Berkeley Writers at Work: Edward Frenkel

(calming music) – So, welcome everybody,
my name is Bob Jacobson. I’m a physicist in from the
College of Letters and Science, and I’m here to welcome you
to Berkeley: Writers at Work, and to introduce our speaker. I wanna say that you’ll probably detect a tremendous smile on my face, ’cause I just love these kinds of events. I think this is sort of the core of what the Berkeley community is about; people who are doing things,
people who are exploring new avenues, writers who
are writing something that, incidentally as a physicist,
I am incapable of doing, and willing to share them
with their colleagues, and talk about how they do
it, and the value of it. So our speaker today, who
will talk a little bit, read a little bit from one of his books, and then be interviewed about his process, and then, I think, answer some questions from the audience, if
there’s sufficient time, is Professor Edward
Frenkel of Mathematics. 20 years ago, he made the decision to come here from Harvard. I haven’t asked whether he’s regretted it, but let’s assume not for a second. In the subsequent time,
he’s published 90 papers with titles that range from, On The Endomorphisms of While Modules Over Aphine-Cackmoody
Algebras at the Critical Level to Google Should Not Be
Allowed to Secretly Collect Private Medical Data, showing the range of Berkeley faculty, and
what they think about. I’m not gonna make any comments about which of those
two is more interesting. (Edward laughs) But he also has one, which
I think is fascinating, and I will now go read, called, The Nobel Prize In Physics Is
Really A Nobel Prize In Math, published a few years ago. (audience laughing) So that pretty much covers the range. He’s also published three books, again covering an incredible range, from Langlands Correspondence
for Loop Groups, and its riveting successor, Vertex Algebras and Algebraic Curves, (audience laughing) to perhaps one that’s a little bit better
known, Love and Math. So without any more to say, I’d like to welcome
Professor Frankel here. Thank you for doing this. (audience applauds) – Hello, I welcome all and
thank you so much for coming. My god I am so moved to
see so many faces here, especially on such a
glorious day, you know? Somehow you chose to be here inside. Although the library’s pretty
glorious as well, isn’t it? It’s been a while since I have been here, and I will make a point
of coming here more often. I was just reading about it. It opened in 1928, believe it or not. And there is a picture
of May Treat Morrison, I’m still trying to figure out, I think also a painting of her, I’m still trying to figure
out the exact connection, but she was a professor here,
professor of literature. So something to explore, to Google about, in the next few days. It’s a great pleasure to be here, and I was asked to, at the beginning, to read a little bit from something that I have written, I
guess to set the tone. I don’t want to make it too long, but I was thinking about it, so I decided not to read
from the book Love and Math, but rather from two short
pieces, which I wrote. Both were published in 2015,
one in The New York Times, and the other on The Huffington Post blog, and I think they kind of cover two sides of things that I like to write about, or things that related to
science and mathematics that I find fascinating. One is sort of the
beauty, and the mystery, and the awe of mathematics and science, and exploration, the sense of exploration, the sense of wonder, the
sense of the unknown, and the other is, kind of opposite side, is the the dangers of
applications of modern science and mathematics in technology,
which is all around us. So if you don’t mind, let me read a little bit from the first one. It is called, The Reality
of Quantum Weirdness and it was published, you can find it on The New York Times website, it was published in February of 2015, and the New York Times has this series of op-eds which is called Gray Matter, they usually publish
it Friday or Saturday, and it’s sort of about weird stuff, you know, related to science, and usually there is an article, there is a particular
article, academic article, which has been published, around
which it sort of revolves. So that explains a little bit, the set up. Okay, here it goes, and please tell me if I am going too fast,
or if I’m not loud enough, if you can hear me, ’cause,
you know, I’m a mathematician, so I’m a little bit nerdy, so you know. I might just go into my own thing. In Akira Kurosawa’s film, Rashomon, you guys know this movie, Rashomon? It’s one of the greatest. A samurai has been murdered, but it’s not clear why or by whom. Various characters involved
tell their versions of the events, but their
accounts contradict one another. You can’t help wondering
which story is true. But the film also makes you
consider a deeper question: Is there a true story? Or is our belief in the
definite, objective, observer-independent reality an illusion? This very question, brought
into sharper scientific focus, has long been the subject of
debate in quantum physics. Is there a fixed reality apart from our various observations
of it, or is reality nothing more than a kaleidoscope
of infinite possibilities? This month, a paper published online in the journal Nature Physics presents experimental research that supports the latter scenario, that there is a Rashomon
effect, not just in our descriptions of nature,
but in nature itself. Over the past 100 years,
numerous experiments on elementary particles have upended the classical paradigm of a
causal, deterministic universe. Consider, for example, the
so-called double-slit experiment. We shoot a bunch of elementary
particles, say, electrons, at a screen that can
register their impact, but in front of the screen we
place a partial obstruction: a wall with two thin
parallel vertical slits. We look at the resulting pattern of electrons on the
screen, what do we see? If the electrons were like little pellets, which is what classical physics
would lead us to believe, then each of them would go
through one slit or the other, and we would see a pattern
of two distinct lumps. You see what I’m saying? So they have two slits, you throw electrons at
this wall with two slits. So they go through either, and then they get registered
on a screen behind. So if they were indeed like pellets, they would go through one or the other, so there would be two lumps on the screen. But in fact we observe
something entirely different: an interference pattern, as if two waves are
colliding, creating ripples. Astonishingly, this happens
even if we shoot the electrons one by one, meaning that each electron somehow acts like a wave
and interfering with itself, as if it is simultaneously passing through both slits at once. So an electron is a wave, not a particle? Not so fast, for if we
place devices at the slits that tag the electrons
according to which slit they go through, kind of put a detector behind the wall to catch the electron through which slit it goes, thus allowing us to
know their whereabouts. Then the interference pattern disappears. Instead, we see two lumps on the screen, as if the electrons suddenly
aware of being observed, decided to act like little pellets. To test their commitment
to being particles, we can tag them as they
pass through the slits. But then, using another device, erase the tags before they hit the screen. If we do that, guess what? Electrons go back to
their wavelike behavior, and the interference pattern
miraculously reappears. There is no end to the practical jokes we can pull on the poor electron. That is not so bad, huh? (laughs) But with a weary smile, it always shows that the joke is on us. The electron appears to be
a strange hybrid of a wave and a particle that’s neither here and there, nor here or there. Like a well-trained actor, it plays the role it’s
been called to perform. It is as though it has resolved to prove the famous Bishop Berkeley maxim, to be is to be perceived. Bishop Berkeley, of
course, the man after whom our great university has been named. That’s his famous maxim,
to be is to be perceived. But actually, I don’t know
if you know the story, it’s a beautiful story why the university was named after Berkeley. So I’ll just leave it with
you, Google it, you’ll find it. It was a beautiful poem
about going to the West, which was read in the first meeting of the regents of the university,
and they were so excited, because they came to the West, to the frontiers of the West, essentially, and that’s why they called
our university Berkeley. So it was kind of nice for
me to name-drop Berkeley in this article, I remember
that, when I was writing it. Anyway, it goes on, but let me switch to another one to save some time. So this gives you an idea of what I see, sort of like, the best
of what science gives us, is this, you know, mind-boggling and mind-bending sort of phenomena, and the effects which make us question our very sense of reality
of what’s around us, what life is about,
what’s going on, you know? That’s where science
can be our great ally. In other instances
though, it can be our foe, and so I want to read a little bit from another piece I wrote, which, I actually had great difficulty publishing in traditional outlets
