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[Assistant] And so, from then on, we've got a board of trustees. I'm still the president. There are twelve or thirteen other trustees who help run it. And a year or so later, we converted it into a wiki.


[User] Please transcribe this text

[Assistant] Some of them are very qualified indeed and others are really experts who may be not professional mathematicians, but they know a lot about sequences and others, not just, you know, mathematical sequences, but all kinds of sequences and computers and so on.


[User] Please transcribe this text

[Assistant] There's a very disciplined group of people who do most of the work now. Wonderful people.


[User] Please transcribe this text

[Assistant] And then the other editors were able to access the database and approve or make changes, suggest changes, communicate, discuss things with the submitters, with the contributors.


[User] Please transcribe this text

[Assistant] In the pit. Wrestling with the contributors, editing the sequences, saying, what exactly do you mean by that?


[User] Please transcribe this text

[Assistant] Quite often a new contributor will send in one or two or three sequences that don't belong. But you know, normally that only happens once with each person. Most of the trouble is people sending in duplicates, sequences that are there already and they didn't look carefully or they had a mistake in their work.


[User] Please transcribe this text

[Assistant] The professional, you know, mathematicians, chemists, physicists use it because they're working on a problem and they come up with a sequence of numbers and they really want to know quickly, what's the formula for this? Is it new? Is it hard? Is it easy? Is this a famous hard problem that I've discovered?


[User] Please transcribe this text

[Assistant] There are many. In fact, I keep a list of all the papers that have cited articles and websites, books that have cited the OAIS. Very often they'll say things like, I couldn't have done this without the OAIS.


[User] Please transcribe this text

[Assistant] We discovered this connection, this unexpected connection, thanks to the OEIS. Yes, exactly.


[User] Please transcribe this text

[Assistant] And the question is, should we have a managing editor who has paid and runs things? Well, that would be much more complicated because then we'd have to raise money every year to pay this person.


[User] Please transcribe this text

[Assistant] But that presumably won't go on forever. And so it may come a time.


[User] Please transcribe this text

[Assistant] When, you know, maybe we have to find a consortium to run it or something. It's not clear. So I'm, I'm happy and unhappy with the fact that it's a volunteer organization and we keep a low financial profile.


[User] Please transcribe this text

[Assistant] It doesn't appeal at all. I've always discouraged. I think it's even in the bylaws of the foundation that we won't accept advertising, that it will always be free. I'm very happy with the editing. We have some really wonderful people.


[User] Please transcribe this text

[Assistant] Yeah, who are just brilliant. And there's also the mailing list. There's a sequence fans mailing list, which is very good. It's like a super computer set for solving problems.


[User] Please transcribe this text

[Assistant] Yes, yes, many lovely sequences. That sequence from, for example, Eric Angelini in Brussels. He alone has made my life very happy. He has wonderful ideas of sequences.


[User] Please transcribe this text

[Assistant] Yeah, that's right. Yeah, Eric Angelini, Remy Sigrist, those are my two.


[User] Please transcribe this text

[Assistant] That's right. Yes, we discourage that of course. You shouldn't just make up a sequence because it's not in the OEIS. Originally, the criterion was it should be published somewhere. Okay. And that's still my fallback reason for rejecting two artificial sequences. I have an abbreviation.


[User] Please transcribe this text

[Assistant] Playful, yes certainly playful, or variations on existing sequences. Legitimate variation.


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[Assistant] You don't know a French chemist whose son is studying for a test. This is something you need to know. Okay. Okay.


[User] Please transcribe this text

[Assistant] Yeah, very, very large. We've noticed there was somebody who for several months was sending in, looking up a sequence several times a second.


[User] Please transcribe this text

[Assistant] Every second of every minute of every day for three months. So we, until we put in some safeguards to throttle back this kind of thing.


[User] Please transcribe this text

[Assistant] It's, uh, discourage it. Yeah. We certainly don't want people setting up any copy of the site because once that happens, things get terribly confused. You never know which version, the database changes all the time. Every minute sequences are being changed.


[User] Please transcribe this text

[Assistant] Several of the editors have written programs that look for near matches between sequences. So Richard Mata, for example, every month maybe runs a program that looks for near matches. Another German contributor, Georg Fischer, has been doing the same thing.


[User] Please transcribe this text

[Assistant] So they, they turn up duplicates or near duplicates, which turn out very often to be duplicates. So we declare, if it's a recent sequence, we just reject the recent incorrect one or merge them.


[User] Please transcribe this text

[Assistant] And they end up with one correct one, and one that's been declared dead, or it's been rejected, and a number, the A number, has been recycled. So there's a lot of that going on, and so we're steadily improving the accuracy.


[User] Please transcribe this text

[Assistant] So I think I can give you a couple. There's the, um, the EKG sequence and there's Rachaman.


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[Assistant] Absolutely, yes. So that one A5132 recommends sequence.


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[Assistant] Maybe that's a video that we should do sometime, but it's a very nice sequence. It grows unbelievably slowly, but it never stops. It keeps growing forever. So it begins one, one, two.


[User] Please transcribe this text

[Assistant] After 220 terms, you get to a four. And the question for quite a while, for a week or two, was do you ever get to five?


[User] Please transcribe this text

[Assistant] And the answer turned out, yes, you do get a five, but you don't get a five until you go out to 10 to the power, 10 to the power 23 terms. Right. Which is a very large number.


[User] Please transcribe this text

[Assistant] 2 played on the, uhm, uh, special effects setting for the, of the instrument. The MIDI file, special effects FX 2.


[User] Please transcribe this text

[Assistant] Or goblins. The goblin setting. That's one of my favorites.


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[Assistant] So, I, uh, got to know Ron, uh, well, I mean, I knew about Ron before I really knew Ron, because I read about him in books about Erdős.


[User] Please transcribe this text

[Assistant] And, uh, I went to graduate school at UC San Diego. I was interested in combinatorics. And, uh, Fan Cheng, Ron's, Ron's wife, uh, she was sort of the best in my, my flavor of combinatorics. And so I, I started working with her, but of course I wanted to work with Ron. And, uh, at least at the very least I wanted to meet Ron because, you know, he's sort of this legendary figure. So.


[User] Please transcribe this text

[Assistant] I ran past him in the stairwell once and there was another time I helped Fan and Ron move


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[Assistant] Two houses, they were about 200 feet apart from each other, so it was really easy. You just carried things out one door into the next. I said, okay, what can I do? And, uh, what I ended up doing was, uh, of course the classic move. I started erasing the chalkboards. So Ron taught this intro to discrete, uh, mathematics course for about maybe 15 years. And so I started sitting in on the class.


[User] Please transcribe this text

[Assistant] I went and erased the boards and this gave me a great excuse to sort of mild chit chat. And then eventually he mentioned that, uh, well, he hadn't had his papers online yet. And I said, okay, good. I can do that. I can do that. And so I spent, it took me probably about six months.


[User] Please transcribe this text

[Assistant] He'd lost track of a few of them. So over the course of that six months, we got closer and closer. He started feeding me problems and, uh, fortunately I was able to make progress.


[User] Please transcribe this text

[Assistant] And, uh, and of course Ron, once he knows your strengths, he can start feeding you better problems and really fine tune like, okay, this is the good stuff. And so, uh, slowly over time, I got to do more and more. And I mean, in some sense, I was kind of an assistant, a friend, a collaborator. And, uh, in the end, I, I almost became like family.


[User] Please transcribe this text

[Assistant] The thing is, I figured out later, I went about it the hard way. You see, Ron, he's very generous. And if he would just go knock on his door,


[User] Please transcribe this text

[Assistant] But it doesn't mean he was an off-putting legend. I mean, he really was very welcoming. And I think part of it was he was, he was sort of too legendary for his own good in the following sense. There were a lot of math graduate students who would probably want to work with him, but they were too intimidated to go and talk to him. And because he was in a different department,


[User] Please transcribe this text

[Assistant] They didn't have a natural way, but like, oh, let me take his class. Well, he didn't teach a graduate class. And so a lot of students really never tried to approach him.


[User] Please transcribe this text

[Assistant] And, uh, they're, they're sort of, uh, on a different level than us and not really relatable. And, uh, Ron is kind of the opposite of that. He shows, look, you can be a nice person and also a great scientist.


[User] Please transcribe this text

[Assistant] Because He was so generous and warm and kind. And you didn't have to be a mathematician or even


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[Assistant] You could be, uh, a young high school person. In Ron's office, uh, I actually cleaned it out for him, uh, about a week before he passed away. There were two things, sort of, that stood out. And Ron had all these awards over his whole career. Uh, honorary doctorates.


[User] Please transcribe this text

[Assistant] So Ron loved, uh, seeing people be amazed. And, uh, one day I went out walking with him. We were walking across campus and he saw a group of jugglers. And Ron is


[User] Please transcribe this text

[Assistant] Of course, former president of the International Jugglers Association, and in fact, there's a very famous trick called the Mills Mess. It's a three ball trick, and it's named after Steve Mills. Okay, well, who is Steve Mills? Well, Steve Mills, when he was a teenager, was growing up in New Jersey, and he learned how to juggle from Ron Graham. And in fact, Mills' mess was basically developed by Ron. So Ron had developed all these amazing things.


