- The Man Who Knew Infinity, matter. - [Ken] Right, great,
thank you very much, David. (audience applauds) So I wanna begin with a
couple of thank you's. I've never been to
University of Alabama before. I'm delighted to be here, I'm still looking for
Nick Saban, but I guess (audience laughs) he's on TV all the time because if you don't lose your, like on TV all the time. I'd like to thank the math department, the department of physics and the library system
here for inviting me. And one disclaimer, if you
want to see a math talk, it's a little bit late,
I gave one earlier today, so this is really not a math talk. I don't really know how
to describe this lecture except that I hope that one of
the answers to the question, why does Ramanujan matter? I hope that at least one of the answers that I offer you speaks to you. And if more than one speaks
to you, then even better. I'm a little bit embarrassed
that my book is for sale here. It came out in 2016, I'd be happy to sign, but make no mistake I'm just
delighted to give this talk, and as you'll probably see this is genuinely a very, very
difficult talk to give. Not because the audience has
many different interests, is because this is kind of my life story. And if the story that
I'm about to tell you, which is absolutely amazingly
true is of interest, then maybe the book is for you. So anyway, let me get started. Here is a picture of Ramanujan, one of the very few
pictures that survived. And if you've never heard of him, I hope that this lecture goes
a long way to convincing you that he should be a household name. I'd like you to think of him as someone that should be thought of
as a Newton or an Einstein, someone whose ideas have
transformed science, someone's whose life is a role model for people who need hope. A lot of his life speaks to overcoming incredibly difficult odds. And for me both of those
roles were very important. I should be a bicycle shop mechanic, I shouldn't be Vice President of the AMS. And I think I'll begin to tell
you some of these stories. I first learned about
Ramanujan one Saturday in 1984. I was in 10th grade, I'm
the son of a mathematician, the apple doesn't tend to
fall too far from the tree, and my dad came to
United States from Japan as a distinguished
promising number theorist. And when I was 16, the
last thing I wanted to be was anything that my
parents thought I should be, much less anything like my parents. You see my parents were
brought up at a time when they were told that
their government was divine. They were told that the
emperor was like God. You know the story, right,
this was World War II, and try to imagine, which I didn't do until
I was in my early 40s. Try to imagine what your
worldview would become as a teenager when you quickly learn that actually your emperor is not divine. Japanese people aren't really superior to the rest of the world because they were humiliated
at the end of World War II. How does a country recover? I'll tell you a little bit about that. For my parents, the years immediately after the end of World War
II were very difficult. I mean, when your country
loses in a World War, life is very difficult,
there are shortages, infrastructure is destroyed,
and it was quite demoralizing, but for my father it was important to him to try to escape the difficulties of life. I mean, they were literally starving, but my dad was also an academic, he wanted to be a mathematician and he was also starving for knowledge. The universities had been destroyed. And one of the amazing things
that the United States did at the end of World War
II was they rebuilt Japan. And they rebuilt Japan
in a very amazing way. And my father was discovered
at one of the conferences that the United States held in the spirit of peace and reconciliation, and before he knew it
he was raising a family in United States in a
neighborhood surrounded by people that he was told to hate growing up. It was a very difficult time, right, try to imagine being from a country that bombed Pearl Harbor, you're probably not gonna
be embraced with open arms. So it was very difficult
time for my parents, and from my parents'
perspective the only way that the three Ono kids could succeed is if we became star students because nothing else about the
United States spoke to them. I'm the youngest of three kids, and so by the time I was growing
up, all I understood was, why do I have to get perfect SAT scores? Why is it so important to get good grades? Why can't I play Little League
Baseball like everyone else? And I didn't actually fully understand what my parents went through
to try to raise a family in a country that they never understood. I loved my parents, they're
in their nineties now. They live in assisted care, but to this day they are still afraid. They are still afraid and they lock themselves
in their room at night because they're afraid
someone will break in. So what was their first few years of life in the United States like? Despite the fact that my
father was a professor at the Institute for Advanced Study and later a professor at Penn, and then finally a
professor at Johns Hopkins. They had people shoot out
the windows of their kitchen, they had people leaving
burning bags of dog shit if I'm allowed, to be quite frank, on the porch when we were growing up. And as a kid I didn't know any of that. And one of the things that I
learned in writing this book and reflecting on my life
was that believe it or not, somehow this man Ramanujan has somehow magically interwoven our lives
as I'll begin to tell you. So how did I first learn about Ramanujan? Everything I just said seem to have nothing to do with Ramanujan. Well, I learned about Ramanujan
when I was in 10th grade, not wanting to be anything like what my parents wanted me to be until this letter arrived at the house. Let me read it to you, it's
a very peculiar letter. It's one of my most valuable
possessions by the way. It's a letter that was
written by S. Janaki Ammal, a woman who I'd never heard of before. And what this letter
clearly is is a form letter. Dear sir, I understand
from Mr. Richard Askey, Wisconsin, USA, that you've
contributed for the sculpture in memory of my late husband,
Mr. Srinivasa Ramanujan. I'm happy over this event, and I thank you very much
for your good gesture and wish you success in
all of your endeavors. Signed, S. Janaki Ammal. And what's strange about that is, I was the one that pulled the
letter out of the mailbox, I gave it to my dad, and a few hours later he comes to me basically in tears saying, I have to tell you the most amazing story. That's the day I first
learned about Ramanujan. I didn't actually understand all of it, I didn't understand how
this related to my dad because my dad basically never cried, I'd never saw him tear up
before this letter came. And we didn't actually come
to terms until the late 90s when he finally explained to me all that was going on that day, but what I did here was
somehow there is a great man who died at the early age of 32 whose ideas came to him
as visions from a goddess, who happen to be a
two-time college dropout. And what I heard was that my dad looked up to a two-time college
dropout as some sort of hero. And that was important to me because up until that point