such as New York Times and Slate and ended up publishing on a Huffington Post blog,
you be the one to guess why, the traditional publications
kind of didn’t want to have it. I titled it simply, Google
Should Not Be Allowed To Secretly Collect Private Medical Data. This is something that
happened in May of 2016, so two and a half years ago,
and it was, I feel as though, it was kind of a forewarning
of many other things to come. Naturally, much bigger debacles
have happened since then, such as the infamous, now,
Facebook Cambridge Analytica debacle where, I’m not
going to get into details. I’m sure you guys have all heard about it. Which made us question
our whole relationship with social media, the internet, data collection, surveillance, et cetera. This was a relatively minor,
one could say, incident. What happened was that, in
September of 2015, the DeepMind, a subsidiary, fully-owned
subsidiary, of Google, the one which became famous in the news because they programmed a computer to win, to beat a Go champion
in a series of matches. They had a secret agreement
with the government agencies in Britain to collect 1.6
million medical records, or medical records of 1.6
million British citizens without any consent,
without letting them know. It’s a secret agreement, and
New Scientist broke the story in May of 2015, so many months later, and it was a big outrage, and so that’s when I wrote this piece. We have grown so accustomed
to vast collection of our personal data and
breaches of our privacy by both government agencies
and private companies that new revelations no
longer come as a surprise. However, we cannot pass over in silence the secret agreement
made in September 2015, but first reported by New
Scientist on April 29th 2016, giving Google subsidiary, DeepMind, access to confidential medical records of 1.6 million Britons. These records, from the United Kingdom’s National Health Service,
NHS, apparently include such details as a person’s full name, HIV status, results of
pathology and radiology tests, past drug overdoses, and
logs of their hospital stays including who visited them and when. NHS has given assurances
of anonymity for this data, but that offers little comfort. In fact, the agreement states that pseudonymization is not required, and besides, even
anonymized data may be used to reveal private information. Concerns have been raised over why DeepMind needs such a wide range of data when its stated goal is to develop an app for the prevention of a
specific kidney disease. Furthermore, the sensitive
data are given to DeepMind without earlier informing
patients of seeking their consent. Questions have been asked whether in order to have access to this
data, Google was obligated to receive a regulatory
approval under a UK law. Google has not applied
for such an approval and has argued that it was not necessary, but critics believe that, in
fact, the law does require it. What makes this case
especially troubling is that Google is the world’s largest information technology company and one of the world’s two
biggest companies overall. Today, given our collective
addiction to technology, Google wields tremendous
power over our tastes, our behavior, and our future. Health care is surely an area
in which technology companies have an important role to play. In particular, properly
supervised data analysis using novel learning
algorithms has the potential to improve the diagnostics and
treatment of major diseases, and, no doubt, Google has
done the world much good with its search engine and other products. However, the company’s secrecy and lack of oversight
are of grave concern. When it acquired artificial
intelligence startup DeepMind two years ago, so that’s 2014, for a reported 650 million dollars, Google promised to set up an ethics board to deal with the issues of
artificial intelligence. Well, I Googled Google ethics board (audience laughs) and there is still no
information about it. By the way, I Googled it today again, and there is still no information. See what’s going on? Well, they created two other
boards in the meantime, but not the one, not the ethics board. It’s insane, to be
completely honest about it, and I was kind of diplomatic in there, an I said that is troubling. I think it’s more than that. Artificial intelligence
is invading our lives through various programs and devices, but it’s a double-edged sword. For example, a facial recognition program can be used to quickly
organize your photo album, but it can also be used in a
lethal autonomous weapon system that identifies suspects and strikes them without human supervision. Thus, along with great promise, AI, artificial intelligence,
holds the potential for unprecedented risks to the humankind. That’s why transparency and oversight are crucial in this area. Alas, Google hasn’t been
particularly forthcoming with an information about its AI project. But here’s what we know about DeepMind. Founded by three brilliant
young scientists, the company was in the news recently because a deep learning
algorithm, AlphaGo, it had developed beat a human Go champion, no doubt an impressive achievement. Unfortunately, the company’s CEO then proceeded to declare
that DeepMind’s algorithms could lead to a meta
solution to any problem. That is a wild exaggeration
given what we know about the limitations of such algorithms. As a mathematician, I can attest that although there are some
elements of 20th century math in them, they are
really based on 19th century mathematics cleverly adapted. The math itself is beautiful, and I salute my fellow mathematicians and computer scientists
pushing the boundaries of what such algorithms can do. But to believe that everything about life can be explained in this way is akin to the exuberance of an 11-year-old who has learned trigonometry
and is so excited about it he thinks the whole world is trigonometry. Pure and simple, this is hubris, and I’m sorry to say it is reflected in how DeepMind has acted in
acquiring the medical data, not bothering to ask for people’s consent, not following ethics
rules and regulations. What these actions
communicate is that DeepMind views people’s medical histories
merely as a bunch of data it wants to feed into a learning algorithm the same way it used the old Go games for training the AlphaGo algorithms, and if a company treats people
as pieces of a board game, why should it care about
privacy and ethics? Well, that is precisely
why we should care. Why we shouldn’t give DeepMind and its parent company
a free hand in using our private data without
proper supervision. Unlike a human, a company is an algorithm, set to maximize a
utility function: profit. Therefore, companies
often become secretive, evading oversight, but we
shouldn’t set the bar low. We must demand transparency and oversight, especially of technology companies that exert such profound
influence on our lives. Ultimately, it all depends on us. This is not about robots and algorithms, it’s about us, humans. It’s about who we are, who we want to be. So it continues a little bit, but I think probably
enough to give you a gist of what this is all about, so thank you. (audience applauds) By the way, the story is still
ongoing because a year later, the UK Information Commissioner’s Office released a report saying that, in fact, Google failed, through DeepMind, failed to comply with
the appropriate laws. They did not ask for any
punitive measures, unfortunately. But at least it’s out in the open, we know that it was wrong, and so I hope that as we speak more
about it, such as today, we will encourage these
companies to come clean and to provide more transparency, accountability, and oversight. Alright, what do we do now? – [Bob] Yes, please, have a seat. – Good afternoon, y name is John Levine from the College Writing Programs. I wanna welcome everyone to
Berkeley Writers at Work. I wanna thank the Morrison Library for hosting us in this lovely space. It’s just such a wonderful
place to spend some time, and we’re gonna spend some time
today talking about writing, among other things, and math as well. I know about writing, a
little bit, I know somewhat. I know very little about math. I know much more now
that I’ve read this book and it’s just a pleasure to have you here. I have an agenda, I’ll just
put it out right up front, I want to find out, I know how humanities people think about writing, I
don’t know how mathematicians, how STEM people think about writing, and if there is a difference. So if we can start with that, since you are both a mathematician
and a very fine writer, can you speak to that question, please? – That’s a good one, yes. By the way, I want to thank
you, John, for inviting me. It sort of came out of
the blue, this invitation. It was like, whoa, I didn’t even know that such a program exists. Now, for sure I know, and writing program, and of course I said, yes, right away. I am honored to be here, especially after looking
at the list of names of people who participated
in this program in the past. Why did I start writing? It’s interesting, I had thought about it so I can give you a kind
of a short version of it. What interested me in mathematics from the beginning is the sense of unity, which is unfortunately somehow often lost, and I think this is sort