[User] Please transcribe this text

[Assistant] So anyways, we were walking across campus. He went up to the students and I was just going to say, yeah, this is Ron Graham. He's this famous juggler. And Ron was like, no, no, no, no, no, don't tell him, don't tell him. Cause he wanted to just sort of like say, well, huh, maybe I can try. Let's see. And then all of a sudden start doing these really amazing tricks. So that.


[User] Please transcribe this text

[Assistant] So that they're like, whoa, wow, how do you do that? That's amazing. That's the performer in Ron. He really liked to perform and he had a bag and almost always, he always had a deck of cards or maybe some coins, a trick, something he can pull out and he can show people or he could pull out his wallet. And one of the things he did sort of towards the end of life, he got kind of interested in, uh, you know, the,


[User] Please transcribe this text

[Assistant] Uh, digits on, on the serial numbers on the banknotes. He said, well look, here's this interesting one, you know, four fives in a row. What are the odds? And all these sort of interesting little things he collected, just ready to pull out whenever he wanted. And he loved talking to everyone and he had this amazing ability to remember people, remember details, especially of course, all the Starbucks employees, because he spent so much time there.


[User] Please transcribe this text

[Assistant] Almost every day, several times a day, he had quite the coffee habit.


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[Assistant] Well, I mean, certainly if you look at some of the math that he did, he did math of magic, math of juggling. I think that, that showmanship, that's certainly an element. Ron had a way of giving talks that made them memorable. I've had people come up to me and say, I remember a talk that Ron gave 50 years ago. And I'm just like, wow.


[User] Please transcribe this text

[Assistant] I don't remember half the talks that I saw in the last year because they weren't memorable. So what would Ron do? Well, he would always think about, okay, it's not just enough to talk about the information. I have to do something to really connect with the audience. So he had all sorts of things. So there was one time when he was using an overhead projector and this was back in the day.


[User] Please transcribe this text

[Assistant] Uh, there are two overhead projectors and you'd walk back and forth between them and you'd put up various diagrams. He was giving his talk and, and then in the middle of the talk he was, he was at one overhead projector and then he said, just like what's over on the other side. And then you'd look at the other one and there was a hand there. It's like, what, wait, what, what's that hand coming from? He had a fake hand.


[User] Please transcribe this text

[Assistant] ...his side, and then he moved across the room. And of course, he didn't draw attention to it right away. So, things like that really set him apart.


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[Assistant] I think what made Ron such a great mathematician is he kinda had a way of just working the problem, breaking things down.


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[Assistant] And he would just work on examples after examples, do computations, look at data. He was really good at looking at data, seeing patterns. And, uh, on his table in his house was a little tiny sign that said, never, never, never give up. And I think it was persistence. He was good at thinking about problems and just working it. Of course,


[User] Please transcribe this text

[Assistant] Oftentimes at the end, it's like, okay, now we have a solution, we've got to go back and clean up the proof that got us from point A to point B. But he would just have it kind of at this


[User] Please transcribe this text

[Assistant] Persistence about it and ways of thinking about things in different ways.


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[Assistant] One of the things that made Ron so good, and I think this comes back to his personality. I was talking with Fan the other day that, you know, he was very successful in part because he was such a great and friendly person and people liked to help him out and share ideas and problems. And so Ron had an amazing ability to sort of collect problems because people were willing to share with him because of how, how good he was and how generous he was.


[User] Please transcribe this text

[Assistant] And then of course he also had the ability to say, all right, this would be a good problem for that person to work on. And so he would hand problems to people. And so he had this great ability to immerse people in problems, the right problem for the right person.


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[Assistant] I think he, he liked it. He certainly, you know, Graham's number is of course an upper bound.


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[Assistant] And of course, everybody just, uh, is fascinated by the size of the number. But of course, there's a problem in it. And the problem is, all right, you know, you have this certain structure that eventually something must be true. And Graham's number is when it was true. Uh, of course, when might it be true? Well, maybe as early as 13. So there's a bit of a gap. They have brought, of course, the upper bound down quite a bit, but still unimaginably large.


[User] Please transcribe this text

[Assistant] Oh no, he loved sharing things and, uh, I think, uh, he had, of course, a big box he labeled PR.


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[Assistant] Because, uh, he was somebody that people could connect to because,


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[Assistant] Look, maybe you can't connect to high level math, but hey, here's this person who can jump on a trampoline and do these amazing trampoline tricks, who also


[User] Please transcribe this text

[Assistant] Can talk about magic and who also can somehow connect all of it together to mathematics. And so he was a wonderful spokesman in a sense to say, Hey, you know, here's this beautiful idea called mathematics. And it's not just for some elite people who sit in academic buildings. No, no math is meant for everybody. And it really is something that has wider appeal.


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[Assistant] Well, yeah, I mean Ron always did math. There's of course Erdős had this sort of goal. He's saying, okay, how, what was his ideal way to die? And Erdős said, well, I'd be giving a talk and I'd,


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[Assistant] And I'd finished the talk and someone in the audience would say, well, this is really good, but what about the general case? And Ernest would say, I leave that to the next generation. And pass away.


[User] Please transcribe this text

[Assistant] That was, that was Erdős' ideal death. He came pretty close. Erdős came close. And Ron also came close. So.


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[Assistant] Percy Diconis is working on a problem with a student about random walks on the modulo, uh, integers modulo of prime.


[User] Please transcribe this text

[Assistant] I can't give all the details because really this is Percy's work, but uh, Ron got interested in it.


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[Assistant] He called me up and said, okay Steve, what, what if we changed the problem? What if we did this? Okay, what happens with these types of problems? You know, what's the difference? You know, how are the quadratic residues distributed? Okay.


[User] Please transcribe this text

[Assistant] And then he'd call me up and ask me more questions, say, okay, try this. And then I'd run more computations and that, we did that about four or five times the day before he passed away.


[User] Please transcribe this text

[Assistant] And on the day he passed away, I came to his house and, uh, well he wasn't up to it.


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[Assistant] Van told me that Ron had something to tell me, but wasn't ready yet. And unfortunately, he never was ready. And so, I'll never know what Ron was going to say. I suspect he probably saw something and said, ah, I think I understand what's happening. I think I understand why primes can go into 1 mod 4 are different than primes can go into 3 mod 4. Because, uh, well, he had a way of seeing things. So, well, now it's up to us to figure it out.


[User] Please transcribe this text

[Assistant] I get to hear these bits and pieces, so as an example, he told me about, uh, back in the day, he would travel to Hungary, and well, okay, that was in


[User] Please transcribe this text

[Assistant] The Cold War wasn't very easy for mathematicians to necessarily travel at that time.


[User] Please transcribe this text

[Assistant] But he, he was able to travel, so he became sort of a connection. Well, one time he traveled, he brought in five programmable calculators. Well, you weren't supposed to take that, you know, because that was advanced technology, but he took it. And he gave them to the various mathematicians there. One of them went to Lotsi Lobos, who's now the president of the Hungarian Academy of Sciences. And, uh, and he took it. And the next day he had written a little program.


[User] Please transcribe this text

[Assistant] And, you know, just a very small programmable calculator, 100 lines of code, but, you know, lots of you figured out how to do it. And then he gave another one to Andre Szemeredi. Okay, very famous mathematician. So Ron once asked Szemeredi, okay, so what did you do with your calculator? And, uh,


[User] Please transcribe this text

[Assistant] Somebody said, oh, I can't remember. I probably sold it on the black market.


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[Assistant] He's not just this mathematical genius. He's also a very kind person. And, uh, like, one of the things I've learned, uh, from, from knowing Ron was just how amazing, uh, of a husband he was. He was married to Fan Cheng in 1983. And, uh, I, I, I think they would probably have one of the best marriages I've ever seen. And he was so caring right to the very end.


[User] Please transcribe this text

[Assistant] I remember the particular moment that turned me towards mathematics. Before that, I was doing quite a lot of things, playing the piano, doing ballet. I also wrote


[User] Please transcribe this text

[Assistant] In seventh grade I even participated in a chemistry Olympiad and I won it to my surprise, but it was because of my math knowledge. That's a different story. Math came to me


[User] Please transcribe this text

[Assistant] And I couldn't, and it became apparent to me that I had not been paying much attention to my classes lately. So the teacher left me there at the board for the rest of the class.


[User] Please transcribe this text

[Assistant] She started the new lesson, she taught it from her desk, but I was there for the rest of the class. I was so distraught, I was crying towards the end and so the bell rings and she calls me to hers and says, Vesda, do you know what grade you deserve? And I said, yes, I do.


[User] Please transcribe this text

[Assistant] Probably was not such a hard problem. So my father is a shipbuilding engineer as it happens. So we sat down in the evening. He explained everything to me. The next day I went back, showed it to my teacher and she said, okay, you escaped this time. You're not going to get the bad grade. But I didn't leave her side.


[User] Please transcribe this text

[Assistant] I asked her, can I join your math circle? She happened to be the teacher leading the math circle in my middle school.


