was already.


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[Assistant] Well along in my career in mathematics. So I said, you know, what makes you say that? And he said, well, you're hopelessly introverted and.


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[Assistant] I had to tell him that for a mathematician I was wildly extroverted.


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[Assistant] Those two spectra don't meet. The singer walks out on stage, you can tell them instantly from the rest of it.


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[Assistant] There's that side of it too. You can like collaboration, you can collaborate a lot, but you have to be willing to sit by yourself too.


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[Assistant] Yeah, I do it less than some people. Some people really keep track of who's scored and what, you know, more like score than like the result. I'm very interested in hearing what the latest result is, but not so interested in who did it or.


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[Assistant] The circumstances where some people really pay a lot of attention to who's going to win the field medal next, right?


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[Assistant] Yeah. They have a list. I'm completely out of that. But you've been involved with the Fields Medal, haven't you? I was on the committee, actually. Not this most recent one, but the one before.


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[Assistant] I was very pleased at the choice of Mariam Mirsakhani and I'm proud of having had a partner. Not that it was a difficult thing, but it was an exciting committee we met in secret.


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[Assistant] It's gotten a little less secretive now, but the tradition was that the committee is completely secret, except for the


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[Assistant] And that all communication in route goes through the chair of the committee. So you can't be lobbied or? So you can't be lobbied. That's right. So we were enjoying, we had meetings in New York once and in a European city once.


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[Assistant] And we were enjoying not to give lectures at the nearby universities when we were there, because all these well-known mathematicians suddenly showing up would be suspicious at that time of year. So it was all the big hush-hush things.


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[Assistant] By statute, there's no repeat of one field's committee to the next one.


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[Assistant] But they're sealed and the idea is that they should be sealed for 70 years. When I was on the committee, 70 years from the first Fields Medal had just come.


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[Assistant] So I thought, oh goodie, I'll look at the records from the first Fields Medal. So I wrote to the Secretariat of the International Mathematical Union saying 70 years has passed, it's my time, I wanna know.


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[Assistant] And they said, we'll look for the records. And a month later they wrote back sadly, they said the records have been lost.


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[Assistant] The IMU kept its record to the shoebox until quite recently.


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[Assistant] Yes. Heartthrob at the moment. Yeah. Should we talk about that controversy? Do you know about that? Well, I, I know a bit. I would love to talk about it. Yeah. Go on then. So.


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[Assistant] Mochizuki, who's done very good things, a very fine technician, claimed to have proved it.


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[Assistant] And he did some odd things. The proof is embedded in a very long series of papers.


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[Assistant] Very few people got beyond a small piece or really figured out where the action was. There is one exception to that, which I'll come to.


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[Assistant] So he had his coterie of supporters and a group of people who said, we don't see the point, we don't see how he could have proved it, we don't see the new idea. He's not telling us the new idea. We're not so sure there is one.


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[Assistant] It's out there, but he refused to come and give talks about it. I put it out there. Go read it. If you want to know how it's done, go read it.


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[Assistant] Give talks on it. Right. Very good talks. Very responsive talk. Okay. Very different. Right.


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[Assistant] Okay, so there's Mochizuki sitting in Japan, surrounded by a group of his students who believe in him.


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[Assistant] And a few other people who have sort of taken up the cudgel.


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[Assistant] Maybe because it's related to their own work, is the worm's eye view of that.


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[Assistant] There's this controversy. It's the most important problem in number theory, maybe, barring the Riemann hypothesis.


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[Assistant] And nobody knows whether it's been proven. It's terrible.


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[Assistant] And years go by, then the rumor comes out that it's going to be published by the journal at the place where Mochizuki is.


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[Assistant] Right. And that's Peter Schultz, who just won the fieldsman. And Peter is an amazing person. He's one of those jaw-dropping mathematicians.


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[Assistant] He is still very young from my point of view. He said, well, other people are going to read it. They're going to find the mistake too. It's not my business to get in there.


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[Assistant] But somehow when it was announced that the journal where Mochizuki is was going to publish it, he felt that was wrong. So he came forward.


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[Assistant] And so there's now a considerable body of opinion on the side of Schulze.


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[Assistant] People say, well, we gotta study it for ourselves, but he pointed to the page and the lemma.


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[Assistant] Which he said is just not proven and was the key. And so even having that pinpoint statement and from a person of Schultz's standing is pretty scary for the proof. So I would bet considerably against it at this point though, you know,


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[Assistant] People do make mistakes on both sides, so who knows.


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[Assistant] ABC trivially implies Fermat, for example.


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[Assistant] And you know, it's just a very central statement. Unlike Fermat, it's hard to state for a layman, but not impossible. And I think you've done something about it, haven't you?


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[Assistant] One that I would personally be very excited by is P not equal to NP. Call it computer science if you like, but I call it mathematics.


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[Assistant] It's sort of the next natural step after girdle. And it's, that's a very big one. There are some that are very central, but I'm not personally so involved like the equations of motion of fluid mechanics and knowing whether they have good solutions and things.


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[Assistant] In both in applied and pure mathematics. There are a number of good things out there.


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[Assistant] And they do get solved sometimes. I've been very pleased. I mean, some conjecture.


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[Assistant] That I was involved in, which seemed untouchable for many, many years, got proven pretty recently, and by a really nice, easy proof, I was just delighted.