of normal, it’s normal, it’s one of the movements of life, is to try to unify and connect
and then a movement of life, So with one hand, we unify and connect. In another hand, we try
to fracture and split, and break into pieces,
and look at the pieces, and try to reassemble. Just like kids playing on
the seashore, you know? And each of us, I think, is predisposed a little more to do one or the other. We all do both, ultimately, but we are predisposed
to one or the other, and I feel as though, for me, the predisposition has always been more to bringing things together,
rather than taking them apart. So when I started in mathematics, after doing a few research
papers, and so on, I came across a vast subject, which became the central point of my research, which is what is known today as the Langlands program named
after a great mathematician who is a professor at the
Institute for Advanced Study. You can read more about this in my book, for example, and online. But, at the time, I was 21 years old, so I didn’t really
understand it consciously in the terms in which
I feel, with hindsight, I can understand now, why I was so excited about it. The purpose of the Langlands program, the idea of the Langlands program, is to see these hidden
connections, hidden commonalities, between different subjects of mathematics which seem to be far apart, such as number theory
analysis, geometry, et cetera. And these days, in fact, these ideas have propagated
to quantum physics. My research has been, lately, on the interface of mathematics
and quantum physics, connected to the Langlands program. So, then I wanted the learn
about each of those fields to really understand how to connect them, and then what I found is that
there are very few people, there are many people
who do number theory, but then they wouldn’t know analysis, or they do analysis, didn’t
know geometry, and so on, and I somehow took it upon myself. I found it very
interesting to go and share what I learned with other
people, so I would give talks, I would write survey articles, and so on. So that was the first impulse of writing. because, okay, it was
still academic writing, it was still mathematical papers. But they were papers addressed to people across the
sub-fields of mathematics, and I found it very interesting. So my next level was to
communicate to physicists because then, kind of,
physicists came into the fold of the Langlands program as
well because of the connections discovered in physics, quantum physics, so then I was there to
explain to physicists what mathematical Langlands
program was about, I was there to explain to mathematicians what physicists are up
to, so then, of course, a natural step after that was to go out of the scientific audience, and that’s how Love and Math came about. – [Bob] So making connections,
that’s been your goal. – Making connections, yes. – And do you think that comes
out of your mathematical mind, for lack of a better term,
making these connections between these various
theories, these various fields, and then to connect to different people, different groups of people? – Yes, in some ways yes. But I think more so, it’s the opposite. It’s the opposite impulse. Because mathematics, the
way I see it now, is, why did I go into
mathematics to begin with? In part because I like the rigor. This objective quality of mathematics. You know, Pythagoras’ Theorem
was discovered by Pythagoras 2500 years ago, and many others, at the same time or even earlier, and it still means the same to us today as it did to Pythagoras. It still will mean the
same 2500 years from now. It’s X squared plus Y
squared equals Z squared. It’s not like next year
it’s going to be Z cube. It’s still going to be Z squared. There is something very special, you know? Sometimes I say, if Leo Tolstoy, you know, since I’m
Russian, so kind of natural to make analogies with Russian authors, if Leo Tolstoy did not
write Anna Karenina, there is no reason to believe that someone else would
write the same novel. Yet, if Pythagoras had not
discovered Pythagoras’ theorem, we would still have the same theorem. So there is this quality of endurance, this quality of eternal knowledge, and it’s kind of a black and white, it’s true or false, and
I was drawn to this. In part because I didn’t
like the uncertainty of the real world and I wanted
something where I could just hold onto something and grasp something, say this is true and this false. I was very comfortable in
that pure intellectual domain where there was absolute certainty. So now, from that perspective,
writing is the opposite, writing is more quantum
in some sense to me. It’s you and a blank piece of paper. What’s going to happen? It’s like the electron
goes through the slits. Which slit is going to go through? One or the other or both, we don’t know. So, to me it was a taste,
it was a first taste of uncertainty where I was
kind of reluctant and afraid to step out of a comfort
zone of my subject. But because writing was not that far away, it was, after all, close to my
writing mathematical papers. This was my way to taste,
to taste that life, that other aspect of life,
aspect of uncertainty, of something dynamic, something living, something
that I cannot control. – [Bob] And how does it taste? (audience member laughs) – Oh my god, I got addicted, you know? I did not know it at the time. It’s funny because now to be
here and to revisit all this, which was not so long ago, by the way. The most concentrated effort on writing the book, Love and Math, was between September of
2012 and June of 2013, so more or less six years ago. But my life has changed so much, and this is one of the
things about writing to me, is I set out to teach the world something, I set out to share something deeply held in my heart with the world, and I think to some extent
I did, but in the process somewhat unexpectedly, I also learned a lot about myself,
and this was surprising because when I set out to write the book one of the reasons was
that I was appalled by how little people know about mathematics, about the treasures of mathematics, and I thought it was really
an untenable situation. I felt ashamed that we don’t share enough, mathematicians don’t share enough. So I wanted to share, I want to show the treasures, and so on. – And you point that out in your book, that if only math were taught correctly, or if it were taught in a different way, more people would appreciate math. – Absolutely. – I do appreciate math and theory. Unfortunately, I’m well
past, well, never say never, but I don’t think I’m
gonna go back to school and study math. I’d love to, maybe we can talk afterwards. (audience laughs) But I feel like I’m one of those people who feels that way, I
just missed the math boat. As interested as I am, I just
missed it, I’m not good at it, But this book brought out a
new appreciation for math. – I’m glad to hear that, thank you. I feel like I was lucky
that I chose this subject and I had wonderful teachers and mentors, even though I also had to overcome some formidable obstacles,
as you know from the book, but I was given a chance to see this beauty and see these treasures. At the beginning of the book, I say that, imagine an art class in
which they only show you how to paint fences and
walls, but never show you the paintings of the great masters like Picasso and Van
Gogh, which by the way is on the cover of the book. It was not chosen by me,
but it perfectly captures by the great artist who
works with my publisher. It was a good coincidence
because Van Gogh was actually one of my favorite painters as a kid. Imagine that they only show you how to paint fences and walls but never show you paintings
of the great masters. In both cases it’s painting, you’re painting something with the paint, so then, years later, people will say, art, art, it’s so great. I say, what’s so great about it? It’s just painting
walls, fences and walls. I don’t find it interesting at all. Also, I don’t think I have talent for it, and besides, I could always
hire somebody to do it. So that’s, more or less, the
attitude about mathematics. People are not even aware that
there are these masterpieces. The museums of mathematics
are basically locked and only the select few, the elite, like myself have the keys. Actually, it’s changing,
the situation is changing even in the last five years
since the book was published. It’s getting better, it’s getting better. – [Bob] Why do you think that is? Do you think that the
field was just proprietary, that they didn’t want others in? – There are several
aspects of it, I think. It’s complicated, it’s been
going on for centuries. Well, I think it’s more
important to understand not why it happened, but what
should we do about it now. I mean, of course, if we had more time I would be happy to tell
you why I think it happened. In a way, one of the reasons by the way, is that the situation is very
good for the powers that be. It’s a very nice situation, because every time there’s
a mathematical formula, the majority of the public go, ugh, math, I don’t get it. By the way, people get
traumatized, also in math classes because they are told, specifically, by their teacher that they’re