[User] Please transcribe this text

[Assistant] So it is an after-school program, uh, it was...


[User] Please transcribe this text

[Assistant] So the problem was not with the teacher, the problem was with myself. And I realized this even at that early age. I also knew that my classmates who had been going to the master call for several years,


[User] Please transcribe this text

[Assistant] So I thought maybe the circle will help me with my performance in class two. What actually happened is three months later, I won first prize at the local Math Olympiad.


[User] Please transcribe this text

[Assistant] That I'm very competitive, this is true. Uhm, that I had already competed at events in other areas. It is also true. I think I had a very hard time taking defeat. I couldn't fall.


[User] Please transcribe this text

[Assistant] Quite amazing story. So I was getting this, uhm, math engineering drift from all over the place and everyone in my family had succeeded to one event or another.


[User] Please transcribe this text

[Assistant] I think at this point I didn't have a choice.


[User] Please transcribe this text

[Assistant] Seventh grade, uh, the whole year, I took extra lessons in writing essays because I wanted to get into the English language high school, not the math high school. That's the interesting part. I knew I could do the math by myself.


[User] Please transcribe this text

[Assistant] But I didn't have a choice. For myself, it was never a doubt in me that I would continue doing something with mathematics since that day in fifth grade.


[User] Please transcribe this text

[Assistant] I saw that I was going to study abroad. It was inconceivable for kids in a socialist country.


[User] Please transcribe this text

[Assistant] To think that way, the furthest I would go probably would be Russia and you don't need English for that. I had a specific problem with writing essay and the problem was I didn't like to write essays.


[User] Please transcribe this text

[Assistant] So I would spend, you know, weekends preparing and writing these essays. Later on I found actually that it was super beneficial for me. So studying languages, writing essays. But I was doing math because I wanted to do it.


[User] Please transcribe this text

[Assistant] They, they had to, you know, give a little bit of affirmative action and also at that time the tradition was to put all of the scores out there. Everyone could see everyone else's score.


[User] Please transcribe this text

[Assistant] Okay, we started learning proofs in 5th grade. That same 5th grade.


[User] Please transcribe this text

[Assistant] Every problem we had to prove that our solution was correct, to supply the evidence, and of course we started with some baby steps. I never saw this two-column format proofing geometry. That's super restrictive.


[User] Please transcribe this text

[Assistant] Neither. It was because of the government. The government had a program.


[User] Please transcribe this text

[Assistant] better and they were higher demand on the knowledge and skills of the students but uh, uniformly throughout Bulgaria everyone had to learn a certain curriculum and proofs were included in it


[User] Please transcribe this text

[Assistant] The Masterclass of course, expanded my knowledge well beyond what was the curriculum.


[User] Please transcribe this text

[Assistant] But in high school, I have to tell you, I almost never sat in a full math class or even listened to what was going on. I had a math context book under my desk on my lap. I was just doing that and the teacher just did not, uhm, bother, uhm,


[User] Please transcribe this text

[Assistant] Classmates, but for the classmates in the next room, so it wasn't that bad. So while my classmates were taking an exam, I would be grading the exams for another class.


[User] Please transcribe this text

[Assistant] Yes, yes, uhm, you know, this practice actually is happening, uhm, here in US with, uh, because there are quite a few advanced students who literally have nothing to do in math classes.


[User] Please transcribe this text

[Assistant] So they, uhm, asked them to tutor to help with grading exams and so on. It's not good though to ask a freshman to do this for the seniors. Some, you know, things might happen to you outside of school.


[User] Please transcribe this text

[Assistant] I went to the International Math Olympiads in Cuba, in Australia, and before that I went to one of the Balkan Math Olympiads in Romania, as a representative on the Bulgarian team.


[User] Please transcribe this text

[Assistant] And those Olympiads really defined my day, month. Whatever I was doing, it was geared towards helping me.


[User] Please transcribe this text

[Assistant] I had no clue that, uh, performing well, uhm, at any of those Olympiads would give me a scholarship to come to U.S. That came later.


[User] Please transcribe this text

[Assistant] I just didn't feel any drive to it. Geometry specifically was my...


[User] Please transcribe this text

[Assistant] Most interesting topic in mathematics. That's where my imagination grew.


[User] Please transcribe this text

[Assistant] There that I could carry on in my college studies.


[User] Please transcribe this text

[Assistant] Because there were fewer countries, and those were very strong countries. And again, no disrespect to any countries here, but those were the founding countries of the Olympiad. Plus...


[User] Please transcribe this text

[Assistant] Yes. It was a very dramatic moment for me there because I had not slept the previous night.


[User] Please transcribe this text

[Assistant] I had not adjusted to the jet lag. I was completely exhausted entering the second day of the Olympiad, so I knew that I had to do it fast, do it well, and go to sleep. Shall I tell the story?


[User] Please transcribe this text

[Assistant] Yes, uhm, so that, uh, problem, the sixth problem was solved by probably 12 people and two of them were Bulgarians. Uh, I was, I think the only girl who solved that problem.


[User] Please transcribe this text

[Assistant] Two Bulgarians solved that problem, uh, Emmanuel and I. And the points on this problem were


[User] Please transcribe this text

[Assistant] Either sevens or zeros, something like that. So it was either all or nothing. I mean, you cannot chop up this problem in half, uhm, so to speak. But I do remember I spent at most 20 minutes on that problem and I had seen vaguely similar


[User] Please transcribe this text

[Assistant] Stuff to it, and it, it's not really the same problem, but the idea of somehow creating similar problems.


[User] Please transcribe this text

[Assistant] So that summer in Australia, the American team, they were only boys at that time, walked around in white t-shirts and asked anyone to write something, uh, for them. Uh, and we thought, wow, they're destroying their t-shirts, but okay.


[User] Please transcribe this text

[Assistant] There was no opportunity for us to go to U.S. much less so study. So I went to Sophie University right after that summer in Australia.


[User] Please transcribe this text

[Assistant] And the moment I started climbing up the stairs to my department, because you applied to a department, I was in the math department, I saw a poster announcing a competition


[User] Please transcribe this text

[Assistant] Interested in applying, because I thought that this would be a waste of my time, that there would be some political concerns there, whom to send, whom not to send, and I didn't have any particular connections, uhm, so,


[User] Please transcribe this text

[Assistant] I didn't apply. My roommate actually was very pushy. She was also my high school classmate. And she said, Zvezda, you apply or I'm not your friend. And I did. And uhm,


[User] Please transcribe this text

[Assistant] It was a sequence of tests. Some tests in, uh, English. And there you go, I went to an English language school, so that paid off. We had a dictation. A dictation in English.


[User] Please transcribe this text

[Assistant] To see how we can write, how we can understand. And it was from my favorite science fiction book as a child. The Day of the Three Fates.


[User] Please transcribe this text

[Assistant] It starts in a hospital with a guy whose eyes have been bandaged.


[User] Please transcribe this text

[Assistant] And he's waiting for someone to take them off and no one comes. So the moment...


[User] Please transcribe this text

[Assistant] Round, the Bulgarian foundation who are selecting us, uhm, had to yield to the American embassy so they make the final decision.


[User] Please transcribe this text

[Assistant] Of so many students finally it's made public. And I was thinking gosh what are they gonna


[User] Please transcribe this text

[Assistant] Uhm, that all 15 students were so good, they're gonna find 8 more scholarships.


[User] Please transcribe this text

[Assistant] I think that that was the major item that put me in the front runners. I heard that the Australian committee, some people on the Australian IMO committee had remembered what they did on the IMO problem number six and so they wrote to the Bulgarian committee about it.


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[Assistant] There were all of these restrictive rules about residence in communist Bulgaria. It was, for example, very hard to live in another city at that time. I had no drive to just restrict myself to live only in my hometown.


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[Assistant] Some other parts of the world. And once you see them, you want to see more. You want to explore.


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[Assistant] It was tough. It was, uh, in the beginning it was very depressing. It was a cultural shock.


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[Assistant] I was at Bryn Mawr College, which is a small women's college near Philadelphia. Now don't get me wrong, it's a beautiful place. And my professors were super supporting. I learned tons there but the beginning.


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[Assistant] Was tough. I felt isolated. I felt literally without any anchor throughout the first year.


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[Assistant] One thing that was very hard and I had not realized this before coming to U.S. was the way U.S. higher education is organized. I went to liberal arts college, which asked me to take classes outside of mathematics. Can you imagine me taking classes outside of mathematics? I had already been for one year in Sophie University.


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[Assistant] Real analysis one, abstract algebra one, and discrete math one. We took algorithms, some Russian, history of Bulgarian Communist Party, and physical education. Not every day, but... What did we do second semester?


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[Assistant] Part two of all of those. And that curriculum alone already constituted two years of what a math major in the United States would be. We were not doing any sciences or western literature or, or humanities, none of this. You had to apply for a department.


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[Assistant] I tried to be smart about it in the midst of being very depressed the first few months. So I took, uh, methods in, was it?


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[Assistant] I don't think I would have done it any differently because you have to take into account my, my psychological setup. In high school we did all of that.