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[Assistant] I notice a difference in how I approach things, yes. A detrimental one? There are pluses and minuses. I'm sure overall it would have to be a minus, but not a fatal minus by any means. What do you notice?


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[Assistant] You know, people don't run four minute miles after they're a certain age. There's a kind of ability to sprint and to have absolutely no focus, but some computation for an extended period. And that's not the way I work anymore. Could I do it? Well, maybe.


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[Assistant] The legs running. My 20 year old son could climb stairs a hell of a lot faster than I could and that was a while ago.


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[Assistant] On the other hand, I know a lot more, and I have a lot of associations that I didn't have when I was young. So I have some advantages too, but really I'm not in it for the great problems, I'm in it to have fun.


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[Assistant] I'm standing in the hall in MIT with Mike Artin. Mike Artin is only a dozen years older than I am.


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[Assistant] But he was already a famous mathematician, he was tenured professor at MIT, he worked with Grotendie, he was really the big stuff. He and I and another postdoc who was a good friend.


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[Assistant] We're standing together chatting, and Mike is a very informal person, always was. So, he said something about, you know, people our age, the three of us.


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[Assistant] And I thought, how could someone be so deluded as to think that I would see him as my age?


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[Assistant] So he was half again as old as I was at that time. Yeaah.


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[Assistant] Now, of course, I understand this error completely. I look at a graduate student and they look to me like myself, but I'm sure they don't see me that way. So there's, there's that.


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[Assistant] Hmm, that's an interesting question. They both mean a lot to me, honestly. I think that the fate of administrators is to be forgotten.


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[Assistant] I've done a lot for MSRI. I've built a wing on it. I've raised money. I don't think that will be well remembered. And that's okay. It's there.


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[Assistant] I think that some of my theorems will be remembered longer, though, whether they're remembered 150 years from now is, well, probably not.


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[Assistant] But maybe. They'll be part of the texture of mathematics then, but...


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[Assistant] Has an individual theorem, I don't know. My book on commutative algebra actually is the best known thing I've done.


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[Assistant] Bar none, I think. Probably better known than my activity at MSRI right now. Just in terms of number of people who've used it or number of people who find it useful to themselves.


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[Assistant] Life as a whole. Students. I mean I've had a lot of students.


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[Assistant] Uhm, I could get a long way into it. Okay. Yeah. I'm sure I would miss a few.


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[Assistant] Some of them have left mathematics, some of them have died, some died very young. Some of them I'm very much in touch with and in contact with and take great delight in. It's an interesting thing when I work with a student or when I meet a student even whom I haven't seen for a while.


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[Assistant] We have an instant connection because we have a language in common and a whole set of associations. It's like children in a way.


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[Assistant] But it's, for me, it's been a very positive thing. I know people who aren't friendly with their students, often jealous of their students, but not me.


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[Assistant] So he had a long career teaching at, uhm, Stony Brook and was part of building up that department.


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[Assistant] And sort of went out of research, began to teach courses on history of science and on anti-science.


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[Assistant] But he taught a course on quantum mechanics over and over and loved that subject very much and wrote a book.


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[Assistant] And my wife and I also endowed a prize in his name for math and physics at the, there.


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[Assistant] But he lived to see me established at MSRI. Alright. I think was very pleased by that.


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[Assistant] No, not for him. I could tell him some things about it, but we didn't communicate on a technical level very much.


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[Assistant] She, well, she read introductions. Uhm, we shared a lot of poetry, actually. And I, I know a lot of poems from that time. She really got me into that. So that was a very rich,


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[Assistant] Stream for me. She would read introductions. She couldn't read the books themselves, but I think she was very proud of me.


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[Assistant] Certainly surprised. He didn't know a thing about the future really.


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[Assistant] Who knows, but maybe the most surprising aspect would be something that came up between me and Yuri Manin once. I was immensely pleased to meet Manin at some meeting finally in Spain. He was just beginning to be able to travel.


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[Assistant] And, uh, he was at some meeting where I was, and we fell in and got to be friends. And we traveled down to Toledo to see the artwork there. He's an immensely cultured person. I don't know if you ever had contact with him or heard of him even, but a great mathematician and immensely cultured.


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[Assistant] Anyway, we went together, his wife was along and my son was along, and...


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[Assistant] We were sitting in the square in Toledo, enjoying the sun, the food and the wine.


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[Assistant] And Yuri said to me, who would have thought that being a mathematician would lead to seeing the world? So,


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[Assistant] She was kneeling at a stone altar, chanting something under her breath.


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[Assistant] The walls were decorated with ancient Egyptian drawings and modern photographs. The glittery shadow no longer surrounded Zia, but something even stranger was happening. I'd been planning to tell Zia about my nightmare.


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[Assistant] She cupped her palms the way you might hold a bird and a glowing blue sphere appeared about the size of a golf ball. Still chanting, she raised her hands. The sphere flew up straight through the ceiling and vanished.


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[Assistant] I thought about backing out of the room. Only problem? The door was gone. No other exits. It was only a matter of time before... Uh oh. Maybe I'd made a noise. Maybe her magical senses had kicked in. But faster than I could react, Ziya pulled her wand and turned on me, flames flickering down the edge of the boomerang. Hi! I said nervously. Her expression turned from anger to surprise, then back to anger.