all I heard was good grades, test scores, get into the right schools. And if you're a student you've heard it. So if you want some hope, do recognize that ultimately
the time will come, hopefully it's already happening for you where you will be evaluated
for the quality of your work, your achievements and the
quality of your character. And I didn't learn that till
I was 16 with this letter because I thought that there was no way that that would be part of my worldview. So what is the story of this letter? It turns out that Ramanujan died in 1920. This is the caricature of him, quite a peculiar letterhead if I must say. Look at the letterhead, widow of late mathematical
genius, Srinivasa Ramanujan, it looks like it's fake, it looks like this stuff
from like a cartoon, except it's totally real. So my dad told me about
this amazing figure who he looked up to as a deity, who happened to die at an early age. And it turned out that by the early 1980s, almost 100 years after his birth, notice here he was born in 1887, the mathematicians of the world
were preparing to celebrate the 100th anniversary of his birth. You must be something if a
community is gonna celebrate the 100th anniversary of your birth. And so to celebrate the occasion,
a reporter for The Hindu, I think New York Times of India thought maybe Ramanujan's widow who he left behind in 1920 is still alive, and he found her living
in the slums of Madras, now known as Chennai. And despite the fact that she lived out the bulk of her life in poverty, she did point out that,
well, I loved my husband, he did great things, he was
always doing his figuring, but if one thing bothers me, it was that when he died
the government of India promised to erect a statue in his honor. And what she did ask for
was, where is the statue? And the mathematicians of
the world got wind of this and they all cobbled
together their 25, $30 gifts and they commissioned the
statue that was given to her and she wrote all the
mathematicians of the world back. And I thought that was a lovely story, and that's how I first
learned about Ramanujan, I knew nothing about the
mathematics of the time, but that was my first experience were actually this is a hero whose
life actually meant something other than like Hank Aaron
hit a lot of home runs. I didn't really know his story, but here was an example of someone who would unknowingly become someone who I've been
following my whole life. So anyway, if any of
that sounds interesting, that's what this book is about. It turns out that I don't
care how spiritual you are, I don't care if you believe
in a Hindu God or not, but something about my relationship and my family's relationship to this man, both scientifically and emotionally and in terms of the need
for hope has appeared in many, many different ways in my life, and is basically
responsible for everything that has happened to
me that has been good, whether it was in college,
the University of Chicago, later in graduate school or the opportunity to work with Hollywood stars, making a film, all of these things have
made my life quite rich, and none of them would've
happened without this letter and this amazing guy. So as I said, a few years
ago we made the film, The Man Who Knew Infinity starring Dev Patel and Jeremy Irons. I cannot help but tell you crazy stories about what it's like to make a film. Dev, he came to fame because
he starred in the film, Slumdog Millionaire. When we made this film, he had just broken up with his girlfriend who was the lead actress
from that film, Freida Pinto. He was all boy then, he's now grown-up, maybe you've seen him in the film, Lion, and later this month he's coming out in, he'll be in two films, one
is called The Wedding Guest, another one called Hotel Mumbai, which will be a thrilling film
about the unfortunate events of a few years ago in Mumbai
and the terrorist attack, but anyway, here is proof that I actually worked on this film. (audience laughs) I still talk to Dev every once in awhile, he still sends me Christmas
gifts, I can't believe that. And here is a picture of us onset talking about a theorem
in complex analysis called Cauchy's residue theorem. What I like about this story is that this film even helped someone like Dev, who was a middling actor at the time. And he was very excited to
work with the Jeremy Irons, who is the consummate actor. So before Jeremy arrived on
set, I'd talk to Dev like, how are we gonna talk to Jeremy Irons? He is somehow gonna elevate
everything about this project. He had no idea that I was shocked that I was talking to someone like him, but it was actually very interesting on many different levels. One of the stories that
I'll tell you about, many of the stories I'll tell you about, if I don't forget to, is to tell you about how important this film,
about this Indian man was to both Irons and Dev Patel. This was a small project, this was not Batman versus Superman, this was a small film, but it was a film that
meant a lot to these actors. To give you proof, one week before the last
presidential election, Jeremy Irons and I were
invited by France Cordova, she is the current, then
and is the current Director of the National Science Foundation. They invited us with the
blessing of President Obama to the White House to
participate in training events for the transition teams
for the two leading presidential candidates at the time. You see when you run for President, it doesn't mean you know
anything about being President. There's a whole operation in place, and so there's training. And shortly before Halloween, right before the election, the two leading presidential
transition teams were invited to the White House, and one of those days was
related to science and education. And as was planned, they
wanted to present lectures and panels describing what the National Science Foundation does, what the NIH does, and I participated in that. And what we decided to do was at the end of a very long day
of talks and presentations, we would have a little party where we would show the film, The Man Who Knew Infinity because at the time there were a lot of very difficult issues that
were in the air that NSF, NIH and EPA wanted us to discuss. One of those issues was, of course, related to the importance
of STEM education. So thank you for coming,
it was very important. And another one is the importance of, of how to bring groups of
people from different cultures, people with very different
ideas together to do something great that would be
otherwise impossible alone. And so they thought the film,
The Man Who Knew Infinity would be like perfect for this. And Jeremy when he learned
about this said, I'm coming. I'm gonna come, support this mission, and he did it for free. And I thought that was
really awesome, right. And so here we are right before the party. We're standing in front of the West Wing, and maybe some of you saw it, if not it wasn't actually very exciting. I think it almost failed
that this is us giving a mathematics problem to the
citizens of the United States. If you can read the
board, it is the question, what is the smallest
number that is a sum of two cubes in two different ways? And that's a question that
you would've been answered had you seen the film. By the way it's the number 1729. So a couple of things