[User] Please transcribe this text

[Assistant] We did science starting from sixth grade with labs. We wrote those essays that I talked so. So when I was going to South University and you apply to a specific department, you are done doing this.


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[Assistant] There was no supposing I didn't have any funding. Even the tickets were paid by that foundation. I had to earn my pocket money by, uh,


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[Assistant] So yeaah, I was supposed to go back to Bulgaria after four years. But what the Bulgarian Foundation was already predicting is that because these 15 students were so strong to start with, they would probably go on to graduate studies. And this is what happened to most of them.


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[Assistant] Yes, it's amazing that from a small liberal arts college like Bryn Mawr I went to


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[Assistant] The father of all universities in US, Harvard, father and mother, the parent. But it is not so amazing because, uhm, as I said, my professors at Bryn Mawr really, really supported me. They could see, uh, how I was different from many of the others, uhm, of the other students.


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[Assistant] Uhm, in from the deduction of logic and philosophy. But one thing that really made it possible for me to be accepted


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[Assistant] Probably in any graduate program in the United States was the research experience for undergraduates that I did for two summers while I was at Bryn Mawr. I went to Minnesota, Duluth.


[User] Please transcribe this text

[Assistant] And that was a very tough program to get in. Joe Galleon, uh, is the director of that program. And he and the other people at the program helped me tremendously. I wrote research papers on open problems. And that's what I think cut it for me.


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[Assistant] I wanted to do something with mathematics.


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[Assistant] And when the finals happened, I went to take them. Two of my professors contacted me and said, Zvezda, can we copy your final as the solutions for the others? I said, no, no, no, you have the wrong person. I was probably the only one who knew nothing about this, but they said, yeah, but you learned.


[User] Please transcribe this text

[Assistant] So it paid off this very hard work. So I wasn't thinking about what I would be in the future, I was just thinking about surviving that first year. And I did it. And after that, after I started working on my PhD thesis with, uh, Joe Harris, another Joe in my life,


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[Assistant] Uhm, it was a completely different type of experience for me.


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[Assistant] Well, you don't have to anymore.


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[Assistant] Study all of these different topics. You are more goal-oriented.


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[Assistant] And Joe Harris had a very nice approach with students. He would feed us, at least me, every week a new example of a phenomena that, that I was supposed to solve. And every week it got more and more complicated, but gradually. Until at 3am one morning.


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[Assistant] The light dawned on me what was happening. So this process was more directed as opposed to spreading myself and studying different topics, which I liked.


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[Assistant] And when I went to graduate school, narrowed it further down, and guess what the area of my thesis was?


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[Assistant] Challenge me with something, it's very likely I'll rise up to the challenge if I like it.


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[Assistant] Starting with my fifth grade teacher in math and going all the way to Sophie University, great teachers who cared about me and who very selflessly gave everything they had to me and my teammates on the math circle team.


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[Assistant] Let's backtrack. The last year at Harvard, I had already solved my PhD problem, so I was just writing technically the thesis and wrapping up some loose ends. But that last year, I entered the Harvard Graduate School of Education program.


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[Assistant] But I was also aware that post-docs


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[Assistant] But public schools, no. There are rules about this. And when I came to Berkeley, I enrolled in the program here at UC Berkeley so that I could get a teaching certificate in California.


[User] Please transcribe this text

[Assistant] Well, that's where I got a post-doctoral fellowship first at MSRI and then at UC Berkeley. Okay. But to tell you the truth, I never used the actual teaching certificate for anything.


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[Assistant] Audience, general public here, what is a math circle?


[User] Please transcribe this text

[Assistant] What a Mass Circle is and maybe to participate if someone else organized. Okay.


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[Assistant] And so at that very conference I asked, uh,


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[Assistant] Seven of my colleagues, so eight total mathematicians, would you like to help me start an example? Just, just a demonstration for one year.


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[Assistant] And the teachers will collect topics and then they would go and do it in their schools. The circle started in 1998? 9? It's still running.


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[Assistant] Yes, yes, so we have students in the pre-COVID times from Sacramento to San Jose.


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[Assistant] Oh yes, uhm, so over the years, uhm, many master calls have, uhm, started around US.


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[Assistant] Some in Canada, all over the world actually. Some of them were inspired by the Berkeley Mass Circle. MSRI played a major role in supporting new circles and they still play such a role with grants, with support. And they organized conferences, in fact.


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[Assistant] The International Congress of Mathematics in St. Petersburg coming up will have a satellite conference called Math Circles Around the World. And so, I will surely be there.


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[Assistant] Uhm, no, because you had math circles in Bulgaria before. So that's your counter example. It wasn't the deficiency in the school system that drove students there to the math circles. So I've been asked this question many times, so what's


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[Assistant] The difference between master calls here and master calls back in Bulgarian from those times. And I would...


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[Assistant] Something beyond. Many students in the U.S. come to the masterclass because they don't like the math in school and they want to see something else.


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[Assistant] Different, not more of it. Of course there are exceptions and we have been working with teachers from great schools that definitely do a wonderful job. But by and large, the kids that come to the MasterCall here don't get what they want in math in school.


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[Assistant] What they see at the master class they will likely never see in school because the topics that we teach are not just beyond what they studied there, they're just very different. Of course they will apply some of the knowledge that


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[Assistant] We are very kind of form about this to tell them that calculus may not even appear in


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[Assistant] Who was the very first year when we started the MasterCall. He was for several years at the MasterCall, but he was also on the U.S. team at the International Math Olympiads. He got gold medals. He got the perfect score.


[User] Please transcribe this text

[Assistant] Also a brilliant pianist. And what did he do? Uh, from what I remember, he...


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[Assistant] Got a math major I think at Harvard, that's right. And then after that he went for a year to teach English as a foreign language in a province in China.


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[Assistant] Is his reference, uhm, to tell them about him.


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[Assistant] The only thing they asked me about Gabriel was his math background. They said, is this, is he exceptional? And my answer was, well, you get...


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[Assistant] So he's right now a professor of economics in Canada. So you don't have to become a mathematician, but what he experienced through Math Olympiads and Mathematics definitely helped.


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[Assistant] I have written several papers, research papers in different areas, so algebraic geometry, but also combinatorics over the years. So I went back in some way to my original research that I did as an undergrad, but implementing the wisdom that I gathered from algebraic geometry.


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[Assistant] Along the way, I started publishing books in math circles.


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[Assistant] Decade of the Berkeley Mass Circle, Volume 1, was the founding book of a long series of MSRI and the American Mass Society.


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[Assistant] I am translating, adapting, and co-authoring books for middle and high school students textbooks. They are originally written in Bulgarian by Professor Paskalev and his wife, but they had to be adapted to the US reality.


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[Assistant] And so I have been doing that and putting a twist, a spin. So a lot of things from the master calls end up there. Some stuff that I have taught at UC Berkeley courses.


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[Assistant] Yeah, this question are very politically charged. So I am treading here very carefully how to answer this. Uhm, the education that I know from Bulgaria is from the communist times. When I came to US three months after that, the


[User] Please transcribe this text

[Assistant] Communist regime fell apart in Bulgaria. So I'm used only to the,


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[Assistant] communist type of education. And it was not perfect. I had to study history of Bulgarian Communist Party for which I didn't care.


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[Assistant] But the rest was fantastic. And it was fantastic in my English language school.


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[Assistant] It was, if I want one word to say it was systematic.


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[Assistant] It was building upon itself from the previous years. So if you have the same math teacher throughout, uhm, let's say from fourth through seventh grade.


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[Assistant] In U.S., people are very afraid, parents are very afraid and with good reason that if they get the same teacher for several years and that teacher turns out to be bad, then their kids are going to suffer.


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[Assistant] And so you have this turnover in teachers from year to year, this kind of slowing down or lack of system.


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[Assistant] Overwhelmed with other things that they have to do in school. Bureaucratic, administrative, and different states, uh, require different things. And very often, very low level.


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[Assistant] In mathematics, uhm, and so you end up with teachers who are doing


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[Assistant] So there's some pros and cons in both systems. I cannot quite see how to institute such a rigorous systematic system in the United States where different states cannot agree on some common standards. You have the common standards, that is true, but how far does it reach?


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[Assistant] That moment when I go back to fifth grade, she literally gave me a second chance. But she gave it in such a way that made me actually do the problem. Not just to give up and skip. No, and I had to do it.


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[Assistant] But I do tell my students something, that Joe Harris, my graduate, uhm,


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[Assistant] I have to say that during this last year and a half of COVID online period, videos have become a major source, a learning source.


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[Assistant] For not just students, for everyone. And as we know, the technology.


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[Assistant] But now I'm thinking gosh, I'm using them in my classes. Uh, I did an introduction to proofs class at Berkeley last fall and this fall it is continued by one of my students. Uh, it's an actual


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[Assistant] Start me again. I've been told that I'll drop, I'm not allowed to drop any tears on the original manuscript of, uhm, Deanna Lisi Newton's...


