So let's start. I would like to welcome you all to the Mathematical Institute for another public lecture.
My name is I don't go really. And I'm in charge of this series of lectures for the department.
So before we start, I have to remind you about the Brexit side.
One, two, three, four, five. It seems the Government cannot quite decide which one is the best to use to leave the building.
We do not plan to have any trouble, but in case of emergency, do not wait for the government.
Just go for the nearest thing. Okay, very good.
So if you. You might have seen.
Now we have nice side now and you might have seen that little extra symbol which looked like a matrix with the sign x x x markets.
It's actually not a mathematical sign, but it's a financial company, X Markets, which is based in London.
It has offices in Singapore and New York, and it's generously supporting not only this lecture but the entire series.
So we're very grateful for the support. So a lot of you have come for a major events to see it tonight, of course.
But we have another major event bringing a lot of eminent mathematician from around the world in this building this week.
It is the 70th anniversary of the birthday of Professor John Bowen that you will see in a minute.
So we wish him very well for according to Wikipedia, his actual birthday is on Saturday from just a couple of days.
So a part of this celebration we have, of course, many, many very high quality, very advanced talks from from different mathematician.
But we thought we would bring something to to the public.
And we we thought that for this special event, we'd try something different.
And that you can see we have a very cosy setting here. And the reason is that tonight's speaker is Michael Atiyah.
And Michael Atiyah, as such an influence is so eminent among mathematics, in modern mathematics,
that it would be completely overwhelming for me to even try to introduce him properly.
So instead of that, my character, Professor Attia, will give a short lecture about certain ideas that he has about numbers.
And after that it will sit and we'll have a nice conversation,
a dialogue with which on board regarding his life, mathematics, their contribution and so on.
So we hope that you will enjoy and I think it will be a very exciting and very enlightening events.
So without further ado, please help me welcome Professor Attia for this.
You also.
Well, thank you very much for the instruction and I'm delighted to see such a large audience in support of mathematics in this famous building.
I spent many, many years in Oxford and although I've not long since retired, it's nice to come back, see so many friends.
Now this lecture the is the title of the lecture is the Titchmarsh lecture used in Oxford
and I represent I'm from the University of Edinburgh and also from Trinity College,
Cambridge. So that's who I am now. I think if I press a button, suddenly something happens.
Let's see. No, it doesn't. Technology support what's happened.
You can always press the button. You don't have to be okay.
Yeah, let's see. See, it doesn't work.
So you can press this mouse button. Such would work. Let's try this one.
No. Let's look ahead. You see, technology is not perfect.
So if you push on any case, you give me the first one.
Yes, this one. No, I want to go. Okay.
Sorry. Small hiccup. Small hiccup. It makes you more exciting.
Okay. So the title of my talk was Numbers are serious, but they're also fun.
If you're a mathematician, you enjoy doing mathematics, whether you're young or old.
And so it's fun. But sometimes you do also play fun games.
You can also get some serious outcomes. And so I want to show you how how that works.
And so let's start very far back in history time with the greatest mathematician of all time.
That was Archimedes. Without question, one of the great geniuses history.
You all heard about Archimedes. He's famous for lots of things, one of which is he jumped out of his bath and ran down the streets shouting Eureka!
In those days, people were more tolerant.
And you may not know this, but he also, by the way, if you didn't know what Archimedes looked like, you can find out.
All you got to do is win a funeral. Read his picture.
So I have a Fields Medal, which I've done in Cambridge, and there is the picture of Archimedes guaranteed by Wikipedia.
Now Archimedes, many, many things.
But one thing in particular, he invented the number of pi.
Now, I think you know what PI is most of you. I know just downstairs.
There's a caveat on the Pi Cafe.
So PI is so famous as a cafe, I buy a number that tells you something about the circumference circle and this very important number.
And there it is, written down a few decimal places, 3.1, four and so on.
So pies is very important number in history. Mathematics.
It was invented by Archimedes. Now.
Second famous mathematician Long Crater.