about Ramanujan's life, and I'll show you some clips, so that you can actually see in film, in action some of the important features. Ramanujan was born a long time
ago in a far, far away place. Think lush tropical India, he was born in 1887 in Southern India. He was born a Brahmin, loosely think of that
as the priestly caste. I think the vast majority of
Indians who you might know in this country are probably Brahmin. Ramanujan won't come as a
surprise, he was gifted, he was a talented student, he won awards. And if you ever happen to travel to India, which I strongly recommend,
it's a beautiful country, the colors are brilliant, the
people are very, very warm. And it's probably very
different from anything you've ever experienced if
you've never been there before. Certainly the food is
very, very different, and I've come to enjoy
Indian food quite a bit. If you happen to travel to a town called Kumbakonam in the south of India, you can actually visit the
house in which he grew up, you can visit his high school, and the high school principal
might actually show you the awards that he won over 100 years ago who keeps records like that. Ramanujan isn't someone
that you could train. His ideas, as I said, came from
his visions from a goddess. So he started finding
mathematical formulas on his own. And as we are told, he
discovered much of trigonometry by himself using his own
notation by the age of 13. If you're thinking, who
in the world does that? Great question, Ramanujan did that. He rediscovered a lot of
trigonometry on his own. And what I like about the story is, when he discovered that
trigonometry was not his invention, he really got upset. (audience laughs) And he took his notebook, he threw it on the roof of his house. And, well, he returned to the mathematics maybe a few weeks later, but what does that show? That shows self-confidence, that shows ambition and that shows drive, which is something that I
think all young students need to remember is one of the critical features to being successful. Think of visiting a kindergarten class, every kid can run fast, everyone can sing. Everyone is good at everything and somehow along the way if
you teach in a university, you discovered that that, that idea of hope somehow vanishes. I don't know how we can rekindle that. So one of the things that
I want you to take away from the story of Ramanujan
was sheer self-confidence. The belief that he could
make something better. And I like that. It's not about what you become, it's not about label, it's not
about what degrees you earn, it's really about what you achieve. And I learned that very early from my dad in learning about the story of Ramanujan. Ramanujan received as
a gift, pretty strange, this book called Elementary
Results in Pure Mathematics. When I was his age, if someone
had given me this gift, I would have to truly wonder
if that person was my friend. (audience laughs) Who give someone math books? I'd have thought my mom, for sure, paid this kid to give me these books. (audience laughs) But anyway, this is a
quite a remarkable book, in the sense that this book
should not have inspired anyone. It's a list of 6000 or so
theorems, just formulas, just, it's like a Wikipedia, articles, just listing 6000 formulas
one after the other, but as the story goes, this book ignited Ramanujan's
passion for mathematics, and he decided from that
day on that he was going to assemble his own findings
in his own notebooks emulating the format that
he saw in these books. I don't have time to go into
what formulas inspired him, but let me just tell you
about the very first page, the very first page begins
with formulas you all know. A minus B equals A minus B, check. So he's got 6164 to go. The second one is a little bit better, A squared minus B squared equals A minus B times A plus B. Maybe only a little bit
better, but I've 6163 to go, but the next one, if
you're a mathematician or if you remember your
high school algebra is actually doing something. When he factorize A cubed minus B cubed is A minus B times A squared plus AB plus B squared. If in high school you saw
that for the first time and thought, that actually
represents a step, an idea. Well, that might offer some insight into how Ramanujan viewed this book because immediately after that formula for A cube minus B cubed, dot dot dot, and then there's a sentence, and there's a general formula for all N factorizing A to the N minus B to the N. And if you know what I'm
talking about on that, about that step observing
difference of cubes, you will know then how
to fill in the details. And I think most experts agree that Ramanujan viewed these dot dot dots, and there's a general pattern as his sort of like video game. I was playing Atari, he
was filling in the dots. If you go to Chennai and visit the University
of Madras Library, it should be against the law, right. It'd be something like going
to the National Archives and demanding to see the
Declaration of Independence, but anyway if you go to this library, you can ask to see Ramanujan's notebooks and they will bring them out. Here is proof, here are
the three notebooks, and I got to tell you,
I couldn't help myself, but to really flip through
and see all the pages despite the fact these
have been reproduced. To literally hold those books is kind of a magical experience. And if you ever do go ask because there are almost no words, these were just pages
upon pages of formulas, and your first thought might be, what are we talking about
on these crazy formulas? What is it about these
formulas that are so inspiring? And if you're thinking that as wonderful because let me tell you,
it's 100 years later, and we're still trying to
figure a lot of it out. I don't know many books that we study for over 100 years and continue to learn. There are a few books that come to mind, and in mathematics these
books, take my word for it have led to several Fields Medals. If you know about the distribution of multi-centered black holes, which has been in the
news quite a bit lately, certainly in terms of mathematical models that are related to the
discovery of gravitational waves. There are formulas in these notebooks that people put to use, to write down those equations, long before anyone was even
talking about black holes. And that is crazy. If there isn't something spiritual about someone writing down
formulas that would be needed to study black holes 100 years later, then I don't know what I could offer you, that would be really quite striking. So Ramanujan became
obsessed with mathematics, and he started to spend all of his time doing his mathematics, and as a result he flunked
out of college twice. I don't recommend that
you flunk out of college, there are certainly benefits
to being a good college student and getting good grades,
but for Ramanujan, people who are artists, the
kind of flights of fancy that you think of that are related to the creative pursuits in the world, Ramanujan was something like that. He spent a lot of his time in temples listening to drums, doing his mathematics. His mother actually sang in temples, and despite the fact he was
a two-time college dropout, he had friends, he had support. This is actually very important to me. Maybe I didn't do a very good