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[Assistant] Carter, what are you doing here? Just walking around. I saw you in the courtyard, so what do you mean you saw me? Well, you were running and you had this black shimmery stuff around you and you saw that. Impossible. Why? What was it? She dropped her wand and the fire died. I don't appreciate being followed, Carter. Sorry, I thought you might be in trouble.


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[Assistant] She stared at the photos behind the altar and I realized she was in some of them.


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[Assistant] There she was as a little girl, standing barefoot outside a mud brick house, squinting resentfully at the camera as if she didn't want her picture taken.


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[Assistant] Next to that, a wider shot showed a whole village on the Nile.


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[Assistant] The kind of place my dad took me to sometimes, where nothing had changed much in the last two thousand years.


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[Assistant] A crowd of villagers grinned and waved at the camera as if they were celebrating and above them little Zia rode on the shoulders of a man who must have been her father. Another photo was a family shot. Zia holding hands with her mother and father.


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[Assistant] They could have been any Felahin family anywhere in Egypt, but her dad had especially kindly twinkling eyes. I thought he must have a good sense of humor. Her mom's face was unveiled, and she laughed as if her husband had just cracked a joke. Your folks look cool, I said. Is that home? Zia seemed like she wanted to get angry, but she kept her emotions under control. Or maybe she just didn't have the energy.


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[Assistant] It was my home. The village no longer exists. I waited, not sure I dared to ask. We locked eyes and I could tell she was deciding how much to tell me. My father was a farmer, she said. But he also worked for archaeologists. In his spare time,


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[Assistant] But somehow, this one survived. He brought it home. He didn't know.


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[Assistant] He didn't realize magicians imprison monsters and spirits inside such statues and break them to destroy their essence. My father brought the unbroken statue into our village and, and accidentally unleashed. Her voice faltered.


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[Assistant] She stared at the picture of her father smiling and holding her hand. Ziya, I'm sorry. She knit her eyebrows. Iskandar found me. He and the other magicians destroyed the monster, but not in time. They found me curled in a fire pit under some reeds where my mother had hidden me. I was the only survivor.


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[Assistant] I tried to imagine how Zia would have looked when Iskandar found her. A little girl who'd lost everything, alone in the ruins of her village. It was hard to picture her that way.


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[Assistant] Then I realized I'd been the same age when my mom died, when Sadie and I were split up. I remembered all of that so clearly.


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[Assistant] I could still see our house in Los Angeles and the way the stars looked at night from our back porch overlooking the ocean.


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[Assistant] My dad would tell us wild stories about the constellations.


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[Assistant] Then every night before bed, Sadie and I would cuddle up with Mom on the sofa, fighting for her attention, and she'd tell us not to believe a word of Dad's stories. She'd explain the science behind the stars.


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[Assistant] Talk about physics and chemistry as if we were her college students.


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[Assistant] Looking back on it, I wondered if she'd been trying to warn us.


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[Assistant] I remembered our last trip to London as a family, how nervous mom and dad seemed on the plane. I remembered our dad coming back to our grandparents' flat after mom had died and telling us there had been an accident. Even before, he explained, I knew it was bad because I'd never seen my dad cry before.


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[Assistant] The little details that did fade drove me crazy.


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[Assistant] The older I got, the harder I held on to those things. I couldn't imagine not remembering anything. How could Zia stand it? Maybe... I struggle to find the right words. Maybe you just... She held up her hand. Carter, believe me. I've tried to remember. It's no use. Iskander is the only family I've ever had. What about friends?


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[Assistant] I realized I hadn't seen anyone close to our age in the first gnome. Everyone was either much younger or much older. I don't have time for friends she said.


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[Assistant] Besides, when initiates turn 13, they're assigned to other gnomes around the world. I am the only one who stayed here. I like being alone. It's fine. The hairs stood up on the back of my neck.


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[Assistant] I'd said almost the same thing many times when people asked me what it was like being homeschooled.


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[Assistant] Several of your friends came to the house while you were away. Michaelus told me that he's moving into a small house in the countryside, just outside of London, near Dover. That horrible man, Carl Jont, came with that equally horrible woman of his. Oh, and Ossipon visited as well.


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[Assistant] Stevie's been very sad, although that hasn't stopped him from working around the house. He's been a great help to Mrs. Neil and me.


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[Assistant] Such hard work. You're lucky not to have to work like me.


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[Assistant] You have only yourself to worry about and feed.


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[Assistant] He needs the air. And if he has nothing to do, he always feels terrible. I can't be comfortable with him, looking so sad all the time.


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[Assistant] Oh, you don't have to worry about that. He'd never leave your side. You're such an important person in his life. He respects you more than anyone else. Besides, if he were to wander away, it would be fine, because


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[Assistant] Never mind, he'll be fine. Trust me.


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[Assistant] Terrible day out there, yes? Did you visit Stevie today?


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[Assistant] My goodness, you've caught a terrible cold. Where did you go today?


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[Assistant] Let's at least dry your feet. They must be freezing.


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[Assistant] How can you say such a thing? You have everything you need here. This house, the shop. Why would you want to throw all of this away?


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[Assistant] No way. Stevie could never be taken abroad. I wouldn't allow it.


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[Assistant] If you go abroad, you'll just have to go alone.