stupid, they don’t understand, and that is the end of it for most of us. It’s really, really, tragic
because, in my opinion, I like this quote by
Picasso, that Picasso said, “Every child is an artist.” The question is to preserve
that as you grow up, and I would say the same about math: every child is a mathematician. If you look at children
who have not yet been told that they cannot do it,
who have not yet been told that they’re stupid, look at them try to solve math problems,
they love it, it’s a game, which is what it should be. Now, okay, so you see, I
can go on and on and on, but how nice for the powers that be because you can do surveillance, you can do back doors, you can
do, there’s dubious schemes like pyramid schemes like the
financial crisis or BitCoin just simply because people are duped because they don’t know mathematics. One of my examples, my favorite examples, is when we found out how
the NSA inserted a backdoor in a very popular algorithm,
an encryption algorithm. They used elliptic
curves, so it was the most abstract and obtuse algorithm that it could possibly come up with, why? Because it was more chance that
people wouldn’t question it, so that’s one of the aspects for sure, and one of the reasons
why we have to change the situation, you see, and
the way we deal with it is, of course, by talking about mathematics. The great responsibility lies with people of my profession,
with mathematicians, that we don’t do enough, and in fact, a lot of my colleagues, I’m sorry to say, are not happy about the arrangement because it makes us feel
good about ourselves. We know something, we know the secret, why should we divulge it? It gives us power, it
gives us a sense of power. But of course, it’s bullshit, you know. Of course you have to share. It’s like Picasso, first of all, when you see this beauty,
how can you not share it? You cannot hoard it and say, oh it’s mine, it’s my
formula, no, it’s like love. By the way, that’s one of the connections between love and math. When you’re in love, you
share your love, you know? You can’t hoard it. Give me more, give me more love. That is not love, likewise
with math, that is not math. – Okay, good, one of the other things I wanted to talk about
is the process of writing and the process of thinking about math. There were so many quotations
that I thought about including in the program, but this one happens to be in here from Love and Math. It’s the first quotation under A Brief Frankel Reader,
I’ll read it aloud: With any math problem, you never know what the solution will involve. You hope and pray that
you will be able to find a nice and elegant solution, and perhaps discover something
interesting along the way, and you certainly hope
that you will actually be able to do it in a
reasonable period of time that you won’t have to wait for 350 years to reach the conclusion,
but you can never be sure. The reason I point that out is because that’s a lot like writing,
and you having been familiar with both worlds, I wanted you to talk a little bit about that. – Right, so 350 years is referring to one of the most famous
problems in all of mathematics: Fermat’s Last Theorem, about
which I talk in the book, and it took 350 years to solve. The last, sort of, steps
were done by a mathematician, Andrew Wiles, who basically,
for seven or eight years of his life was
exclusively working on this topic without knowing whether he
would be able to succeed, and in secret, he didn’t
want to tell anybody, which is something, by the
way, which our academic system certainly doesn’t encourage,
because the academic system encourages us to publish and so on, and do things which are more safe. So that also brings me to
perhaps correct a little bit what I said earlier about
certainty in mathematics. So on the one hand, there is a certainty about the knowledge, of
mathematical knowledge. This is true, this is false, and so on, but there is already that inherent element of uncertainty when you do mathematics, when you talk about mathematics
as a human activity. For instance, when you
set out to solve a problem which has not be solved,
you cannot, in principal, be sure whether you will succeed or not. For some problems, though, it’s more safe, they feel more safe, they feel like yeah okay, I don’t know
how, but I pretty much know the methods, the tools, and
I’m 99% sure that I will solve it within a year,
within a month, or whatever. But there are problems which
are not even like that, you see, and so in that
sense, that’s also another way in which we get the
taste of the uncertainty, being a mathematician, that’s true. – So when you sat down to write this book, or let’s look at a smaller piece, when you write your New York Times essays, when you write your Huffington
Post, whatever it is, do you know before you set pen to paper or hands to keyboard,
what you’re gonna write, or do you experience that
uncertainty or an uncertainty? – Very much uncertainty,
so the idea of this book evolved so much, and there
have been so many people who contributed to my evolution. I thanked some of them in the book, and by the way, this is important because it connects
also to something which, my book, in many ways, is a love letter, the way I see it, is a
love letter to my teachers, because if you read the book you will know that I experienced serious problems, difficult obstacles to
becoming a mathematician. I was not accepted to
Moscow University in 1984, like in Orwell’s book, because
of rampant antisemitism and discrimination that I faced. But, I was able to overcome
that because of the generosity of some very specific individuals. Mathematicians who took
me under their wings, and who helped me to go around the door. The door was closed, but they kind of say, okay we’ll take you to the VIP
entrance around the corner. They did it for no, there was
absolutely nothing for them. This was real love. Love is something where you don’t ask for anything in return, and this love, it can be romantic
love, but it can be love between a teacher and a student, or it could be love for
a mathematical formula, and so on, right, or a work of art. The key element is you don’t
ask for anything in return. Otherwise, it is not pure love, it is not. It simply is not, and
therefore in some senses, it can never really experience the flight that comes with that sense of everything, what comes with real love. This happened to me,
and the book helped me to appreciate how much I benefited from this generous human beings who, you know, it could be a small gesture, it could be a small thing, it could be an amazing, sustained effort, but they did it without
asking for anything, why? Because they saw promise in me, because they wanted to help
for no reason, just because, and it’s very important,
I think, as I grow older, for us to appreciate those people. Remember your teachers,
call them up, you know. Call them up, send them an
email, say how are you doing? It’s an amazing thing. You know, sometimes, I’m also on the receiving end, nowadays, of this. You cannot underestimate
how beautiful it is to receive a letter from a student, from your former student,
just to say hello. It doesn’t have to be profuse thanks and so on, just a gesture. So, returning to your
question, same for the book. So many people contributed. It takes a village, you
know this expression? It takes a village to live a life. It also takes a village
to do a serious project like writing a book. I could not write this book without dozens of wonderful
people who contributed, who changed my views, who helped me to see other sides, other angles, and so on. What comes up to mind is Thomas Farber, who actually teaches
writing here at Berkeley, he helped me a lot, I learned
a lot about writing from him. It’s a longer story, time is limited, but just to mention the name, Marie Levek, we were dating at the time,
so I was in love with her at the time, and she used
to say, Edward, your book, and she was not a mathematician, she was a musician but
she read every chapter, every chapter, and she commented, and she said, she kept saying, “Edward, your book is
called Love and Math, “I see a lot of math, but not enough love, “so Edward, there has
to be love in there.” You see, it’s how can I ever be, you know, this is gratitude, this is love. – We talk in our program about writing being a collaborative effort. I think it has this misconception that you go off into an ivory tower, into a corner and write by yourself, but even if you are writing by yourself, you have all of those people who have come before
you and who are there. – They were kind of around me in spirit. I was here in Berkeley, I
lived in a tiny apartment at the time, Virginia Street, where my dinner table doubled as my desk, and I was just sitting there many a night, you know, by myself, without
a page, but with a laptop. Yes, but you’re right, those
are the voices who were present and they were steering me in many ways. A lot of it was just me
and the book, for sure, but there were crucial moments where it could go this way or that way and that’s where our network of supporters and guides, comes in effect, in action. – So, back to the
process, and I don’t know if you’ve ever thought about this or you can even verbalize it, but when you’re working