job of explaining this before, but to be successful, nobody is successful by their own merits, everyone needs help, whether it's a friend or a parent or a teacher
or maybe many people like that along the way. And Ramanujan certainly needed help and the first people who supported him offered him work as a
clerk despite the fact that he was a two-time college dropout. What I'd like to say here, and this is what I told
my parents way back was the amazing fact that
despite his circumstances as a two-time college
dropout, his parents, or at least his mother
continued to believe in him. And I thought that was a
great part of this story, and I certainly needed
that when I was young. Nobody could understand his mathematics. So imagine being utterly
infatuated with some subject and not having anyone to share it with. How terrible would that be? It takes a strong person
with self-confidence to continue working under
those circumstances. So as I said I can't resist
to show you some film clips. So the first film clip I want to show you was one of the hardest scenes
that we had to assemble because early on we have
to explain to the audience that Ramanujan is desperate for a friend, he is desperate to have someone
to share his ideas with. We also had to introduce a character, we had to introduce Ramanujan's wife who he married when she was nine, so you can tell we lied. Devika who plays Ramanujan's
wife was certainly not nine. And the challenge that the
director asked of me was, you guys talk about mathematics being beautiful all the time, what's with that, help us
early on, try to explain that it's okay for someone
to be infatuated with numbers and try to get across the idea that it's something that
people could find beautiful without actually having
to write down an equation. So let me show you what we did. Lights. - Go ahead, you can look, please. - What does it all do? - It's like a painting, I think. Only imagine it is with
colors you cannot see. - What good is that? (laughs) - Not much for you, I'm afraid, but for me it is everything. Maybe there is someone else who can see and understand it as well. And for them it will be important. - Have you met them? - No, not yet. - I want to understand more
than just colors I can't see. - What do you see? - Sand. - Yes. Imagine, if we could look so closely, we could see each grain, each particle. You see, there are patterns in everything, the color in light, the reflections on water. In maths, these patterns reveal themselves in the most incredible form. - Lights. So that's one scene, okay. So that was Devika, she is
actually premiering a film called Swords and Scepters later this week at the Vancouver Film Festival. I encourage you to see that certainly if you're interested in some
classical Indian history, stuff that I don't really know. So anyway, as I've now told you, Ramanujan was filling his
notebooks with formulas. He couldn't share his ideas with anyone and this couldn't go on forever, and so he reached out for help. He began to write letters to the most distinguished
mathematicians of the time, which were professors
at Cambridge and Oxford, and he ended up writing one to a professor by the name of G.H. Hardy. Hardy is a name I think most of you know or at least wants to know whether or not you are a mathematician. If you remember your genetics class, you may have learned
about something called the Hardy-Weinberg law, which by the way for a mathematician is just a statement that one half times
one half is a (mumbles) but we'd like the applied nature of that. (audience laughs) And Hardy received this
letter from Ramanujan that begins with very famous
but very beautiful words. By the way if you're wondering, Ramanujan despite the fact that Tamil was his native language, he went to an
English-speaking high school, so he was very fluent. So if you're wondering, that's, he was very, well, these are his words, let me read them to you, I love, and his handwriting was
actually quite lovely too, but most of, certainly puts me to shame. The letter he wrote to
Hardy begins with the words, I beg to introduce
myself to you as a clerk. I have had no university education, I have not trodden through the
conventional regular course, but I'm striking out
a new path for myself, and the results that I get are turned by local mathematicians as startling. And the paper goes on,
the letter goes on to have pages upon pages of crazy formulas. Here is a famous photo of the
real G.H. Hardy on the left, and one of the best things
about all of this moviemaking was that we had Jeremy
Irons portray Hardy. And one of the first
things we asked him to do after showing him this picture
was emulate that picture. And I blew up the picture
so you just see his face, but there was a perfect picture like this and it was incredible. And if you're a fan of films and Jeremy Irons is someone
that you look up to, let me say this guy was literally amazing. It's not just the velvety
voice, it's not just his ability to use his face in many different ways to express even the subtlest of emotions, he was really incredible, in
fact he was fun to have on set. He raised everything about our project. And if you want to know, at the time he was set to
play Alfred, the Butler, in the film, Batman Versus Superman. Maybe some of you saw that poor movie. (audience laughs) And you might remember that that film, Batman Versus Superman was delayed by a couple of months for some reason, is because Jeremy wanted to play a Cambridge professor in our small film. And I thought that was the
most awesome experience. To put this in context, we
filmed the Man Who Knew Infinity in England and in India the summer that Harrison
Ford broke his leg at Pinewood Studios in London. So to put the context and the timing, we were there, it was crazy. What was in this letter
the Ramanujan wrote? There were some things that would make you think he was crazy. All right, so hopefully
that doesn't continue. In this letter you can find the expression that one plus two plus three, summing up all the
positive integers in order equals negative 1/12. So there's several problems with that. (audience laughs) But it turns out that to Hardy
who is a world-class analyst and analytic number theorist, believe it or not you can make
sense out of the equation. So if you've never seen
the mathematics related to what's called the Riemann zeta function, just take my word for it, equal
sign doesn't literally mean what you want it to mean, and there is a way to make
this statement precise. And Hardy would have recognized the brilliance in this expression. And so in Hardy, Ramanujan perhaps had finally found someone who understood him. What else was in this letter? The stuff in this letter
that really shocked Hardy, I'd like to take a moment to teach you. So for a teaching moment I
could ask this funny question, what is the value of X? And if you hated math and math class, it might be the first few
words of your nightmare, but let's have fun with it. What is X? I'm asking you, what is
X in this expression, if X happens to be this
crazy number on the right? If you know about the golden ratio, you might know this connection, but if you don't know about
that, it doesn't matter, all I want you to observe is that the part of this number in red is exactly the same as the whole number on the right-hand side. it's an example of a number