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[Assistant] That's right. You would be very unhappy without me. Admit it.


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[Assistant] My husband will find you an excellent place to stay. The continental hotel is quite nice.


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[Assistant] Have you known my husband a long time? Did you perhaps meet in France?


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[Assistant] Oh no! This is the only door to our home. Just a moment, I'll see what he's doing.


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[Assistant] You've been talking in your sleep lately.


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[Assistant] I couldn't really understand. It all sounded kind of silly, really. It didn't make much sense.


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[Assistant] Her husband and her two young brothers went off for their date shooting. They never came back.


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[Assistant] In crossing the moor to their favorite snipe shooting ground, they were all three engulfed in a treacherous piece of bog.


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[Assistant] And the places that were safe in other years gave way suddenly without warning. Their bodies were never recovered. That was the dreadful part of it.


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[Assistant] Here, the child's voice lost its self-possessed note. Poor ant, always thinks that they will come back someday.


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[Assistant] They and the little brown spaniel that was lost with them, and walking at that window just as they used to do.


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[Assistant] That is why the window is kept open every afternoon till it is quite dusk. Poor dear Ant.


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[Assistant] She has often told me how they went out, her husband with his white waterproof coat over his arm, and her youngest brother saying, birdie, why do you bound? As he always did to tease her. Because she said it got on her nerves.


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[Assistant] Do you know, sometimes on still quiet evenings like this, I almost get a creepy feeling that they were all walking through that window. She broke off with a little shudder.


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[Assistant] It was a relief to Frampton when the ant bustled into the room with a whirl of apologies for being late in making her appearance. I hope Vera has been amusing you, she said. She has been very interesting, said Frampton. I hope you don't mind the open window, said Mrs. Sampleton briskly.


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[Assistant] My husband and brothers will be home directly from shooting and they always coming this way. They've been out for snipe in the marshes today.


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[Assistant] So don't make a fine mess over my poor carpet. So like her manfolk, isn't it?


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[Assistant] She rattled uncharitably about the shooting and the scarcity of birds and the prospects for duck in the winter.


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[Assistant] To Frampton, it was all purely horrible.


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[Assistant] He made a desperate but only partially successful effort to turn the talk onto a less ghastly topic.


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[Assistant] He was conscious that his hostess was giving him only a fragment of her attention, and her eyes were constantly straying past him to the open window and along beyond.


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[Assistant] Chapter 13. The Three Pirates. Tom now felt hopeless again. He felt that no one cared about him anymore. He didn't want to be a bad boy. It's just that people gave him no choice. How can someone be good without love?


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[Assistant] So Tom decided that it wasn't his fault that he was the way he was. It was everyone else's fault.


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[Assistant] He left the village imagining that he would never return. After walking quite a long way, he found his good friend, Joe Harper. Joe seemed to be feeling pretty terrible himself.


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[Assistant] When Tom told him that he was planning on traveling the world, looking for new and exciting adventures, Joe said that he had had the same idea.


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[Assistant] He was angry because his mother had hit him for no reason.


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[Assistant] He didn't feel that she loved him or wanted him anymore, so he ran away.


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[Assistant] The boys decided that since they had both lost their families, they would have to be a family now.


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[Assistant] Just the two of them. Tom and Joe. Friends and brothers forever.


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[Assistant] So, now they had to plan what they would do next.


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[Assistant] After a few moments, they agreed to become pirates.


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[Assistant] Near the village, at the widest part of the Mississippi River, was a small island about one mile wide.


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[Assistant] Tom and Joe decided to make this their new home.


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[Assistant] It was totally empty of people and there were lots of trees. So no one would be able to see them from the shore.


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[Assistant] It was the perfect secret hiding place for pirates. While looking at the island, they met Huckleberry Finn. He didn't have family either.


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[Assistant] So they asked him if he'd like to become a pirate too. He very happily agreed to join them.


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[Assistant] They plan to meet at 12 o'clock that night and take a small boat over to the island.


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[Assistant] This way, no one could see them going there.


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[Assistant] They were all to bring food and any other useful supplies to help them live on the island.


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[Assistant] Tom brought some meat, a compass, and his knife with him that evening.


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[Assistant] He waited for his friends up on a hill above the river.


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[Assistant] It was a very quiet night, so he started to whistle.


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[Assistant] Then he heard someone whistle the same song somewhere down the hill.


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[Assistant] Tom tried whistling again, and someone said,


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[Assistant] These were all names that Tom had found in one of his favorite books.


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[Assistant] Once they were together, they looked at what everyone had brought.


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[Assistant] Joe had some meat with him, and Huck had brought his tobacco.


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[Assistant] Seeming happy with this, the black pirate said,


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[Assistant] They decided to steal some firewood from one of the river boats.


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[Assistant] This would be pretty easy to do now that most of the workers were in the village. But just in case someone had stayed behind to guard the boat, they were very careful when they went aboard.


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[Assistant] Once they had the firewood, the pirates then found the little boat that would take them to their island.


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[Assistant] Tom stood at the front of the boat and gave orders to the other boys.


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[Assistant] At one point, they could see the village they had left forever. Tom was happy to be leaving it, and everyone he ever knew. He thought about his aunt and Becky, and he wished they could see him now, being so brave. A couple of hours later, they landed on the shore of the island.