on, and excuse my naïveté about what it’s like
working on a math problem, but when you find yourself
working on a math problem, struggling with it, finding your way, and when you find yourself
sitting down to write an essay, cognitively is there a
similar process going on or are they completely different? – I surely approached it
as a mathematical problem at the beginning because that’s
all I knew in some sense, and a lot of that is going
to be very productive, because it helps you to organize. I had notebooks upon notebooks of stuff. I even had, every time
I would find a nice word I had a page with nice
words, you know, like, I wanna use this one,
and especially, you know, not being a native speaker,
and I wrote it in English, that was a slight challenge of that too, but also made me
appreciate the words more. Perhaps if I were a native speaker, maybe I wouldn’t look at those words as this kind of little treasures either. So, yes, so it helps to
organize your thoughts, so in other words, there’s
a certain work process which is already in place,
then you follow that, but the trick was to then break it up and go further, go
further, because otherwise it would be a book, I
don’t think it would touch, and I think it has to, well, I
mean, it’s not for me to say, obviously, but I have
received enough feedback and now it’s in 18 languages and so on, so I have received a lot of feedback, so it has touched some people,
there’s no denying that. It has touched; why did it touch? My opinion, it did not touch because of the words themselves. Something else came
through between the lines. It’s too trite to say from
the heart, or whatever, because it’s overused, you say
heart, heart, all the time, but in this case, it was,
it came from the heart. It was a sincere effort,
I was a very reticent guy. You may not see that now, but
I was a very reticent guy. I was very closed, I was
shy, and I did not want to open up to anybody, you
know, even in relationships. I wouldn’t share information about myself. I was very uncomfortable when
people start talking about me, about what’s really deep inside. I don’t want to deal with
it but I wanted to open up, so how I could open up to mathematics, I could open up to writing. I could allow, that was
one channel through which I could truly be myself, you see, and so that’s the way in which
that experience of writing can be truly transforming and
transformative for the writer. You enter as one individual and you leave as a totally different person. – Thank you for saying that,
and all of our writing students who are here, you heard this from this esteemed mathematician:
writing is transformative. – Edward Frankel has said. (audience laughs) – Yes, not that I’m keeping count, but in our conversation, you’ve
used a number of analogies to make a point, and you also
do it in the book as well, so my question is, is this
something you’re doing at the courtesy for the non-math audience? – Yes. – Is that how you as a mathematician, I won’t ask you to speak
for all mathematicians– – Yes, both, yes, very good,
that’s a very good point which actually I hadn’t heard that. – I wanna credit one of my students, they pointed that out as
well, they noticed that. – That’s a very good
point, very good point. I hadn’t heard this articulated
so well, which, absolutely. When I do mathematics,
when we do mathematics, I think it’s universal,
I speak to my colleagues, and when we give presentations at our professional meetings and so on, we often use analogies because
it helps you to understand. In a sense, I mean what is this all about? It’s about stories, we love stories, so yes, of course, yes you
can have theory and proof, you know corollary and
so on, but it’s boring and it doesn’t really stay with you. When it is accompanied by a story, it has a much bigger chance of penetrating through the barriers of misunderstanding. It is natural to us, I think all of us, to use analogies, especially
when you do something so abstract as mathematics,
so therefore, for me, it was very natural to use that as a tool, but also I knew that
explaining the details was not really that important. By the way, it’s also true,
for instance, for art. You don’t want to go
and explain every detail of a painting by Picasso,
but you want to give a certain vantage point, you
have to give some pointers, which is kind of like analogy. I was testing them on my guinea pigs, you know, early readers. I mentioned one of them, my
father was the other reader who read everything and was I was like what do you think of this analogy? Some of them, it really come
out through this process. Some of them I knew from
my mathematical work, but some of them were
completely new to me, and they also helped me to understand mathematics better in some ways. – Okay, interesting, interesting. Well, I appreciated them
because it really helped me to wrap my mind around
some of the theories that you were talking about. You just mentioned storytelling, it’s a way to understand things. This book is, you spin a good yarn. It’s a good story, I mean
you have your personal story that you tell, which is fascinating, but you also weave it in
with all of your research on Langlands, so I’m wondering, when you sat down to write this, again, did you have any idea of,
I’m gonna tell this story beginning to end, did you have a sense of how it would come out? – Very good question. First of all, I knew that
I wanted my personal story. I did not yet know exactly why. The reason I thought I
should include it is because I had this intuitive sense
that people really would like personal stories, people can relate. Because when we share something and it really comes from the heart, when there is a sincere,
you know, it’s like if you tell a story which is not yours, you could use the same
words, for instance, you tell me a story, you tell me something that’s happened to you,
right, so I memorize it and then I go and tell somebody,
that will be different. It’s only the greatest
actors who can do that. Most of us cannot, and the
other person will know. It’ll be a totally different reaction when you tell your story and
you tell it from the heart people will cry and laugh and whatnot. When somebody else uses the same words, not going to have the same effect. I had an intuitive sense
that personal story is what captivates us, and it
was kind of clear to me why. Because the point is, this
mathematics is so abstract. I talk about these
things like braid groups so I try to put myself
in the shoes of my reader and they would be like, why should I read about this,
why, there’s so many things? And the reason why I
want to convince them, because I want to tell
them this compelling story of this guy who grew up
in a small town in Russia, and he was in love with mathematics, he wanted to become a mathematician but they didn’t let him, didn’t let him. But he loved it so much that
he was able to overcome it. So, when we get to that point, and that is a universal
story, overcoming obstacles. A hero’s journey, so if
you read Joseph Campbell or Carl Jung from who it
really came, hero’s journey, it is an archetypal story of a hero who goes out to kill a dragon, and he comes back, or she,
could be a heroine as well. When we get to that
point, the reader says, okay, so what happened next? So guess what, he
started doing this stuff. See, it’s completely different. If I just started with braid groups, this was my first mathematical problem. If I did not have to suffer
through all this ordeal, if I didn’t have to fight
to get to that point where I could work on this, you see, like, how much is it worth? Yes, it could be the same
mathematical theorem, but who cares, who cares? But, it was earned, you see? It was earned because I had to fight, I had to struggle, I
had to make an effort, I had to overcome, and when I did, I felt that I earned a
little credit from my reader that I could tell them a little
bit about the math itself. What was it that this
guy was so excited about? It was this. – Yes, right, and that’s what
I appreciate about the book, and you even, you offer
a guide for the reader. I don’t know if you did this at the end, but very generous of you. You say there are certain chapters, and you point out the chapters
that might be math-heavy, and I saw those and I made a note and I said I’m gonna skip those. (audience laughs) But I didn’t, I went right through them. – That’s totally legitimate. – But I didn’t because you
gave me that encouragement, because the story’s still there, and I did it and it was a challenge and I felt proud of myself for doing this, and I want my daughter to read this who’s a high school senior
who’s very good at math, but that’s another story. I appreciated that, and
again, I feel like I’m asking the same question and you’re
answering it beautifully, but did you know how you
were gonna lay your things? Were you conscious of, okay,
here’s some math, more story, not that they’re separate stories, but when you constructed it,
were you mindful of that? – Well, there were a
few, sort of milestones. There were a few things
that I wanted to talk about, the Langlands program, which, by the way, I just started writing, so
how it came about, I was like, I want to write this book
in which, first of all, I will tell my personal story,