that lives inside of itself. And because of that, if
you want to solve for X, it turns out to simplify dramatically, so you get that X is a solution to X equals one divided by one plus X. And by high school algebra
you can cross-multiply getting this quadratic equation
when you bring the one over. And by the quadratic formula,
you get two solutions, and by positivity this crazy expression becomes a number negative one plus the score to five over two. It's a trick, the number
lives inside itself. If it's sufficiently complicated, it doesn't matter how complicated it is, just declare the number to be a symbol and you get an equation. This is kind of a thing that we do in mathematics all the time. Well, another thing that
we do in mathematics is ask questions like this. When someone offers you
a beautiful expression or a beautiful formula, a
mathematician is going to ask, is that a one-off? Is that just a curiosity or
is it a glimpse of a theory? That's a very easy question to ask, it's very hard question to answer if the answer is that it
is a glimpse of a theory. So the question I just asked
could be rephrased as follows. Define this function, this
infinite fraction called R of Q, which is one divided by one plus and it descends forever, and the variable Q appears as increasing powers of Q in the numerator. And when I say that mathematicians are in the business of building
theories from examples, what I want you to remember
is if you let Q equals one, we're back in the realm of my trick. If we're like Q equals
one, it was my trick. The problem is, if Q is
a number other than one, that trick no longer works. So is there a theory or not? So if you are a working scientist, one of the first things you might do is, well, let's plug in spot values for Q, like maybe negative one
or a half, a quarter, maybe we can get our hands dirty and see glimpses of a theory because we can manipulate numbers. I invite you to do that, and you probably won't get very far, okay. So at the time when Hardy
received this letter, the question would have been, can anyone on the planet evaluate R of Q for other values of Q? And the answer would've been no. And Ramanujan ended his
letter to Hardy with, he knew he could shock a
world-class mathematician by saying, by the way, that
function, let's plug-in for Q, E to the minus pi root, and I want you to pause and
think about that for a moment. What is the nastiest number you know? It might be called pi. What is the next nastiest
number you might know? It's called E, it could be E. If we have to denote a number by a letter, in particular a Greek letter or E, it's probably pretty nasty. It means we don't want to write it down. So Ramanujan said, instead of plugging in
one or negative one, let's come up with the nastiest
numbers in the universe, let's raise E to the
minus pi root and power. And he said, and I took
this high resolution scan of the letter and cropped it, the last three entries in his letter are, by the way that, so if you let N be one, I'm sorry, let N be four,
you get equation five, and it evaluates to something that looks not very different from what
I showed you in the trick. And if you let these other
parameters be chosen, he claims that these numbers
all look like simple things that you could derive from
the numbers I could produce from you, from the trick. And that takes a genius. Most people would try to plug in a hat thinking that's hard. 1/7th, right, I never liked
the number 1/7th, right. 1/4th I know 0.25, 1/7th I had
to stop and think about it. Forget that, he goes to E
to the pi, minus pi root N, and for Ramanujan that
was somehow natural. And not only was it natural, his evaluations involved numbers that we had actually already known. Where does that come from? All right, so in this film
we had very little time to explain any of what I just did too. And maybe I didn't do a good job anyway. By the way that last
line, Ramanujan's claim was not confirmed until
about 10 years ago, and it took a full professor
at Stanford to figure that out. Remember, Ramanujan died at 32, it took Brian Conrad, a very distinguished
professor at Stanford, a student of Andrew Wiles,
a name you might know to finally nail down what Ramanujan knew in the first letter he wrote to Hardy. Anyway, in this film we
need to make it very clear that Hardy was utterly shocked by a letter from an Indian clerk. So let me show you this scene,
which I happen to be in. (audience laughs) - You know, Littlewood, this year alone I've
received correspondence from those who profess to prove the prophetic
wisdom of the Pyramids. the revelations of the Elders of Zion, and the cryptograms, which
Bacon supposedly buried within the plays of the
so-called Shakespeare. But a letter from an ill-educated
Indian clerk in Madras, challenging assertions I
made in the tract series really takes the biscuit. - Well, I have to say, I've
made similar assertions myself. - So you admit it? - But this was three years ago. - No, no, no, I'm
talking about the letter. Bloody brilliant, I thought. I don't know where you got the postmark. Almost had me fooled. - I simply don't know
what you're talking about. - Oh, come on, I'm not a complete idiot. - I don't know how to get
this into your thick skull, but whatever it is you're talking about, I'm simply not involved. Play. - Sir, you've missed Hall. - Not hungry. - I tell you, there is a war
coming, no doubt about it, because we are being led like
mindless, spineless sheep, and no one bothers to question any of it. It's coming, all right, you can smell it. - You're as paranoid as Hardy. - With all due respect, Bertie,
you couldn't hold a candle. Littlewood, could I have a word? - Yes, of course. Integrals, Infinite series,
God knows what else. Oh, excuse me. I always forget you don't
believe in a supreme being. - Right. - If this chap turns out to be genuine, you might have to reconsider. - He must be genuine. - Who would have the
imagination to invent all that? - Well, I'm rather
flattered, you thought I did. (laughs) These two infinite series
are the more intriguing. - Yeah, they defeated me completely. I've never seen anything like them. - Well, it's deceptive. I'll wager the hypergeometric
series. (laughs) - Our great Littlewood stumped. He's Hobbs class, I'd say. Being inexperienced, I would very highly value
any advice you give me. Yours truly, S. Ramanujan. - What does the S stand for? - You can ask him yourself. - You intend to invite him here? - Well, no, no, no, no, no. Much better, let him rot away in his office in Madras, right. - All right, did you see what I mean about the facial depressions is
really quite extraordinary. I couldn't help but say that
I was in the last scene, the tennis balls that
bounced into the court, yeah, that's, you know. (audience laughs) They tried very hard
to get me a cameo role, and we filmed a few scenes, but there just weren't
many Japanese people in Cambridge at the time. (audience laughs) So I made the cutting room
floor on a couple of occasions. So you learned a lot. Put things into
perspective, this was 1913, at a time when India was part
of the great English empire. How great was it? It was awful to be Indian. India was basically a colony. The Indians were subjugated