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[Assistant] The first thing they did was hide their boat and find a place to keep their food safe from the animals.


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[Assistant] They decided not to build a shelter for themselves, as they liked the idea of sleeping outside like real pirates. Later that evening, after dinner, they relaxed around a fire.


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[Assistant] Huck thought this was the perfect opportunity to smoke.


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[Assistant] So he took out his tobacco and started rolling a cigarette.


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[Assistant] The other two pirates watched him and wished that they knew how to smoke and then they could really be like pirates. Huck lay back and began to smoke.


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[Assistant] Soon they all became tired, but the only person to really sleep was Huckleberry.


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[Assistant] The other two pirates were feeling a little guilty about having stolen the meat, the boat, and the firewood.


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[Assistant] They agreed never to take anything of anybody else's in the future.


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[Assistant] When I returned to London, I realized my poor daughter was much worse.


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[Assistant] She stayed upstairs all the time now, and the sitting-room seemed very quiet without my little child-wife in her usual place. One day, when I was sitting with her in her room, she said lovingly, You know, David, dear, I'm afraid I was too young. Don't say that, Dora, I whispered, conscious that she was speaking of herself in the past. I was a silly little girl, David, and you know it. It's just as well that I won't live much longer. Perhaps if I lived,


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[Assistant] You'd wish you'd married someone more sensible, more practical. Someone like... She did not finish what she was saying. But we've been so happy, Dora, I said, trying not to cry. She took my hand and kissed it. We have, haven't we? David, do you think if you asked Agnes she'd come and see me? I have something particular to say to her. Of course, my love. I'll write to her tonight.


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[Assistant] Agnes came the next day, and went straight upstairs to see Dora.


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[Assistant] Although the doctor and my aunt had told me there was no hope that Dora would live,


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[Assistant] When I held her hand and saw her love for me in her innocent blue eyes, I could not believe she would be taken from me.


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[Assistant] But when Agnes came downstairs so calmly and silently, and said nothing, but raised her hand and pointed upwards, I knew it was over.


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[Assistant] And I remembered only darkness for a long time afterwards. In the middle of my terrible sadness, I received a message from Emily. She asked me to take a letter from her to Ham, her last words to the man who had loved her so much, before she and Daniel left England for Australia.


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[Assistant] They were sailing in two weeks' time, and the McCorbers were going on the same ship. I remembered my childish love for little Emily, and agreed to do what she asked.


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[Assistant] I was so frightened, Huck. You remember when I tried opening the door, but couldn't? Well, then it was suddenly very easy to open. I didn't know why.


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[Assistant] Must have been going to open the door when he heard me trying to get in, and then I guess he fell asleep while doing it. Lucky for me. So, did you see where that box was? What? Are you joking? I just turned and ran. I didn't get to see anything, Huck. If he's drunk, we should be able to get that box easily, Tom. Okay, then you go and get it from his room.


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[Assistant] Wait until we know that Indian Joe is not in there. Then we can go fast and get that box.


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[Assistant] We'll just wait until he's not in his room, then we'll go and get the money.


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[Assistant] Sure, I'll watch the room and then let you know when they're gone. Okay, you know what to do. Come to my window and make a noise like a cat.


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[Assistant] When we arrived in Yarmouth and got down from the cart, we said goodbye to Mr. Bacchus. Daniel and Ham Peggety were waiting for us.


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[Assistant] Daniel and Ham were exactly the same as I remembered them, cheerful and generous as ever, but little Emily seemed different somehow. She was taller and prettier, but she did not want to play with me or spend her time with me. I was rather disappointed because I still considered she was the most beautiful girl I had ever seen, and I thought I was in love with her.


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[Assistant] Daniel and Ham were very proud of her intelligence and beauty, and just smiled when she laughingly refused to sit next to me.


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[Assistant] But they all listened with interest to my stories of school life at Salem House.


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[Assistant] I told them about the other boys, especially the handsome clever steerforth.


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[Assistant] I admired him so much that I could not stop myself telling them all about him. Suddenly I noticed that Emily was listening eagerly, her blue eyes shining and a smile on her lips. She blushed when she saw that we were all looking at her and hid her face behind her hands.


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[Assistant] I saw it had doors and windows and a chimney just like a real house. I could not imagine a nicer place to live. Everything was clean and tidy and smelt of fish. Now I was introduced to the Peggety family. There was Daniel Peggety, a kind old sailor.


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[Assistant] Although he was not married, he had adopted two orphans who lived with him and called him uncle. Ham Peggy was a large young man with a gentle smile, and Emily was a beautiful blue-eyed little girl.


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[Assistant] They all welcomed Peggy and me warmly.


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[Assistant] I decided to go back to the village, to thank him for all his help, and to carry out a plan I had been considering for some time. I wanted to ask Biddy to marry me, and I knew I would be happy with her. So I went by coach to the old town, as I had done so many times before, and walked to the forge. But as I came closer, I could not hear the sound of Joe's hammer.


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[Assistant] And I noticed fresh white curtains at the windows, and bright flowers everywhere.


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[Assistant] Suddenly I saw Biddy and Joe at the door, arm in arm. PIP! Cried Biddy, happily, running to kiss me. PIP! It's my wedding day! And I'm married to Joe!


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[Assistant] I was still weak from my illness, and the shock was too much for me. They had to help me into the house and let me rest in a chair.