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[Assistant] First write-up of calculus meant for a broader consumption. I mean, he had plenty of manuscript for himself, but De Analisi is his attempt to write something coherent for, still not for a wide audience, but for his disciples, for his little circle in Cambridge. But still, I was getting so, um, agitated.


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[Assistant] Overwhelmed to see his hand. Oh, I will again, I'm sorry.


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[Assistant] And it's not, you know, it's not some kind of deification of Newton. You might think it's that. It could be that.


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[Assistant] But I see, well, probably it is, something like that. But I, you know, the one that got me going here just a minute ago was Isaac Barrow, who is often regarded as Newton's mentor to the extent that he ever had a mentor. And Barrow is saying something about Newton to his, uh,


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[Assistant] I'm sorry, I'm just having so much trouble getting through this. But, you know, he talks about his friend such, uh, extraordinary proficiency and genius in these things, these mathematical things, uhm, which is quite an understatement.


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[Assistant] Well, I think it's, this may be the smartest person of all time that we're talking about here. I mean, this is the world's greatest geniuses. Einstein is wonderful. Archimedes is wonderful.


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[Assistant] And so immaculate. And for some reason I'm moved by the cross outs. That here's, you think of him as superhuman, but he's not. He makes mistakes and he crosses things out just like the rest of us. Well, not maybe just like the rest of us, but still.


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[Assistant] Uhm, it is a, it is a person that we're looking at. And he was, he was quite young. I mean, we're seeing someone who's in his early


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[Assistant] He's not really writing for publication. Something about his fear moves me. You know, what is he afraid of? But you know, going back to his own story, for people who don't remember or don't know, he was born without a father. His father died while he was in utero, and so he was born


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[Assistant] His mother and his stepfather would die and he also wished that he would die himself. So, you know, this is a very troubled, lonesome little boy who grows up to be an extremely troubled young man who then goes on to be this towering intellect. I see all of that when I see his hand and his secrecy and you know, writing this book for nobody.


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[Assistant] You know, it's a strange thing. It's a book for himself. And maybe to be shared with a few people, but I think even there, he was uncomfortable doing that.


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[Assistant] Yeah, I don't think I'm making any kind of implicit comparison there. It's, it's, I think I feel a sense of awe that for other people might be religious awe.


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[Assistant] Deify, you know, am I deifying him? I probably am in some way that for me as a non-religious person maybe there is some version of reverence happening here and so the same way that a worshiper of some other more traditional religious figure would feel


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[Assistant] Seeing the shroud of Turin or something like that. I think I'm having some of that right now.


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[Assistant] I'm fanboying, but it's a little more cosmic than that, a little more reverential than that. But yes, it's something like that.


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[Assistant] Sure. Good, good question. Yeah, that's a challenge. I like visualizing my, this anonymous character in the pub. Right, so if the person is willing to listen to a discussion about mathematics, I guess I would first say that mathematics and calculus specifically have been used to give us the modern world.


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[Assistant] Our cell phones today or microwave ovens or the GPS gadgets that help us find our way home. But calculus is actually built into all of those things too. They're not pure technology.


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[Assistant] They are technology that use mathematics relating to questions of how things change. So if I had to give it to you in one sentence or even one word, calculus is the mathematics we use to describe things that change. Specifically things that change continuously or smoothly, not in jumps, not in jerks, but things that change


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[Assistant] Gradually and smoothly, they could be quite rapid, but so what sorts of things? Well, anything that's moving is changing its position.


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[Assistant] So when we study how to get a person on the moon, you know, the mathematics of rocket science is calculus. If we want to understand how uhm, the amount of virus in the body who has HIV decreases as they're given triple combination therapy to keep their disease at bay,


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[Assistant] Studying the dynamics of a viral load, the changing levels of virus or the T cells in their immune system. Calculus is used for that too and has helped us create those therapies that I just mentioned. It's calculus is the mathematics of change and until it was invented, mathematics was sort of a static


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[Assistant] Motionless, inert thing, which is sometimes what you want. I mean, you don't want a building to move. You don't want a bridge to shake or fall down. So sometimes you're happy with things at equilibrium, at rest, unchanging.


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[Assistant] Yes, essentially it was. It was, it was something that was as plain as, you know, the fact that we all get older.


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[Assistant] Or that children grow up. I mean, everyone knows that things change. We see leaves falling. We see water moving in a stream. But mathematicians and scientists couldn't really describe it. Not very well. There was only one case that could be described, which was the simplest kind of change.


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[Assistant] Which was change at a steady rate. So if something changes at a constant rate, meaning like, you know, if I give you, uh, if I say one banana costs, I don't know what would a banana cost, a dollar or a pound or something. I don't, that's a pretty expensive banana, but.


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[Assistant] You know, how much will it cost if I change the number to 10? And then you say 10 times 1 will be 10.


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[Assistant] ...was a mystery to science forever. Aristotle had theories of the motion of a falling object and...


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[Assistant] I think it's more a typical case of human curiosity. That the circle was a natural shape. People see circles when they look each other in the eye. They see the circular iris and pupil. We see the moon has the shape of a circle. We see circles in the ripples on a pond. So we've been aware of circles forever.


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[Assistant] Yet we can't answer the simplest thing about a circle. Like how far is it around the circle, the circumference, or how much area is inside a circle.


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[Assistant] And so that was the original beginning of calculus, was answering questions like that about simple curved shapes like circles and spheres. And there was no way to do it. You won't find the answer for the, believe it or not, the area of a circle does not occur in Euclid's elements. There is no formula pi r squared that we all learn in high school.


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[Assistant] Number that, that, you know, has infinitely many digits that never repeat and show no pattern. That's already a clue that there's something deep happening with circles. That, that pi is so intimately connected with them. And so the first person to really solve the riddle of area or circumference of circle was Archimedes.


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[Assistant] To solving questions like that was the strategic use of infinity. This amazing, scary for many people concept of something that never ends.


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[Assistant] Uhm, Archimedes showed that if he imagined chopping up a circle, say for the area question, if he chopped up the circle into infinitely many pizza slices, infinitesimally thin,


[User] Please transcribe this text

[Assistant] He could rearrange them to make a rectangle and then find the area that way. And so it was a magnificent leap of imagination to see a circle as equivalent to a rectangle.


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[Assistant] Through the bridge of infinity and infinitesimals. But that's his accomplishment and, you know, making it very careful and rigorous, but that's essentially the big, uh, new ideas, that you could use infinity


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[Assistant] To solve questions about curved shapes. And so back to your question, what was it that gave rise to calculus in the time of Newton? You know, this outgrowth of Archimedes work thousands of years earlier. It was a similar question instead of now analyzing curved shapes, which was still actually a live question for Newton. There was a new question which was analyzing


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[Assistant] Motion that changed its character as it proceeded. So something that sped up or slowed down that accelerated.


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[Assistant] That was the kind of question that arose in thinking about the motion of the planets.


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[Assistant] The motion of falling bodies that Galileo had worried about, Kepler's laws, the Copernican system of the planets going around the sun, all of those raised questions about variable motion. Although Galileo and Kepler had laws, they couldn't explain them. And so that was really the big million dollar question for Newton was could you explain


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[Assistant] Yes, alright, so these are the facts. Newton invented his version of calculus around the middle 1600s. So you could date it 1665 or 66, but it's around then.


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[Assistant] Leibniz is definitely later, about 10 years later. He, he first becomes interested in advanced mathematics at around the time of 1672 when he's in Paris meeting with Christian Huygens who is the greatest mathematician on the continent. And it's a measure of Leibniz's genius that


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[Assistant] Starting from, as a beginner, within just a matter of four years, he is almost at Newton's rank.


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[Assistant] And he's not even particularly, mainly interested in mathematics. He's also a diplomat, he's a logician, he's, he's a linguist. I mean, he's an extremely versatile genius himself.


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[Assistant] Uh, maybe the most versatile in a century of geniuses, and that includes Descartes and Galileo and Bach and, you know. So Leibniz is, he's got game, you might say. Okay. I mean, he can do everything. I mean, what's confusing is that he was shown some of Newton's manuscripts.


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[Assistant] Who would then manage to get the letters to Newton. So we have inquiries in this book that sits


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[Assistant] To my right, I have the letters in the hand of Leibniz and in the hand of Newton. Back and forth with Leibniz's questions to Newton and then Newton's responses. And so there was always a question of did Leibniz somehow plagiarize Newton? Was he given clues from seeing these manuscripts?


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[Assistant] And then somehow incorporated those clues into his own version of calculus.


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[Assistant] So I'm not a historian, I should make that clear. I don't really totally know what I'm talking about. But from what I can see, I think it's clear that Leibniz essentially independently thought of calculus. His version of it is quite different, notationally certainly.


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[Assistant] You could, you could publish a book. You could send a book to a publisher and it would be published. And so Leibniz does publish his version of calculus.


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[Assistant] And certainly he has disciples who publish the first textbooks on calculus. So this has always been the argument, who's first? I mean, if you measure it by publication, you have to say Leibniz is first, but who is first conceptually? There's no question that Newton is first.