in particular that part, which was very important to me, which I had never shared,
overcoming that obstacle, but also to talk about
the Langlands program, this beautiful archipelago of knowledge which is completely hidden away. Nobody knew about the Langlands program. By the way, this year
he got the Abel Prize which is like the Nobel
Prize in Mathematics, and he is kind of in
the public domain now. You can Google Langlands program you will find lots of articles about it. Six years ago, nobody knew
outside of mathematics what the Langlands program is about, and I thought that was scandalous,
we have to talk about it. I wanted to talk about this,
but I wanted to do both, and I started writing, and
at some point, actually, I went to New York in January of 2012 because I was invited
by Columbia University for a semester to be a visiting professor, and I was like, great,
this is the perfect time because publishing is based in New York. I thought okay, so now all the publishers will fight over this manuscript. (laughs emphatically) (audience laughs) Boy was I wrong, you know? So, I through some friends and so on, I got in touch with
agents, because it’s like, oh, we have to first get you to an agent. It’s a very structured thing. You cannot go directly to publishers, they’ll be like, no, no, come on. It’s kind of like bad manners, you know? You have to go through an agent. An agent presents to publishers. I always do everything the
wrong way, so as it turns out, you’re not supposed to
even write anything, you have to first write a proposal and then find and agent, and
the less you write, the better. Otherwise they get
nervous, because the agents and the publishers, maybe
we should stop the video, it’s a well-kept secret, you know, in the publishing industry,
they all want to participate in the project so they don’t want to be with these unruly authors,
demanding authors like, no, I want it this way
and not any other way. They don’t want to deal, so
the less you have written, the better, but I already
wrote, like, 150 pages and I didn’t have a proposal. So they look at this and they say, no, it’s not going to be commercial, nobody will buy this book, we pass. So nobody wanted to take me on. I still don’t have an agent, by the way. As it turns out, I didn’t need one. – [Bob] And how many languages
has this been translated in? – 18, but some of them said
just write a straightforward book about math, about
the Langlands program, then we’ll publish it. It’ll be one of the popular books in math but autobiography, nobody
likes autobiographies. Luckily, there was a guy, TJ Kelleher, was an editor at Basic
Books, which, by the way, Basic Books is a fantastic publisher, they published Escher, Godel, and Bach, which many of you may
know, so they publish kind of unusual books, but
it’s a very good publisher, and so I was lucky to be introduced to him by a friend of mine, Eric
Weinstein, who knew TJ, and TJ looked at it and he
invited me to his office, and basically he made
me an offer on the spot. I am kind of like a professor now, sort of senior figure, so I
can say things to students, you know, from my experience. Most important thing is just
do what you feel is right. Don’t listen to anybody and
the miracle will happen. This is a miracle because
officially you go, and the whole publishing
world of New York said, no, we don’t want this book,
Edward, we don’t want it. But I said no I would
like it to be like this, and guess what, a miracle happened and there’s somebody who
says, I will publish it. Now, if you don’t follow through on what you believe is
right, it will not happen, and then you will go and
complain about the system, oh the system is so bad, the
system is stifling innovation, which, by the way, that’s what
the system is supposed to do. The system is doing your
job, and you do your job. You do something that is yours,
that’s your job, you see? And the funny thing is, when
it looks completely hopeless, which, by the way, it looked hopeless to me when I was 16, it worked out. Much later it was not such a big deal if I didn’t publish this
book, okay, I wouldn’t die. I was a Berkeley professor, you know, a very comfortable living, but
it happened again in my 40s. There was a book, there was
something I wanted to share. It was different, and many people thought it was not something that
would have an audience. I did not compromise, I decided to stick to my guns and it worked. – [Bob] Well, and that’s
a perfect metaphor for the entire story that you tell here. I mean, that has been your motto. – But this is the story of
all of us, this is the point. So this is what I’m trying it say. It is your story, for each
of you, it is your story too. Now, for me, maybe it’s a bit dramatic. Okay, this guy was not accepted
to university and so on. It’s a particular
variation on the same one and the same story, and
each of you, each of us is living that story right now, so what do you do today
in which you proceed here and you push and you don’t succumb and you don’t compromise,
but you stick to your guns? What is it that you do today? It is today, it starts now, you know, it’s not next month or next year. I didn’t see it when I was doing it. So obviously I compromised
on some things I now regret. Some important things I did not. For instance, on the book,
on the contents of the book, on the idea of the book, on
what it’s going to be about, I did not compromise and I’m
so glad I didn’t compromise. I stuck to my guns, and
so now I see the secret. I didn’t see the secret,
and so this experience helped me to understand
the secret, which is push. – Right, right, yes, yes,
so to move from the grand, and this is the hero’s journey, you also share little
details of your life, for example, you learned
English from David Letterman. Not exclusively, but can you just talk a little bit about that. – Not personally. – No, not in person, but you
do owe a certain amount– – By the way, one regret I
have that I was never invited to David Letterman’s program,
but I got the next best thing. I was invited to Steven
Colbert’s Colbert Report, and actually it happened
exactly on the day when it was announced that Colbert would take over from Letterman, so it’s kind of close
enough, you know? (laughs) – You can find that, that is online if you want to see that interview. – Right, but Letterman was my hero. I came to America in
1989, I was 21 years old, and I didn’t speak English very well. Well, not much has changed since then, as you can see. (laughs) I really had difficulties, so I was like, how do I learn English? And I remember, I was a
graduate student at Harvard, and one evening we came to my place, I had a TV so I was very
proud of it, I bought the TV, and he says, “Oh, hey, you
know, there is this program “which is very funny, it’s
called David Letterman.” And we turned it on, and
I saw David Letterman. It was an old show on CBS,
by the way, you can find on YouTube some clips, it’s hilarious. Sometimes I watch, I love it. Not CBS, on NBC, the old show. I look at him, I said,
I want to understand. I couldn’t understand a single
word of what he was saying because first of all, I
couldn’t understand English very well at the time, and
he was speaking very fast, and there were a lot of colloquial things, and a lot of cultural references, so I thought, I would be so happy when I finally understand
everything this man says, and I made it a point to
watch him every night. It was at 12:30 at night, so sometimes I had to go to bed early,
so I would videotape it, you know it was like VHS, I
had a VCR, it was ridiculous, and I would watch Letterman in the morning with my cup of coffee,
and I would look through the dictionary like,
what is he talking about? So, guess what, a couple years later I understood what he
was saying much better than my American-born friends, you know? So anyways, David Letterman, thank you. – [Bob] Yet another person who helped you. – He helped me. – And you also share things
like a borscht recipe in here. Not your mother’s secret, but you gave us a different borscht recipe. – [Edward] There is a picture
of my mother’s borscht, yes. – And there’s a cup trick, I mean, there’s just so much in here, and again, it’s ways of explaining concepts, so for example, did you
know the borscht recipe was gonna go in this book
when you sat down to write it? – [Edward] No. – Okay, how did you get
to the borscht recipe? – So this, I’m trying to
explain electromagnetic duality, so it’s a very interesting
idea that if you take the theory which describes
electromagnetic forces, if you look at the mathematical equations, if in the mathematical equations you exchange the variables
responsible for electric things, such as electric charge and so on, with quantities responsible
for magnetic forces, you just exchange them, the
equations will stay the same. But it sounds a bit too abstract, so I said how do I explain this, and I think I was on
the phone with somebody and I was trying to explain
it a couple months earlier, and it just came to me. I said it is like a recipe. In a recipe, you may have,
you know, potatoes and onions and then the same amount. And, so, if you switch but
there’s always in the recipe. In the text of the recipe. The recipe will stay the same.