as part of this colony. What you also learn here is
that Hardy was so surprised by this letter from an Indian that he couldn't believe
that it could've been, that it was even genuine, he thought it was a hoax perpetrated by his good friend, John Littlewood. And by the way you are also
introduced to Bertrand Russell, and it was fascinating
the circle of people that were at Trinity College
at the time in Cambridge. Here you learn for the
first time that Hardy was a distinguished English professor who happen to be an atheist. In fact he's quite well-known
for having a feud with God. If you know anything about Hardy and you know his readings, he had a feud with God, talk about ego. God will not let me die because so it was very interesting. And I told you that
Ramanujan was an Indian who said his ideas came to
him as visions from a goddess. For many people who saw
our film, the message was, how do people from very
different cultures, from very different stations in the world, social structure wise
ever get together to, A, understand each other, and B, produce something great
that they would've neither, neither of them would've
been able to do alone. So for many people that was the story. And it was actually a
very interesting story, Hardy never really had many
friends, he was a gay man. Ramanujan had no friends
who understood his math, and in a way they were
perfect for each other, although at the same time they could not be more
different as people. And I thought that was a lovely thing. So as you heard, Hardy invited
Ramanujan to Cambridge, and this scene that I'm going to show you is their first meeting in Hardy's office. - Ramanujan, we've decided
that for the good of everybody, you should attend some lectures. - But I'm here to publish. - Yes, all in good time, I hope, but first we need proofs of your work. - It's really nothing to worry about. It's simply a question, acquainting you with
the more formal methods that will benefit our
future work together. - I mean, we need a common language. You wouldn't expect us to
converse with you in Tamil. (laughs) - No, but you expect me to speak English. - Quite. So, there will be plenty
of time for publishing. - I'm sorry, but with all humility, how does anyone know that? I don't want this to die with me. - (laughs) I assure you it won't. - Thank you, sir, but I have
much more to share with you. As I told you, the letter only contained a small sampling of my discoveries. You'll see I have even found a function which exactly represents the number of prime numbers less than X in the form of an infinite series. - Exactly? - Yes, I thought if you
were going to publish, it should be something ground-breaking. - This is most unexpected. - Hardy, this will take a lifetime. - Maybe two. - So I'm showing you
scenes that I helped write. It was one of the things I'm
most proud of on this project. What I like about this is that, we had to make it very clear that Hardy did not yet
understand the true genius in the person he had invited from India. So that's what the
notebooks are all about. We also had emphasized
that Hardy felt superior as he naturally would, there is a lot of implicit
bias in the world, but is not implicit bias, this was just how things
were supposed to be. And then you also see
the humility in Ramanujan knowing that his situation
was quite fragile. And if you do remember World
War I was about to break out, this was a very tumultuous time. I also had a little bit of
fun poking some of my friends who've devoted their entire careers to studying Ramanujan's
notebooks to the line where Littlewood says, this
will take an entire lifetime. That was a little poke to my friends, Bruce Berndt and George Andrews who have devoted their entire lives to making sense out of these notebooks. And that's a true story. So what you also see here and this is something I
like to tell my students, and I wish I'd told my kids, but I didn't because I didn't
yet understand it fully. You have to somehow
experience things a long time and sort of remove yourself from situations to understand things, but to be a good professor, there is no single way
to be a good professor. Sometimes to be a good professor, you have to recognize that in your student you have someone that you cannot
mold an image of yourself. And it is that's, and often these students that are clearly talented,
but are hard to reach, just like kids could be hard to reach, are the ones that you
remember years later. And you might actually regret, I wonder what happened to so-and-so. I knew they were smart, I wish they had just come to office. If you're a professor, I'm
sure you know what I mean. And so one of the important
stories for us in terms of reaching the audience members
who happen to be teachers or parents or university professors is in this scene where Hardy who thought he knew how to be a professor finally has to come to grips with in Ramanujan I have a genius, and I have a moral
responsibility to science to do the right thing and
how do I break the rule, so that we can really find
a way to work together. So the scene I'm about to show you, I think is the last one I'm gonna show you before we start talking
about a few other topics, and then into the conclusion
is that in this story, I think Ramanujan matters
because he represents that being a good teacher
requires flexibility on the part of the mentor, and how Hardy broke through with Ramanujan was to finally get the genius
to understand that in him he had gifts that the world would need. If you're really gifted like Ramanujan, you might be writing down your formulas for your own enjoyment. It was pleasing to you
to write-down formulas, you might not know that the
formulas you're writing down might actually matter to someone, except in this case I assure you they do. I'm gonna end this lecture with something that's very surprising to you. You use Ramanujan's mathematics today, all of you, probably
30 or 40 times in a way that has only been introduced
in the last couple of years. I'm gonna prove that to
you later at the end, but anyway, this is a beautiful scene. It was actually filmed at Oxford because the library at Oxford
is prettier than Trinity, but I hope certainly for
the professors and students that you can appreciate. - How did you know that theorem? - It came to me. Mr. Hardy, I don't understand why we waste our time
doing all these proofs. I have the formulas. - It's not that I can't
see what you've claimed. It's that I'm not sure that
you know how you got there. Or indeed your claims are correct, there are subtleties which-- - But they are right, sir. I have more important new ideas. - Yes, but intuition is not enough, it has to be held accountable. And a little humility would go a long way. Why do you think they want us to fail? - Because I am Indian. - Well, yeah, there is that, but also because of what we represent. Now, Euler and Jacobi, who are they? - Mathematicians. - Just names to you. Euler was the most productive mathematician of the 18th century. Most of his work done after he was blind. Jacobi, like you, was