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[Assistant] And also to my reading, there's no question that Newton is the superior mathematician. He just goes much deeper, and you see this in some of the letters, and I would be curious to talk to our, uh, librarian friend Keith about this, because one of the letters has Leibniz trying to show that he has credibility.


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[Assistant] And he, he offers an infinite series to Newton. It's a particular kind of calculation in, in calculus, use of infinitely many algebraic terms, or, or numbers sometimes. Anyway, he has a particularly impressive, he thinks, infinite series to show Newton that, that he's...


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[Assistant] And then I don't have a paraphrasing, the gist of it is, considering that I already know three other ways of doing it myself, I never expected to see a fourth way.


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[Assistant] You know, this is supposed to be a compliment, but it's really a very sarcastic insult. Like why are you bothering to tell me something I already know how to do three other ways?


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[Assistant] That's exactly what Newton says to him. And then, in response, he sends him a letter that is filled with extremely arcane, difficult fruits of the calculus that he has developed. And Leibniz doesn't understand where these come from.


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[Assistant] Which demonstrates that his calculus is not up to snuff compared to Newton's and he even asks questions and Newton then in another letter gives him a very pedagogical almost condescending explanation as you would like lecturing a child. Okay. So, okay, I mean I think I've answered it but as far as this document that I've got in front of me,


[User] Please transcribe this text

[Assistant] When Newton was president of the Royal Society, he, uhm, convened, I believe this is the correct history, or someone convened a priority dispute, like you say, a trial. You know, the documents to establish, well, in the case of the Royal Society, the hope was to establish that Newton was first.


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[Assistant] The study of things in flux. And he, uhm, for him functions are, he calls them fluent, affluent quantity, something that flows. He's very much thinking about time. Leibniz does not think about time. He's thinking more about discrete objects. He, he,


[User] Please transcribe this text

[Assistant] Uh, is very visual and geometrical, but he comes at calculus by thinking about discrete things that become more and more nearly continuous. But he doesn't, time is not nearly as important to him, nor is physics. It's, it's an outgrowth of geometry for him. I mean, Newton is very geometrical too, but, uh,


[User] Please transcribe this text

[Assistant] And his d by dx, all of that is Leibniz. It's just a much better notation. Newton has a funny notation with dots over the letters. And so to do a fourth derivative, he would have to write y with four dots over it. We don't, we don't do it that way anymore.


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[Assistant] So we have derivatives and integrals, or we speak of differential calculus and integral calculus, which roughly speaking means chopping things into infinitely, uh, many small parts, that's differential calculus, and putting them back together, integrating them into a whole is integral calculus, and you need both to do


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[Assistant] The analysis in the style that I say Archimedes pioneered of breaking hard problems into all tiny, you know, many, many tiny pieces that are simpler, solve those, put them back together. That's the, that's the heart of calculus, that idea.


[User] Please transcribe this text

[Assistant] The infinity principle, uhm, nobody really calls it that, but I would say that is the, the methodological heart of the subject, that you break anything that's continuous, whether it's a shape, a continuous curve, a motion, anything changing smoothly can be broken into infinitely many infinitesimally small parts,


[User] Please transcribe this text

[Assistant] That then we can think of as being constant or somehow changing at a constant rate or being a straight line. That's the great bridge to the existing mathematics of straight lines and constant speeds and so on. Anyway, both of them have that idea, both Leibniz and Newton, and they both see the connection between the two halves of calculus, the putting together and the taking apart.


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[Assistant] Through something we now call the fundamental theorem of calculus. So since both of them, I mean I hesitate to say discover it because historians will point out there were also precursors of them. People like Isaac Barrow and James Gregory. But okay, roughly speaking, Newton and Leibniz make calculus systematic.


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[Assistant] They put all the different techniques that are lying around together into unified theories that are very close to the theories we still do today. I mean, they've been improved over the years by disciples of both, but uhm,


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[Assistant] It is the beginning. It's the first course for us in college. We don't use it very much. When I speak of calculus nowadays, I'm thinking of it and all its outgrowths. Everything that's spun off from calculus, but that would be unconventional terminology. We would normally speak of differential equations.


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[Assistant] And then there are subcategories of ordinary ones and partial differential equations. You know, that's a distinction whether we're concerned with things that only change in time, let's say, or in both time and space simultaneously. We also concern ourselves with waves and putting waves together to make.


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[Assistant] You know, we'll say if you're looking at the question of how do you compress all the songs that fit on your phone. Data compression uses techniques called wavelets that grew out of Fourier analysis of sine waves, representing complicated functions as sums of sine waves.


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[Assistant] But then spins off in I don't know how many hundreds of directions and it is the, uhm, the dominant framework for mathematics today except for


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[Assistant] Uhm, so it's not all calculus all the time. I mean, what's been great in the hundreds of years after calculus is that other older branches of mathematics were reinvigorated by fusion with calculus. So,


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[Assistant] A subject like number theory, which goes back to ancient times, even to the Mesopotamians, you know, thousands of years before Christ. When we combine it with calculus, we get modern subjects like analytic number theory that give us things like the Riemann hypothesis, the greatest unsolved problem in mathematics today, which by the way has been wonderfully covered on earlier episodes of Numberphile.


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[Assistant] Uhm, but certainly Newton himself would have been astounded by what we can do. It's interesting though, you know, I mean in terms of say computers, there are, in these pages in front of me, we can find calculations where Newton is computing logarithms to 50 digits by hand.


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[Assistant] He's just carefully writing out row after row of 50 digit numbers and adding them together and occasionally crossing out little mistakes. This is an unusual mind who wants to write out 50 digits and is, and he even says in one place, maybe we can find it in these pages that, that he's,


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[Assistant] I mean, again, paraphrasing, he's embarrassed by what he has done because he had, he says something like, I took altogether too much delight in these inventions for having no other business at that time.


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[Assistant] You know, like he had nothing better to do, so he just goes and calculates everything. But anyway, no, it would be wonderful to show him what we could do today. I wonder whether he would have a generous spirit.


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[Assistant] Maybe not. Yes, it was an education. It was a very, very positive experience. So my editor was, uh, a gentleman named Eamon Dolan who has become a very good friend of mine through this ordeal.


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[Assistant] Writing a book under his tutelage. I really think of it that way. I had never tried to write a book before.


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[Assistant] My previous book, um, Joy of X, was a collection of chapters, each about only 1,500 words or 2,000 words, that appeared in the New York Times as, as very short pieces. You could read them in 5 or 10 minutes. Right, so that was quite disparate.


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[Assistant] I didn't really know how to do it and suffered greatly just to produce a first draft.


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[Assistant] And when I did, I was surprised it wasn't the book I meant to write. It was much more about history than I thought. I'm an applied mathematician. I'm very interested in how calculus connects to the world around us today.


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[Assistant] He said that was a very compelling example. If you could have one thing like that at least in each chapter, that would really, wouldn't that be interesting?


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[Assistant] And I thought, god damn, you're right, that would be, that's what I meant to do in the first place. I need to do that. But it required another, like half a year of work to figure out what belonged in each chapter of contemporary interest. Anyway, it was, it was a lot of work and, you know, at the end I thought what I had produced was a book that should be called The Language of the Universe.


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[Assistant] But Infinite Powers was my editor's name for the book and I said I don't really even know what that means. And he said well everyone here in the marketing department, you know, thinks it sounds cool and that's the point. Maybe you don't know what it means but the people you want to read it.


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[Assistant] Do you know what it means now? Uh, well I think it's supposed to be a play on my idea that infinity is such an important concept in the story of calculus. And it's powerful, but has it given us infinite powers? Well, that's a bit of an exaggeration, but it has given us a lot of power.


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[Assistant] And there's probably a play on the word power series because Newton uses powers of the variable x, x squared, x cubed and so on to take the use of infinity to a new level.


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[Assistant] But I think response to this seems to be okay. You're anyway, you're right though. It is a word that has come to be synonymous with complicated and difficult and


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[Assistant] That, my editor, for him this was a big aha moment. He said, I realize now after reading this,


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[Assistant] Calculus is not about complexity, it's about simplicity. It's about breaking problems into smaller parts to make them simpler. And it's a systematic use of this idea except


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[Assistant] That it's a manic idea where you never stop. You keep cutting and cutting the problem until you infinitely often, until it's infinitesimally small. So it's taking this idea of divide and conquer to a frenzied limit, no pun intended. I mean, we're going all the way to infinity. That's the big new idea.


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[Assistant] Yeah, breaks my heart. Yeah. Well, I found I couldn't get out of the 17th century. I felt I needed to talk about Galileo and Kepler, although it's not customary to have them in a book about calculus. But because they were so powerfully motivating for Newton, and then likewise Newton studied Descartes.


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[Assistant] And, and learned a lot about how to combine algebra with geometry through the work of Descartes and Fermat. So they had to be in there. And of course, Newton and Leibniz. So I have six important people to discuss and they're all in the 1600s. And I want the book to be a 21st century book.


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[Assistant] So, that's what I mean when I say it became too much about history of math. And as a result, partly the time was running out. I mean, there are real world considerations. I needed to finish this and get back to the rest of my life. And also the book was getting too long.