– M-hm. – So, then if you add a few other things, it should have the same property then. So, then when I’m writing this,
I remember that conversation and then, of course a recipe of what? So then, since I’m Russian,
it has to be Russian dish and it has to be dishes
cooked by my mother. (laughs) – Okay, all right.
– There we go. – I have so many other
questions I wanna ask you. Can we move a little bit
to your writing process. Do you have to be in a
certain place, a certain time, what is the ideal writing
situation for you? – Yes. It has to be quiet. It has to be quiet, I think. Like I said, I was writing,
most of it I wrote in a very, in my tiny apartment at my dinner table. On my MacBook Air. So, but sometimes I would listen to music. Sometimes I would listen to music. So, it has to be, I think
one has to concentrate. One has to concentrate. – What kind of music? – Oh, at that time I was mostly listening to house music. (laughs)
– Okay. Okay.
– And electronic dance music. Which is kind of funny because some of it, I wouldn’t listen to it now
if I were writing something. But, at that time, it kind of
gave me this boost of energy. – Uh-huh. Do you listen to music when
you’re solving a math problem or tackling a math problem? – Not when, and likewise
with the book, only when, so at some point it
gets to issue of skill, eventually writing and re-writing. And it’s like tedious. It could be slightly tedious.
– Yeah. – Just kind of honing it, you know, and improving it and so on. That’s where music could be helpful but when I am at creative stage, on the stage of that certainty, when I am the electron who doesn’t know which slit is going to go through. – M-hm. – I prefer complete silence.
– Okay. Since you mentioned re-writing,
how is re-writing different? How is that a different
process for you than writing? Are you in a different head
space when you’re re-writing? – Yes. No, but that’s more like… That’s more like an effort. So, this is the thing, also. Which I didn’t realize. For instance, when you make a discovery, I didn’t realize this. Think consciously, at the time, but now I can see it very clearly. Let’s say mathematical discovery. So, I’m talking about the
most cerebral subject of all. Now, what is the process of discovery? Of new equation, of a
new idea in mathematics? It is tempting to say
that I gain knowledge, then I start applying this knowledge. So, then it kind of
looks like an algorithm. So I do this, then I
do that, and then it’s, the question is; what’s
the difference, then, between a mathematician, a human
mathematician and computer? Why wouldn’t a computer do the same thing? And the answer is that actually
at the moment of discovery, the thinking stops. It sounds, it used to sound, now it doesn’t sound strange to me but it used to sound very strange. Because I used to think
that the more I think, the more I get. But, in fact, it’s the opposite. Or, it is good for some
things, like re-writing, for instance, or typing a
paper, mathematical paper. And you have to go through, it’s Italian mathematician’s
beautiful phrase, mental tortures. You have to go through
these mental tortures of thinking and over-thinking and so. But, at some point, you’re
lucky to be able to stop. And that’s when the idea comes. It comes without effort. Instantly, you know it
and it’s effortless. It is like you’ve always known it. In some sense.
– M-hm. – It’s hard to explain in words precisely because it is
non-verbal. (chuckles) – M-hm.
– You see? And so, to me, that is the difference between the creative
stage of writing where, in some ways, you’re
just allowing yourself to express yourself, or whatever. – M-hm. – That is magical. There is some mystery
in it which can never be captured by words or
by thinking, and so on. And that is why I think we are so, people who get to writing and so on, if it’s sincere effort,
one way or another, you will feel it, I think. It doesn’t have to be a
long-form like a book, it can be something smaller. You will feel, and this is
what, I think, we love about it. And why we come back to it. Is because it helps us to
experience that levity, that flow state, you know? – M-hm. – Now, re-writing, for
me, is not flow state. It’s more like, okay, so
now technique comes in. So, now how do I make it better? Make it more articulate? How do I make it more succinct? And so on. – And do you have collaborators? You mentioned when you were
writing this book you had– – I let people, ask people to read. – Okay. – And they would, you know. Thomas Farber was a very
harsh teacher for me, so. Mostly there was a moment when I decided I wanted to learn how to
write op-eds, so short-form. It’s very different because
they give you 1,000 words. In the whole book I didn’t
have any limitations. And I remember once, it’s so interesting because some of that stays with you. And it’s invoked every time you get, you hit the same territory. – Yeah.
– So, he, I would send Thomas, my friend Thomas Farber, I would send him drafts of my op-eds, such as the ones which you have heard. And he would say, he’s an amazing writer, and he also is one who can
see, has very good eye. And he said, “Again, I see the word very.” He said, “You have to prune
your sentence in the text.” He says, “By the time
I’m through with you, “you will forget the word very.” (laughing)
– Uh-huh, uh-huh. – And this is very good advice. – Yeah.
(audience laughing) – I just used the word
very, you see? (laughs) – Yes, I underline very many times. Yes. What is it like working
on, so you’ve written, and there is so many more, I
just had room to include a few, writing an academic paper, for example, Baxter’s Relations and the Spectra of Quantum Integrable Models. Did I pronounce that correctly? Okay, close enough. And you work with other people. What is the process? Are you actually writing together, or is it you do part, the
other person does part? – It depends. I mean, I have written
90 papers like that. Plus two academia books, not counting Love and Math,
which were mentioned earlier. So, I like to collaborate. I like to, so, most of my papers,
actually, in collaborations. But each time it’s different. It’s very interesting how it’s done. So, it’s really hard
to find a commonality. – Okay, there’s no one way. My last question, and then I want to open it up to the audience, is you are a professor, you’re a teacher. Do you talk to your students, do you have time to talk to
your students about writing? Is writing, well, I’ll just, I’ll say it. Do math people need to know how to write? – Yes.
– Okay. – Absolutely. Yeah. And we are not good at it. I mean, we have a very
serious problem in my subject. Which I would kind of
keep it quiet for now but I don’t know for how long we can keep. But we are losing the ability to communicate with each other. We have lost the ability to communicate with the rest of the world a long time ago and now there is sort
of a process to go back, which, by the way, one of the
reasons why we have to do it is because we are also losing, as a consequence of not being able to articulate something, an
idea, to a non-mathematician. If you’re not able to do that, then eventually you will not be able to articulate to somebody who works in a different sub-field of mathematics. And this is happening so we
have now quite a serious issue, situations where there
are mathematical papers, where you have groups of
people, some of them say this is correct and this presents
a new, crowning achievement. And others say it is
false, or we don’t get it. And it’s kind of, we are at an impasse, in a few situations like that
in my subject, in mathematics. In a way which I think we
have never been before. And I think the reason is that, one of the ways in which we
could get out of this situation, unfortunate situation, is by
improving our writing skills. – [Bob] And is that being
addressed from your perspective? – Not enough. Well, we are addressing it right now. – Yes, right. – How many math majors
are here, by the way? Can you guys raise your hands? Okay, well a few, okay, good, good. So, you guys, it’s very
important to write. (laughs) – Okay. – No, I am hopeful always. People always say, oh,
it’s horrible, and so on. It’s horrible because we
have not done our job, our generation, but I am always, I always think that the
next generations comes, people who are here, the students. They’re going to do much better. I mean, there’s no way
they won’t do better. Of course, my job is to share
some of the difficulties and some of the issues that I experience and some of the things
that where I have failed, or we have failed as a
generation, as a group, so that they know to not
repeat those mistakes. So, I feel as though younger
people, they know more. – Okay. That’s good to hear. At this point, I’d like to
open this up to the audience. Do you have a question? If you could raise your
hand and we’ll call on you. If you could speak nice and loud, or I may repeat the question. Yes, the person in the front
row here, would you, yes. – [Audience Member] So you
said that when you sat down to write this book that
you were setting out to teach the world something and our activists use their
understanding of the aesthetic in order to generate affect in the viewers in the hopes of creating an effect that causes people to
initiate social change. You mention in the book
the untapped powers and hidden reality of
the world of mathematics that would lead to a shift in society. So, I wonder would you consider
yourself as a math activist and how do you envision the
unveiling of this hidden reality as causing people to
initiate social change? – Well, yes.