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[Assistant] They were both so pleased that I had come, by accident, to make their day perfect.


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[Assistant] Water dispenser.


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[Assistant] Stephen came to depend on Elaine for emotional as well as nursing support.


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[Assistant] As Jane and Stephen grew apart, Stephen felt more and more drawn to Elaine.


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[Assistant] Finally, his feelings grew so strong that he felt he had to end his marriage to Jane.


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[Assistant] Although his two oldest children were grown, Stephen did his best to remain a supportive, involved father to Robert, Lucy and Timothy.


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[Assistant] Lucy was touched by the way her father always managed to surprise her with gifts of perfectly fitting clothes.


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[Assistant] It means more to me that he knows what size I am and not just what size galaxies are, she said.


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[Assistant] He once spoke on a radio show of his need for strong family bonds and friendship.


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[Assistant] On March 6, 1998, he presented a science lecture at the White House as part of a series called Millennium Evenings.


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[Assistant] Stephen gave an overview of important developments in physics and biology, and his view of the future.


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[Assistant] U.S. President Bill Clinton called him a genuine living miracle because of the power of the heart and the spirit.


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[Assistant] The next year, he made a guest appearance on the animated television show The Simpsons.


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[Assistant] Enjoying his funny lines, he complimented Homer Simpson for his idea that the universe is shaped like a doughnut.


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[Assistant] The first successful appearance on The Simpsons led to others. Because he was constantly on the go, Stephen felt he needed an even better wheelchair. In 2001, a husband and wife team from the United States delivered and fine-tuned his new Quantum Jazzy 1400 Power Chair.


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[Assistant] The woman, Terry Roziski, who was expecting her first child was also wheelchair-bound. Stephen waited for just the right moment to speak to her from his heart.


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[Assistant] It might seem awkward being a disabled parent, he told her, but I did not find it so. Children accept as natural that you are in a wheelchair. Ask for their help.


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[Assistant] Don't worry, just make them part of the family team.


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[Assistant] His caring words meant a great deal to the expectant mother.


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[Assistant] Stephen brainstormed names for his new chair. Hawke's Comet, Wormhole and Thunderbolt were among the contenders. His personalized license plate reads T4SWH, which stands for Tea for Stephen William Hawking. It's a drink he loves.


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[Assistant] Stephen put his new power chair to work when he went to Germany to launch his new book, which had the catchy title, The Universe in a Nutshell. Although it covers some of the same material as a brief history of time, it goes far beyond it.


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[Assistant] Aimed once again at a popular audience, the new book discusses such topics as the possibility of time travel and the Star Trek vision of the future.


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[Assistant] The book makes the point that although humans have all sorts of physical limitations, there are no limits to our imagination.


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[Assistant] Our minds can take us anywhere in the universe.


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[Assistant] Once again, Stephen's writing proved popular. In June 2002, he received the Aventus Book Prize, an award managed by the Royal Society and Great Britain's National Academy of Science.


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[Assistant] Sponsored by the Aventus Pharmaceutical Company. The prize is given to books that best explain science to the general public.


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[Assistant] Wherever I go around the world, people want to know more, Stephen declared on accepting the award.


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[Assistant] Scientists came to Cambridge from all over the world to greet him and participate in a special birthday conference. Some of them gave talks about cosmology.


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[Assistant] Scientists Leonard Susskind called Stephen one of the most obstinate people in the world. No, he is the most infuriating person in the universe. Seated toward the back of the room, Stephen flashed his famous grin.


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[Assistant] Another cheerful note was his friend Kip Thorne's promise that by the time Stephen turned 70, all his theories about black holes would have been tested. Then the audience grew very silent. It was time for Stephen himself to speak.


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[Assistant] It has been a glorious time to be alive and doing research in theoretical physics.


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[Assistant] Our picture of the universe has changed a great deal in the last 40 years, and I'm happy if I have made a small contribution.


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[Assistant] But sometimes such moments can work in reverse. Two and a half years later in July 2004, newspaper headlines proclaimed Hawking admits being wrong.


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[Assistant] At a jammed conference in Dublin, Ireland, Stephen explained that he no longer believed that black holes totally destroy everything that falls inside.


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[Assistant] Some information, he declared, might be returned to the universe.


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[Assistant] Stephen said he had been thinking about the problem for 30 years.


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[Assistant] His new theory meant also revising his previous ideas about baby universes branching out from black holes.


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[Assistant] I'm sorry to disappoint science fiction fans, he said, but if information is preserved,


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[Assistant] There is no possibility of using black holes to travel to other universes.


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[Assistant] If you jump into a black hole, your mass energy will be returned to our universe, but in a mangled form.


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[Assistant] All over the world, scientists discussed Stephen's new views. But John Preskill, a physicist at Caltech, was especially pleased with Stephen's turnabout.


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[Assistant] Preskill had bet Stephen and Kip Thorne that information falling into a black hole was not lost forever. It was time for Stephen to pay up. He gave Preskill a book titled Total Baseball.


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[Assistant] Preskill gladly accepted his prize but admitted afterward, I'll be honest, I didn't understand Stephen's talk.


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[Assistant] He was eager to study the paper that Stephen planned to publish.


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[Assistant] As for Stephen, he didn't mind admitting an error, though he had had to search long and hard to find a book on baseball in England.