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[Assistant] I didn't get to cover some of the greatest mathematicians of all time who are very, very important in the story. Gauss is not mentioned. Euler is not mentioned. There's no Lagrange. There's no Cauchy. You know, it's ridiculous what's left out of the book. It kills me.


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[Assistant] Not by choice, just that's the way it turned out. I thought he, if you had to pick one person who could summarize the 300 years after Newton to the present,


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[Assistant] I think Fourier carries the most punch because his work on waves and how we use waves in everything from radar to microwave ovens to GPS and all the rest, image, you know, face recognition, all those sorts of things. Uhm, I thought Fourier was at least


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[Assistant] Get me some of the way there. And then there's, I wanted to talk about very contemporary things like artificial intelligence and what that's, you know, may do for the future of calculus. Will calculus be obsolete as computers become more powerful? So those are some of the things that are touched on towards the end.


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[Assistant] Certain genes go awry in cancer, that cells start dividing uncontrollably. What's going wrong? You know, what is it that's wrong in the cell at that point?


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[Assistant] They're all described in their changing behavior by differential equations, so calculus would still apply, but we can't visualize what happens in a space of a thousand dimensions. You know, that is, we're used to Descartes with his x and y axes. We're good at picturing things in two dimensions and three, but a thousand dimensions we can't picture.


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[Assistant] And so a lot of what we use calculus for is limited by our, our neural hardware, our wetware in our brains. We're just not up to it. But computers don't care about a thousand dimensions or a hundred thousand. They can calculate in any number of dimensions with any number of variables.


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[Assistant] So that's where I foresee calculus going, trying to understand the behavior of complex systems that are that complicated. With the help of computers, I don't think we're going to be able to keep up. I think it will, it may be that computers will solve cancer and have to tell us the answer. And we'll have to accept it. But we won't understand, but it will turn out to be right.


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[Assistant] And then as I say, differential equations, partial differential equations for problems in space and time, both. We have dynamical systems and chaos theory. All of these things are, are still very active fields. And every year, or sorry, it's every four years we award fields medals.


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[Assistant] You know, to the greatest mathematicians, young mathematicians, and you can check. Calculus is very well represented among the Fields medals every time.


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[Assistant] But, you know, they help us understand from beginning to end why something is true. Some of them are problems with the flavor I talked about, with complex systems, enormous numbers of variables. You know, but I think the future may be more in computation, I'm afraid to say, that calculus is, and it's...


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[Assistant] Its style of continuous mathematics is giving way, it seems, to machine learning and linear algebra and data science and all that. That seems to be the most exciting part of what I can see in applied mathematics today.


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[Assistant] Well, okay, I'm sure there are some listeners who are cheering right now for you because I hear this from many people that mathematics is magnificent on its own and why cop out with these applications? We don't need that. I agree with you. You can make that case and half of me agrees with you.


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[Assistant] And the ingenuity of the arguments, the elegance of them, the, the human creativity.


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[Assistant] All of that is there in pure mathematics. Forget about the applications. So in, in each chapter, I try to show examples of that kind of ingenuity. And as you say, it stands on its own and in the same way that fine art, you know, I mean, you learn to read


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[Assistant] Not just so you can read street signs, but so you can read Shakespeare or the best, you know, poetry. These things have worth in themselves. Certainly mathematics does, and I get that. I think for my reader that


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[Assistant] Is not going to be as easy a case to make. And as you say, I am an applied mathematician and in my heart, I don't only want to make the pure mathematical argument, but I also don't want to neglect it. I try to give fair


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[Assistant] Congenital malformations in the way that they look. That's very important to many people. Getting to the moon was important. Nuclear weapons and what they, you know, are, what we have done to the world. Calculus has not always been a force for good, but it has had world-changing impact.


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[Assistant] And we might as well tell the truth about that. You know, it's like one thing to talk about.


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[Assistant] Something I'll just throw out some jargon, the P-adic numbers. The P-adic numbers are pure mathematics.


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[Assistant] That the great mathematician Paul Erdos said once to some other mathematician, you know, they're not really real. Which is kind of funny for a pure mathematician to say about a mathematical concept like the peatic numbers. They're not really real. Well, really none of mathematics is real. It's all made up. I mean, it might have some mirror to reality, but it's all


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[Assistant] Conceptual, it's all in our minds. And yet, for someone like Erdős, the peatic numbers seemed a little too contrived.


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[Assistant] They seem too artificial for him. Alright, so, I mean, I think if we only make the case for calculus that it's a marvelous way to find areas of curved shapes, first of all, that's a lie, that's not all it is, and that's not really why it matters. In my heart, I think I do believe the applied


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[Assistant] Reason is the reason that this matters most, but I certainly love the beauty of being able to find the area of a circle.


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[Assistant] That, that is not about finding how to tax the poor farmer whose field happens to be circular. It's a, it's a case of uhm, the human quest for understanding. Like a lot of pure mathematics is. So that should be celebrated too. I, I agree with you.


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[Assistant] Right, it's a very fair point, because you could say we wouldn't have gotten there without the addition symbol, right? I mean, we need to know how to do everything in mathematics. Why are you singling out calculus? Okay, rather than concede that point though, although I accept that there's a lot of merit to the point,


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[Assistant] Whether it's the motion of objects, whether it's even quantum mechanics, where we can't speak of classical trajectories, but only probability waves. Well, Schrödinger's equation for the evolution of probability waves is a differential equation. It is phrased in the language of calculus. So even though Newtonian mechanics doesn't work in quantum theory,


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[Assistant] That's a pretty spooky and interesting thing. And so this is a big claim for me, you know, in the subtitle of the American version of the book, How Calculus Reveals the Secrets of the Universe. That's what I'm talking about. The language of the universe, meaning these fundamental laws, whether it's motion of water or air or heat,


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[Assistant] Or uhm, objects, like I say, flying around, or quantum waves. They're all governed by differential equations. And they're not governed by linear algebra. They're not governed by group theory. I mean, I know some people will disagree and say, yes, group theory is fundamental to particle physics. But I still think


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[Assistant] If you had to pick one branch of mathematics that is the language of the universe, it would be differential equations. And that happens to be a part of calculus. So I, I really do think, you know, maybe it's dumb to signal it out, single it out. People have asked me why not just say mathematics is the language of the universe, like everyone else would say. Yes, okay, we can do that. But I think it's a sub-dialect.


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[Assistant] That is the very specific language. It's differential equations. So I'm...


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[Assistant] Happens to be where my research is, you know, I guess I'm very parochial about that, but I think a case can be made. But I also don't want to oversell it, having just oversold it.


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[Assistant] Do you know what? I actually was convinced that I was no good at maths and at school I really wasn't the biggest maths fan. Uhm, it was my maths teacher who actually talked me in to doing an A level in it.


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[Assistant] And it was really then when I did my A levels, so sort of college level, that I really fell in love with mathematics and particularly that was the first time that I was ever really properly introduced to statistics.


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[Assistant] And I really loved the application of mathematics and I loved the fact that you could see a data set, you could plot it, you could, you know, mess around with it. And that was then I.


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[Assistant] Really fell in love with mathematics and then decided to take it on further into university.


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[Assistant] Always convinced that this was it, the last one, I'm not doing anything else after, and then ended up doing more and more and more.


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[Assistant] I think I potentially hadn't found my bit of maths that I loved. Uhm, and I'm, I'm a bit of a perfectionist and if I'm not the best at something I'm convinced then that I'm really bad at it. You know, it has to be all or nothing type of thing. Uhm, and I think that when it came to some of the more


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[Assistant] There were people in the class who were better than me at it and I think I just then thought, oh, that means I'm rubbish and I'm no good at this. Uh, and I, you know, when I...


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[Assistant] Do you know what? I started out, I was actually going to do a degree in maths and German. I really loved languages and, uh, really enjoyed doing German. Went out to Germany, uh, as part of my school course.


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[Assistant] Uh, so I think, yeaah, maybe I'd have done languages. Whenever anybody asked me what I wanted to do for a living, I always said a teacher.


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[Assistant] And I did work in academia as a lecturer for a long time, so I do think that there was that sort of teaching part always in me that I always wanted to do that.


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[Assistant] I don't know what they saw in me. Maybe a problem-solving mind or something like that. But yeaah, she, she...


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[Assistant] I picked my other A levels and I was just trying to think, oh, what can I do as my last one? So I picked, uh, psychology, German and history and, and it's a real random mix of A levels. And I was trying to decide what my last one should be. And, uh, it was my form tutor.


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[Assistant] Who was my maths teacher and she just said, oh, well, I think you're really good at maths. I think you should do it and.


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[Assistant] Why not? Let's give it a go. Uhm, and my mum actually, uh, bumped into her in the shops whilst I was doing my PhD and said, you'll never guess what Jennifer's doing now. And she couldn't believe it that I was now doing a PhD in statistics and they put me up on a little wall of fame in the school. So, uh, just to say, you know, here's what can happen.