(audience laughing) It’s a very good point. I’ll have to be brief with
this, we are almost out of time, but I think yes it definitely
effectuates change in society. For instance, in the following way. So, on the one hand, it’s very easy to traumatize students
learning mathematics. By calling a student to the blackboard and saying solve the problem
in front of everybody, so the student panics. He or she is frozen, and
she’s just, sit down. You no good, you don’t understand. That’s it. And, in fact, such experiences, if you talk to people directly about it, they may not even know. They may not remember,
because we tend to push these kind of unpleasant,
difficult experiences underneath, in the unconscious. But it’s still there, and
it informs us everyday in, for instance, I’ll
say, I hate mathematics. I’m not good at mathematics, and so on. So, that’s one side of it. The other side, though, is that with a talented and loving teacher, a student can actually
solve it by themselves and they have this, and this is incredible when you see that. It’s incredible when somebody gets it. And it’s better when you see it. The joy is infinite, you know? It’s like, I got it, and nobody
can take it away from me. That’s where this quality of mathematics that it’s not up to discussion. It’s not a matter of opinion. X squared plus Y squared is Z squared, and be done with the problem. That’s it, right? I did it. I got it. Nobody can take it away from me. It is so empowering. And I have heard many stories
of kids, for instance, from immigrant families
who come to this country and they don’t speak the language. So, they feel like outcasts. They feel that they don’t belong. And they would tell me, after, you know, the grown-ups would tell me those stories and say, but then what kept me afloat, what gave me confidence,
is the math class. Because I was very good at math. – M-hm.
– And I could do it, and that gave me the agency,
that gave me the power. I knew that I was good. – M-hm.
– At something. – M-hm.
– You see? So, how do we use that energy? How do we… I feel like it is such
a waste that we are not using this positive energy of
mathematics in our classes. Under-using it to
empower people, you know? So, that’s one way in
which it could be done. And effectuate change. Not to mention that our kids
will grow up to be informed. They will not just take
stuff the government or the various corporations deal them. They will question things. Because they will not be afraid. So, that’s with the power of mathematics. Yet untapped. But we can do much better. – [Bob] Other questions? Yes, please. – [Audience Member] I remember you mention how the public should be more informed about using technology such as
elliptic curve cryptography– – Yes.
– Or artificial intelligence. Yet the mathematics
behind those technologies is very complicated. Do you still hope that we can improve the public’s mathematical literacy so we can at least gain
a basic understanding of those technologies? – [Bob] Sorry, this is a question about mathematical literacy. – Right. – [Bob] Just to make sure
that everybody can hear that. – So, I have no illusions that, you know, 90% of, or whatever, or
majority of our electorate would know what elliptic
curves are, specifically. And that’s not the goal. People know about art
without knowing the details. People know about music without knowing, not being able to recite by heart the names of the pieces of
Bach or Beethoven or Mozart. And, yet, they know that
they exist and so on, and they have a certain,
most of us educated people, we have a certain basic
understanding of what it’s about. That’s what I think can be done and should be done in
regards to mathematics. ‘Cause, after all,
mathematics is our heritage, it’s part of our cultural heritage. It’s just what we have
done for, in some ways, I think it’s a historical accident. We just kind of took the
wrong turn at some point with our math education, and there we go. Two or 300 years later, we are here. But it doesn’t have to be this way. So, for instance, in the case
of elliptic curve cryptography and the way it was
misused, today’s situation is that you cannot even
have a conversation with most of our electorates, so to speak, on this because the
reaction of most people is, unfortunately, I don’t wanna hear abour it because it’s math, and I hate
math, and I’m not good at it. So, next subject. You know? So, that’s what we have today. But imagine a world in which I’m not afraid to speak about it. I appreciate the fact that
I don’t know the details but I have heard something. For instance, you know,
in biology and physics, things like DNA and evolution
and elementary particles and the Higgs boson, they
are very much in the air. Now, does everybody know
what Higgs boson is? No, but they’ve heard about it. You’re not afraid you’re going to run away if I say Higgs boson. It’s like, oh, my God, I have to run away. I cannot deal with it. But if I say elliptic curve,
most people will run away. So, why? Because physicists have done a much, biologists have done much
better job sharing this ideas. Number one. Number two, it is ostensibly
closer to our lives because we are talking about
our bodies, you know, DNA. Or we’re talking about the solar system. – [Bob] Right. – And atoms, and so on. Mathematics appears to be very abstract and not connected to
reality, but guess what? It is now through social
media, through computers, through internet, it is
just as much integrated into our lives as atoms and DNA. So, there’s no excuse anymore not to know. And to be afraid. Because fear is the worst factor. – [Bob] Right. – The fear is what allows
manipulation and misuse. – [Bob] Yeah. And as you point out in your
Google piece that you shared. We have time for one more question. Yes, in the back, and
could you speak up please? – [Audience Member] It appears a lot because of the cross-section
between like writing and math, and I was hoping a genuine answer, where do you see yourself
in maybe 10 or 15 years in the mathematical world and
the non-mathematical world? What sort of impact would you
like to leave on those two, both different, yet similar worlds. – [Bob] So, where do you
see yourself in the future with these two worlds of sort
of mathematics and writing? – I want to, it’s a good opportunity, I wanted to read a quote. If I can open it. From Sofia Kovalevskaya, who was a mathematician,
a woman mathematician. So, she was Russian-born, and she lived in the second
half of the 19th century. And she was a trailblazer in that she was the first woman appointed as a professor of mathematics, in Sweden. And she was the first PhD,
she was the first editor, woman editor of a major
mathematics journal. So, really an incredible story. But she was also a writer. You know? And so it is really fascinating to me. She wrote in this letter. She says, I understand
that you’re surprised that I can do literature
and mathematics at once. She actually wrote this. I’m not making this up. It’s really amazing to me. Many people who had never had a chance to know what math is about and think of it as basic arithmetic consider it a dry and fruitless subject. Sounds familiar, right? But, in fact, it is a field that requires, most of all, imagination. And one of the top
mathematicians of this century, she was referring to her
teacher, Weierstrass, says, absolutely correctly, that it is not possible
to be a mathematician without being a poet at heart. It seems to me, she continues, that the poet should see
what others can’t see. See deeper than others, and that’s the job of a
mathematician, as well. So, in that sense, who knows what will happen? You know, if 10 years
ago somebody asked me, Edward, you will be sitting
in the Morrison Library, in this beautiful place, and a hundred people will
come listen to you speak about writing, I will be, get out of here. (laughs) That’s not possible. So, it’s a mystery right? It’s a mystery. – We’re here, and it is true, you are here talking about writing. I want to thank the Morrison Library, once again, for hosting us and I want to thank
Professor Edward Frenkel. – Thank you so much. (audience applauding) (upbeat music)

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