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[Assistant] Do you feel that scientists correct themselves as often as they should? A reporter asked him early in 2005.


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[Assistant] Through his writing, Stephen had awakened many people to the wonder of cosmology, but he felt that a brief history of time was too difficult for many readers. Stephen still wanted to reach the broadest audience possible, so he wrote a simpler book. He called it A Briefer History of Time.


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[Assistant] He also developed and played himself in a movie on the universe beyond the horizon.


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[Assistant] Written for a popular audience, it aims to show that cosmology is relevant to our lives and to the way we view our place in the universe.


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[Assistant] Stephen had to change his prediction that the theory of everything would be found before the end of the 20th century. But he remains hopeful that scientists are close to finding the ultimate secrets of the universe. And he continues to take great joy in his work.


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[Assistant] Even if a theory of everything is discovered, that will not mean the end of physics or the end of Stephen's work.


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[Assistant] On Christmas Day 1999, talk show host Larry King interviewed Stephen on the CNN network.


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[Assistant] At the end of the program, he asked his guest what keeps him going.


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[Assistant] Stephen said his secret lay in his boundless curiosity.


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[Assistant] He had so many questions and he wanted to find the answers. Stephen told Larry King that he loved life and that he planned to keep working as long as possible.


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[Assistant] Because he always refused to quit, Stephen has vastly increased our knowledge of the universe.


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[Assistant] His accomplishments have made him an inspiration to people all over the world.


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[Assistant] Just the tastiest darn thing y'all ever did see.


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[Assistant] Well, at least we know two of them, right? Death and taxes. So these two are universal. They never change. But what is the third thing?


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[Assistant] Yeah, you have AI correct. Well, I would say the third thing in 2024 would be AI is actually changing humanity.


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[Assistant] So last year I saw this article that some law firms are using gender of AI to drive legal documents and some startups even try to use AI to help clients argue in court as opposed to using a human attorney.


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[Assistant] So here I think it's important to define what we mean by AI. And I want to, uh, use, uh, Mark Riddell's definition. AI, uh, in the context of this talk refers to algorithms that perform tasks or behaviors that a person would reasonably deem to require intelligence of human to do so.


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[Assistant] Uh, of course, uh, AI is too much umbrella term and in this talk, I sometimes use it to refer to non-traditionally AI things. But for the sake of simplicity and consistency, I'm just gonna use AI throughout the talk.


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[Assistant] To refer to a bunch of these kinds of algorithms.


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[Assistant] So despite the promises of AI, I think there has always been a gap between what AI can do and how AI can serve humanity.


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[Assistant] In the 90s, uh, Rich Carana's research project found that doctors actually prefer rule-based models over better performing neural nets. Does anybody want to know why?


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[Assistant] So, rule-based models allow the doctor to see the list of rules AI used to make a diagnosis or to predict the risk of pneumonia.


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[Assistant] As opposed to neural nets that function as a black box that doesn't allow any changes or any correction of AI mistakes.


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[Assistant] I think it's the 90s, but the day was cut off in this image. You can search for the title. It's published in KDD, if I remember correctly.


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[Assistant] Well, this paper, actually I was wrong. This paper was probably published much later, but the project I mentioned was in the 90s. So this particular paper is, I think it's in the 2000s.


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[Assistant] Alright, so how do we close this gap? I believe by conducting human-centered design, we can close this gap to some extent.


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[Assistant] For example, in this project I work with my students and pathologists to consider how we can use AI to help them examine histopathology images.


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[Assistant] However, there is currently a lack of consensus about the adoption of AI among pathologists because AI as of now is still not good enough to completely replace humans. So it's really unclear


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[Assistant] To tackle this problem, we conducted human-centered design, few studies with pathologists from UCLA Health. Our key finding was that


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[Assistant] Pathologists could work with AI just like how they work with a trainee.


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[Assistant] In the way that they can see AI's findings as if AI as a trainee reporting back to them and they serve as the expert following a top-down workflow to verify these AI findings.


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[Assistant] So here's the use interface we designed based on these insights.


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[Assistant] A pathologist would start by seeing the AI's result. Here it shows it's WHO grade 3 tumor.


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[Assistant] And then they will see at the top level a number of criteria based on which the AI model comes up with this diagnosis. And it shows that mitosis is the top


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[Assistant] So if they're still unsure, they can pick some of these sample evidences and then drill down to the original slide.


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[Assistant] With full context of the image to verify that AI is indeed making the right decision on this particular part of the image. And along the way, if they see any mistakes, they can override those decisions and the entire diagnosis, if necessary, will be updated.


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[Assistant] In a study with twelve pathologists from three medical centers, within less than an hour of training, they could achieve more accurate grading using this tool called CrossPath, compared to an existing digital tool.


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[Assistant] I think this project I just showed you is an example of how human-centered design can close the gap between what pathology AI can do and how this kind of AI can actually help pathologists work.


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[Assistant] So generally speaking, my research goal is to develop interactive systems that can catalyze AI advances by working towards three levels of human centered objectives. Augmenting human abilities,


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[Assistant] Assimilating human intents and aligning with human values.


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[Assistant] So next I would, uh, give you some examples, uh, for one of these, each of these three levels.


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[Assistant] For augmenting human abilities, which is actually the majority of my work in the past five years, I have explored the space of medical diagnosis and research.