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[Assistant] Can I say that? I was really into science and I was really into meteorology as well. I used to, uh, stand in the kitchen and do my own weather reports, but I used to collect data on the weather, uh, you know,


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[Assistant] I think my dad, my dad has a chemistry background.


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[Assistant] And we used to do a lot of science experiments together and maybe now I think back on it I was more focused on the collecting of the data for it than actually


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[Assistant] I've always been a scientist. My dad, when we used to, you know, go to bed at night, used to teach us how to recite the first 20 elements of the periodic table. So not your sort of typical bedtime stories.


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[Assistant] So, you remember it, why, if I, it's gonna sound really stupid, but it's H-H-E-Lebeb-Kanofny-Namgal-Sipsklar-K-C-A. That's how it is phonetically, and if you go through all of them then you can, you can actually recite the, the first 20 elements. Nice. Really stupid random things.


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[Assistant] Yeah, uhm, pretty much. I mean, I did a maths with statistics degree. I, you know, I still enjoyed pure mathematics and I didn't want to lose that part and I still think that


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[Assistant] The, the number theory modules that I did whilst I was at university were some of the most beautiful modules that I did. I always think of number theory being this really beautiful language and these really surprising wonderful things about numbers coming out and I'm really glad that I, I did that as part of my degree.


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[Assistant] Very much statistics was always where I wanted to go and I think when I did my masters, uh, in statistics, it was really medical statistics that I was particularly drawn to. I've always had a love of medicine and this idea that


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[Assistant] What I do for a living can help improve people's lives, improve their quality of life, help keep them alive longer. That's just always been something that...


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[Assistant] Uhm, I've been really proud of and really keen to pursue.


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[Assistant] The application path, I think I probably would have been quite happy doing some engineering as well as, you know, statistics. I think it was, any pure mathematician is probably going to absolutely hate me for saying this, but I always saw it as more sort of maths for maths sake.


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[Assistant] It wasn't immediately obvious to me what the applications would be, whereas in statistics it was very clear that this is what you could do with it. And so I think with statistics I could very much see a path as to


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[Assistant] What my career trajectory could look like. I've always been a planner and so having an idea of what I could do and that being very clear to me did appeal to me.


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[Assistant] Yeah, I mean, I don't want to badmouth any of my pure colleagues, but if I had a pound for every time someone said to me, ooh, I don't like stats, I would be a very rich woman. And it does upset me sometimes that I think some people don't necessarily see stats as being


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[Assistant] So yeaah, I dunno, I, I really hope actually throughout all of the, uh, the coronavirus pandemic, I think it's really shone a light on statistics and the role that statistics has in society. And I, I really do hope that a silver lining of the pandemic is that people may have, uhm, a new


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[Assistant] Maybe not love, but at least an appreciation for statistics and see it as being sort of a credible part of mathematics.


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[Assistant] I'm a methodological statistician, so a lot of what I do is developing new statistical models. So I have to do quite a lot of, uh, pure mathematics and I have to do a lot of computer programming.


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[Assistant] There are some parts of statistics that are not as mathematically challenging as others. Uh, there's an awful lot of thinking about designs, especially in clinical trials, you know, how do you design your trial, trying to formulate hypotheses. So I think that sometimes if you are a real pure mathematician that loves your numbers,


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[Assistant] Statistics can be a deviation away from that at times and so, uh, maybe it's seen as a little bit of a black sheep and maybe a bit of a standalone within the wider field.


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[Assistant] I think I've always had a little bit of an interest in medicine. I sometimes wonder to myself,


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[Assistant] Uh, the medical backyard is a particularly interesting one. Uhm, you could find yourself getting lost in all the different areas. So I've worked a lot in cardiovascular disease and just having that opportunity to learn about cardiovascular disease and heart disease and


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[Assistant] Uh, my PhD was looking at epilepsy data and that fascinated me and then


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[Assistant] When you start talking to people and you realise that a couple of your friends know someone that has epilepsy or one of your friends themselves has epilepsy and the work that you're doing can have a direct impact on their lives,


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[Assistant] That just makes me feel so wonderful about going to work every day, knowing that I could be helping people.


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[Assistant] I remember going to a big cardiology conference and them talking about a new treatment that had been licensed and they put my work up on the big screen, so some of the plots that I'd produced and that was helping them decide.


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[Assistant] Who should get the treatment and how it should be administered? And I just remember sitting there thinking, wow, the work that I do...


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[Assistant] It actually matters. I think sometimes when we work with numbers, it's easy to just sit in our offices and plug away at our code or our calculations and


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[Assistant] Not really appreciate the work that we're doing.


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[Assistant] Does have a follow on effect and will end up actually having a big impact and uhm, yeaah, I just, I've always been really fascinated by medicine and just love the fact that I'm helping people.


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[Assistant] That being said though, my master's dissertation was on extreme value theory and I do love extreme value theory. I find that really interesting.


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[Assistant] So it's uhm, it's dealing with extremes, so extreme weather, uh, extreme sort of flood levels, uhm, and so the idea is, you know, we think about


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[Assistant] Statistics, or probability a lot of the time in terms of relative frequencies. If you roll a dice lots of times, you get a number six about sixth of the time, and that's how you work out your probability.


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[Assistant] What extreme value theory thinks about is how do you try and


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[Assistant] of the curve could look like and you can sort of then, you know, take that, extrapolate that out into the future. And I found it, yeah, I found it really, really interesting, uh, to, to think about that. So I did a master's dissertation. I think it was on, uh, different flood levels.


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[Assistant] Exactly, exactly. And you, you sort of talk about it in terms of, uhm, sort of what's in a one in a century event and, and things like that. And, you know, uh, people who were looking at offshore oil rigs and things would, would use all that information when they're trying to decide where to put them and also, you know, how to build them.


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[Assistant] Yeah, so I worked at the London School of Hygiene and Tropical Medicine for a few years. That was my first job out of my PhD. Really enjoyed my time there. I got a research fellowship whilst I was working there as well for the NIHR, which is the research arm of the NHS.


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[Assistant] Uhm, I took the last year of my research fellowship with me to move to Oxford University.


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[Assistant] Uhm, and I worked there for, I think it was probably about


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[Assistant] Three or four years in total. Once my grant had finished, I actually took on a role building and running a consultancy unit within the statistics department. And that's where I really developed a love for consultancy work. So working with sort of small biotechs.


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[Assistant] A lot of them within the university, uhm, who had new treatments or new devices or


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[Assistant] New, uh, AI models that they were wanting to develop and commercialize.


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[Assistant] So we work with lots of, uh, big pharma, smaller pharma, uh, again, the tiny biotech kind of companies, uh, helping them with their studies. It might be a randomized clinical trial. It might be an observational study. Um, just, yeah, helping them all the way through from,


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[Assistant] Designing them all the way through to analysis and, and final regulatory approval. Um, and yeah, I really enjoy it. So, uh, my role there is to direct the research strategy within the company. They decided that they wanted to really start investing in research because it would, you know, put them right at the edge of all methodological advances.


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[Assistant] Uhm, and I manage all the sort of smaller consultancy projects that go on within the company too.


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[Assistant] It was a little bit of a shock to the system, uhm, we do quite a lot of regulatory work, so uhm, you know, the way all our folder structures are, version controls, QC systems, standard operating procedures,


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[Assistant] All of that sort of thing took a little bit of a while for me to get my head around. All the acronyms that get thrown around took a long time to figure out. I spent a lot of time Googling every time someone said something on a call to try and figure out what it actually meant in real terms.


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[Assistant] But yeah, it's been interesting. It's been really interesting. And it's been interesting the fact that, you know, the pandemic's thrown up, all of these sort of working from home.


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[Assistant] Issues and I think it's been a bit of an interesting 18 months or so, but really exciting and I've really, really enjoyed it.


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[Assistant] The world is constantly changing and the way clinical trials are run are constantly changing. So let's think for example about heart failure. That's where I've done a lot of my research. Heart failure, when people first started treating it, the main thing that people were trying to prevent were deaths.


[User] Please transcribe this text

[Assistant] We wanted to stop people dying from it. It was a bit of a death sentence when people first started looking at it. As our treatments have improved we can actually keep people alive longer. So when we want to try and decide whether or not a new treatment works


[User] Please transcribe this text

[Assistant] We might not necessarily be just interested now in whether or not it prevents them from dying. Because we can keep people alive longer, we might also be interested in, okay, well,


[User] Please transcribe this text

[Assistant] Does it stop them from dying, but also, or dying sooner, can't stop someone from dying, but does it stop them from dying sooner, but also does it prevent them from having to go to hospital more often? And as our studies get more and more complex, standard statistical methodology fails to be adequate.


[User] Please transcribe this text

[Assistant] Can we analyse these repeat hospitalisations through time for individuals? Yes, there's methodology that exists for that.


[User] Please transcribe this text

[Assistant] Is really important and so it's can I analyse hospitalisations and deaths at the same time in some way and that's where standard methodology, that just doesn't exist. So you have to come up with a new way of analysing it and so when you come up with a new way of analysing it,


[User] Please transcribe this text

[Assistant] It's a new method and as I said you have to do all the background then mathematics of how do you get the numbers out that you need.