snatched from obscurity, and was almost as impressive as Euler. Now, I think you are in their class. What they had in common, what I see in you is a love of form, it's all through your notebooks. Let me ask you something. Why do you do it, any of this? - Because I have to, I see it. - Like Euler, form for its own sake, an art unto itself. And like all art, it reflects truth. It's the only truth I
know, it's my church. And you, just as Mozart could hear an entire symphony in his head, you dance with numbers to infinity, but this dance, this art, does little to endear
us to certain factions who see us as mere conjurors. So if we are going to
challenge areas of mathematics that are so well trod, we
cannot afford to be wrong. I need you to attend your lectures, don't offend your professors, and keep doing your proofs, otherwise this experiment of
ours will be doomed to failure. Come with me. I wanna show you something. There are many ways to be honored in life. For us being elected a
fellow is certainly one, but in my humble opinion to leave legacy here at the Wren after
we're gone is the greatest. This library houses the
epistles of Saint Paul, the poems of Milton, Morgan's Bible, but in my estimation as a man of numbers, the piece de resistance is
Newton's Principia Mathematica. Now, just as Newton represents the physical aspect of our work, your notebooks represent the abstract. Took a long time with Newton to be proved, which is why we have an
obligation to prove these. And if we do, I believe that one day, one day these notebooks
will find their place here. Now, do you understand
what's at stake here? Good. - That's a beautiful scene. All right, so how does the story go? Unfortunately the true part of story has a little bit of glory,
but it's got a lot of tragedy. Ramanujan in his time in England wrote 30 papers, some with Hardy. He overcame great difficulties to do this. Racism, World War I, the food, right, he was a
vegetarian trying to live in England at a time when it'd have been very difficult to be a vegetarian, but despite these hardships, he ultimately was elected
fellow of the Royal Society. That is a big honor, it's a big
deal, it's part of our film. We make that very clear. He was the first Indian scientist ever to be elected fellow of the Royal Society. It's a great honor and he was
elected at a very young age. By the way he was elected in 1918. Last October 2018 marked the 100th
anniversary of his election. And what did the Royal Society do? My friend Venki Ramakrishnan who is now current President
of the Royal Society, the first Indian President
of the Royal Society took to the 21st century
for that to happen. He has actually won the
Nobel Prize in chemistry despite the fact that he
grew up in South India himself overcoming incredible obstacles. He was inspired by
Ramanujan as a young boy. He arranged for us to celebrate the 100th anniversary of
his election in London. Now let me remind you, if the Royal Society celebrated
everyone that was famous, that was part of the Royal Society, they would have no time to
the actual work of science. So really it says something
that the Royal family and the Royal Society
celebrated this Indian man, and it was awesome, we had tuxedos, it was like super to remember this. Unfortunately Ramanujan returned to India because he fell ill, he
would die within the year, and as I said he died at the age of 32. Despite that fact in his last year of life although he didn't return to good health, he continued to do mind-blowing math, and time is limited so I won't tell you why I got into his mathematics, his maths, so I'll skip that, but let me say the work that Ramanujan did in his last year of life is
the study of black holes. And just last week at
the Simons Foundation, we had our third of a
series of conferences on string theory, black hole physics, and Ramanujan comes up in
probably every third lecture, despite the fact nobody
believed black holes existed, they were supposed to be an
anomaly in certain equations. So to begin to wrap-up, what
do we learn from Ramanujan? We learn a lot of mathematics. People have won Fields Medals for it. Every prize I have won, I
have to sort of make clear that I've won largely
because I finally understood something that Ramanujan
gave us a glimpse of. What else do we learn from Ramanujan? Well, I said that all of you use some of his mathematics
dozens of times today. This is my friend, P.P.
Vaidyanathan, he is a professor, he is an electrical engineering
professor at Caltech. In 2016 he won the IEEE Kirchhoff Award for his work in signal processing. What is signal processing? It's like one of the most important things that we use every day, your cell phones have to receive
signals and process them, so that you know how to communicate. The Internet, satellites, so much of the modern world
depends on signal processing. And it turns out that P.P. discovered that in certain frequency wavelengths, a formula of Ramanujan
was what would be used, should be used to make
cell phones work well. So you may have noticed
a couple of years ago I don't care what Verizon says, your cell phone probably started to sound a whole lot clearer a couple of years ago, and PP is largely responsible for that. He won a prize and if
you ask him about it, he'll apologize that
he just happened to be flipping through Ramanujan's notebooks because someone said, you never know, maybe there will be a
beautiful formula there. And amazingly there was. If that isn't shocking to you, then I can't really surprise you. All right, here I am with
Ramanujan deathbed letter. He wrote this letter to
Hardy shortly before he died. And let me say these few pages
have driven a lot of my work for the last four or five years, and I just can't imagine where I would be in my scientific career if this letter had not been received. It's mind-boggling to me to think about what our state of knowledge
in science would be if those notebooks had been lost. And in fact it turns out
that there is a notebook called The Lost Notebook that was scheduled to
be incinerated in 1960, but a mathematician by the
name of Robert Rankin said, you might wanna go through
that notebook carefully, this box of papers carefully and see if there's
something worth salvaging. And in fact those
notebooks are the notebooks that included the formulas
that PP wrote down that you take advantage of every day. I think that's incredible. All right, so what is
the idea of Ramanujan? This title of this lecture
was, why does he matter? He matters for science, he matters for many of the
reasons that I've described. Together with my student,
Robert Schneider, we wrote a little piece
in a Hollywood magazine describing why we want
people to see the film. And here's a little paragraph, I call it the idea of Ramanujan. I think Ramanujan matters because he represents endless curiosity and untapped potential, which
we all have to believe in to proceed in the sciences. Science usually advances
on the work of thousands over generations fine-tuning and extending the scope of understanding where from time to time created fireballs like Ramanujan burst onto the scene propelling human thought forward. So to close let me tell you
that I read those very words in Silicon Valley at Yuri Milner's house. Yuri Milner is one of the main funders of what's called the Breakthrough Foundation. You may know about them