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[Assistant] So to give you an example, I want to focus on the second area, mechanical and robotic design.


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[Assistant] So in this project, uh, which is the, actually the last project of my PhD. So people ask me, uh, when did you change your research from fabrication to AI? So this is the, kind of the point where I realized, hm, there is something that is really interesting.


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[Assistant] Uh, it's, so it's called generative design even though we're not really using generative AI in particular.


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[Assistant] So the goal in this project was, uh, we want to augment humans' abilities to design both structure and appearance.


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[Assistant] Structure and appearance are both important, but they often trade off each other in the traditional mechanical design tasks. Existing tools often prioritize structural integrity.


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[Assistant] But they lack the interactiveness for users to explore. Within the goal of structural integrity, how can I explore appearances?


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[Assistant] To understand this tool called Forte, let's walk through the process of using it to design a leg for a quadruped robot.


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[Assistant] To start, the user would perform some simple sketches and describe the loading scenario. So here's the original robotic leg we want to redesign.


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[Assistant] And the user can just sketch some shapes like this curvy structure they want to create the robotic leg of.


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[Assistant] And then they will also specify the load, which is the weight of the robot's body onto this leg, as well as the bulging condition, which is where, uh, this, this robot leg makes contact with the world on the ground.


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[Assistant] As well as the design domain, you can think of it as a boundary, uh, as a bounding box that, uh, covers the space in which, uh, this lack can take place.


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[Assistant] Next, the user can use Forte to generate structures based on the sketch. For example,


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[Assistant] The user can ask the tool to add additional support because the initial sketch might not be sturdy enough to support the weight.


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[Assistant] So here, Forte adds a parallel structure next to the user's original sketch.


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[Assistant] All the user can ask the tool to create a variation based on the original sketch. So here it looks a little bit different, but still the resulting structure tries to stay similar to the original sketch.


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[Assistant] As defining a boundary within which, uh, the optimization can put in more structures to provide support.


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[Assistant] You can think of these three, uh, techniques as incorporating the appearance information, the sketch.


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[Assistant] Into the optimization by trying to mimic the user's sketch in the generated process of the structures.


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[Assistant] Importantly, we need to allow users to control this generation.


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[Assistant] So we provide this global similarity slider. By increasing the similarity value, uh, AI would try to stay as close as possible to the original sketch versus a lower value will allow AI to go a little wilder to generate structure that look more different.


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[Assistant] You can see the differences between two similarities.


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[Assistant] And then once the user sees a result coming back, they should be able to think about it and make some edits. And then AI should take into consideration in the next iteration.


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[Assistant] So it allows the user to perform this direct edit onto the AI's result by erasing certain parts of the structure.


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[Assistant] Which then prompts the AI to consider those erasions in the next iteration.


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[Assistant] And the user can keep doing this back and forth until they are happy with the result.


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[Assistant] Or they can add more structure if they see this. It's probably too empty.


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[Assistant] And they want to add a truss and then the optimization process would try to incorporate the kinds of intents in the next iteration.


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[Assistant] And importantly, we need to inform the user along the way, what's the trade off? Because not all kinds of structure would have the same type of structural integrity. So we provide this visualization view, a heat map that visualizes the stress distributed over the structure.


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[Assistant] And lastly, we can go into the fabrication process. Uh, in this case we use a laser cutter.


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[Assistant] Alright, so that is a process of designing the leg as an example of using this tool.


[User] Please transcribe this text

[Assistant] So what's happening under the hood is this algorithm called topology optimization that is based on a well-defined, well-established method, finite element analysis.


[User] Please transcribe this text

[Assistant] The basic idea is that the process of generating a mechanical structure is, given a design domain, you need to decide within this bounding box which elements I want to keep and which I want to throw away.


[User] Please transcribe this text

[Assistant] Uh, you can think of it as, like, sculpting, right? You have a bunch of material and then you have to carve away those you don't want and then whatever is left is what you want to create.


[User] Please transcribe this text

[Assistant] So we have a design domain, in this case 2D of, uh, these finite elements, uh, XE. And then this entire domain of elements will undergo the optimization process where each iteration tries to either increase or decrease each element's density governed by this objective function.


[User] Please transcribe this text

[Assistant] Until eventually the compliance, uh, converges, uh, with minimum compliance means that with maximum structural integrity given the limitation of the material as well as the user sketch to follow.


[User] Please transcribe this text

[Assistant] So this FEM, uh, method is already, uh, out there. And we didn't change it at all. We used it as a black box. But the way we enable these novel interactions is to tweak whatever comes out of this black box in each iteration.


[User] Please transcribe this text

[Assistant] So in each iteration, uh, this black box would spit out for each element a new value.


[User] Please transcribe this text

[Assistant] And I'm gonna go through some of the approaches that enable the three techniques.


[User] Please transcribe this text

[Assistant] So for adding a new structure, we simply say, whatever is on the user sketch, we keep it. Anything else, we follow what the objective function says.


[User] Please transcribe this text

[Assistant] For obtaining a variation, instead of manipulating this, uh, x e nu, we instead distribute initial value.


[User] Please transcribe this text

[Assistant] When we assign, uh, the mesh, the material to the design domain, we say the closer the space is to the original sketch, the more initial material we assign.