because Mark Zuckerberg and Jack Ma are also on this foundation, and they've been giving out million dollar prizes to scientists. A few years ago, they started a campaign to send little spaceships
out to Alpha Centauri to search for extraterrestrial life. You may have seen even Hawking in one of the press conferences. We screened the film that night, people from SETI were there. And after the screening I got up on stage with the famous, rich people, and some of the actors
and I read those words. And I don't know what got over me, I probably had too many glasses of wine. (student laughs) I'd actually had dinner with Jill Tarter who was the first director of SETI, she was the Jodie Foster
character from the film, Contact. It was really cool, by the way. I think I said something like this, it's really appropriate
for us to be here today because you guys are searching for evidence for extraterrestrial life, the world is a big place, shouldn't we be searching our towns and our villages for the
Ramanujans right here on earth. And I thought that was
kind of a funny way to end, but Andrew Serazin, you may know the name, he is the President of the Templeton World Charity
Foundation was in the audience. He came up to immediately
after said, I love that, what can you do with a
half million dollars, let's find these people. Let's give them scholarships,
let's find them. So we do that, it's now called The Spirit of Ramanujan
Global Talent Search. We've now been doing it for three years and we give scholarships to people who otherwise would not
be able to afford to come to the United States
for a summer program. We discover people. Here are some of the people
that we've discovered. Boy, on the right, his
name is Ishwar Karthik. At nine he developed
his own formula for pi, I thought I knew pi, this nine-year-old living
in a desert outside of Qatar discovered his own formula for pi. They're out there. This boy in the middle,
his name was Martin Irungu. I found him in Nairobi, Kenya, hanging around the math department. He couldn't even afford to go to college, but it turns out he knew more math than any of the professors teaching at the University of
Nairobi, it was shocking. Who is this guy? Now he's studying to get
a PhD at ICTP in Trieste. If you don't know ICTP, it's a famous center
for theoretical physics. He skipped college,
this is a boy from Kenya that we discovered and made it possible, so that he didn't have to do
whatever you do if you can. Like (laughs) I said, I'd only wanna know what he would've done otherwise. And so if you know someone out there who could use help, look us
up, SpiritofRamanujan.com. You know a nine-year-old who
is not challenged at school, who could make use of a $5000 grant to participate in a summer program but they can't afford it, look us up, and maybe we can help them. And I think Ramanujan
matters because of that too. All right, thank you very much. (audience applauds) (mumbles) Yes. (mumbles) - Oh, so they're working at (mumbles) Ramanujan's notes or his notebooks. Bruce Berndt has published
seven or eight volumes, which include commentary on his formulas. You can visit a website at
the University of Cambridge where they have already
scanned in all of his papers. You can even in fact read
them in his own handwriting. So it's all freely, Amazon.com,
Ramanujan's notebooks, you can buy them, they're not, the Springer Publishers,
they're not cheap, but you go to the library
here, I'm sure that they are. (mumbles) Ah! (mumbles) Yeah, yeah, I was kind
of alluding to this. There is no such thing
really as The Lost Notebook, I object a little bit too,
but I know why he did it. The Lost Notebook that I'm
referring to was the notebook that was in that box of
papers that was rescued and then archived in the
Trinity College Library, but it was forgotten. And on a lark in 1976 George traveled to a conference in France and decided to stop in Cambridge just to rifle through Hardy's papers, and there he found about
100 sheets of papers, sheets which he called them Lost Notebook, it was really forgotten. The librarian in Cambridge lectured me the first time I got there when I said, here is the The Lost Notebook. No, no, no, here in England, we take our documents very
seriously, never lost, but never mind. (audience laughs) And these 100 pages, it's
actually a beautiful story. It turns out these were the 100 pages that Ramanujan scribbled his last ideas on when he was in India and Janaki saw to it that they
were forwarded to England. And that's the stuff what's
called the mock theta functions that George ended up
writing his PhD thesis on without being at all aware of
those pages in the library. (mumbles) He didn't really discovered them, he was the first person
to recognize their value. I mean, if you work in history
or if you're a historian, it's part of your business to travel the world doing archival work. We are not accustomed to
doing that in mathematics. So that it was lost is not quite true, that he discovered is not quite true, it was forgotten, it was
very carefully recorded. The librarians at Trinity
are excellent librarians. Nobody, it's better to say
that he was the first person to recognize the value of those papers, which is very important. Yes? (mumbles) Okay, several questions there. I think there is some people that we were never meant to understand. I think he was really
passionate about his formulas, that was clear. Whether his ideas really came to him as visions from a goddess, who knows? But what was very clear from his work is that he had this gift
for discovering formulas that he found to be beautiful. That was his hobby, and it's been the work for the rest of us over the last 100 years to figure out how to translate what
he thought was beautiful into a theory that we could develop. That doesn't really answer your questions, but that's how I view it. I don't know how to answer
why he felt he had to do it, but I'm so grateful that he did. I hope you do recognize that when we started to make the film, it was a small project. For Irons it was just, he wanted to play a Cambridge professor, he played so many other roles, he'd never been a Cambridge professor, he was like a little boy. So if you ever visit Cambridge, there is a river that
circumnavigates the campus called the Cam River and he says, we have to film a scene, I have a boat. I'll bring my own boat
and we'll punt the cam. It was like seeing this kid come out, so I will do it. Those scenes never made the film, but the point I wanted to make is what started out as a very small project ended up being several years of work for two people who ended up really
believing in this project. Jeremy actually came to Silicon
Valley with us that night when we were in the room, The Spirit of Ramanujan
STEM search was born. He saw that, he goes, I can't believe, I've had the fortune to be, a good fortune to be part of
a film that means something. All the Academy Awards and
all the awards that he's won and he's won many, he said
this actually like mattered. And I thought that was beautiful, and if you don't know, he's now an honorary chancellor
for the University of Bath, so his work continue,
and I think that's great. I think that's really great. (mumbles) Okay, thank you, all right (mumbles) (audience applauds) So if anybody wants to buy
a book from the library, maybe you guys have to.