About 2000 years later, it was Euler.
There's a picture of Euler. He was a remarkable man. He published so much that they still haven't finished editing his works.
He was after he died and later on last part of his life, he was going blind.
But that didn't stop him. He carried on right to the very end.
If he's lost amount of work and almost everything that mathematicians now use is it goes back to Euler.
Now, for example, Euler in invented numbers does like.
Pythagoras invented numbers. Pythagoras invented pi.
Sorry, Archimedes, young Archimedes, even pi.
Euler invented a number called E. E Well, what is he written down there for you?
It's 2.718. And so what is it?
Well, the easiest way to describe you don't know what is is you you go to a friendly bank which offers you, let's say, 100% interest.
Very friendly bank. So you give it £1 at the beginning of the year, then the are in just one.
We end up with £2. Good profit. But suppose you decide to take your money.
And take the first bit out. Six months. And the bank is also friendly enough to give you the same rate if you do compound interest.
And on this, when you come to the second six months, you get not only interest on the whole money,
interest on the interest and then obviously a bit more.
But if you took your interest every quarter and every quarter of quarter.
So the limit, well, how much would you get into what you would get would be so easy, the amount you'd get from a very friendly bank.
Now, of course, fortunately, the formula is such that you can work it out whatever the interest rate is by small change.
E still give you the answer very useful number and you might say, well, I'm not interested in money, but suppose you've got something else.
Suppose you do want to count populations. You have you could you breed rabbits?
Okay. Sorry with two rabbits. Sorry for them it's for you.
And that is called exponential growth. And the world population sometimes suffers an exponential growth and it also come by so is very important.
Number E now is a stands for exponential things that go by multiplication, multiplication and the same formula the Euler e very important number.
Now one of the things that happened between before Euler was people discovered things called complex numbers,
things that don't exist, imaginary numbers. If you squaring number, whether you saw the positive number or negative number, the answer is positive.
So minus one cannot be described any number.
But this aren't put off by things that don't exist.
The less imaginary number you can imagine I and we call it I because I imaginary.
So I gave an imaginary number. There's always doubt it was some scepticism.
You had to use imaginary numbers. Well, yeah, no. Yes or no.
But eventually they find it so useful they allowed it. And so now Euler combined these two together, he took the AI and he says,
You take E and you raise to a power and you raise it to the power using Archimedes.
You were in pi, you write to pi I that was this marvellous collection you find, you get the value one.
And this formula easy to buy who's one is regarded as the most beautiful formula in mathematics?
Anyone who knows you ask them. Almost without exception.
This is the most beautiful formula in mathematics. It's fantastic.
It combines important numbers pi e ai and you get one.
It is staggeringly beautiful and it is so famous, so beautiful that you know this.
If you only want to invent one thing in your life, you can do that and you're famous for that.
But all of the many, many things but this was one I like to explain it to people.
One is like this. If you ask are you a mathematician, by the way, are not illiterate, we can read.
And if you know your hamlet Shakespeare, it is a famous phrase to be or not to be is very beautifully short use.
Only two syllable letters to be is is extremely short.
And yet if you think about this, it's a very deep statement to be or not to be, basically.
Are you going to kill yourself? Yeah. Well, so what could be more important that and so I think Hamlet and Shakespeare to be or not to be,
is the literary equivalent of Euler's formula or other way around.
Euler's formula is a mathematical colon or to be or not to be, they are two perfect gems.
C Remarkably short, succinct, and yet deep.
That is what you aim to achieve in mathematics or nature.
I hope you're convinced now. That was my first slide.
I don't have many slides. I don't believe hundreds of slides, one after the other for the next.
It doesn't work. Now I'm going to spend the next bit talking to my my wife.
Have you don't mind personal. My wife Lily.
Sandy died a few months ago. Well, the mathematician and women mathematicians were rather rare in that time.
And he did his successful life as a mathematician many ways.
And he picture shows here that together we don't eat cakes.
And the photographs of mathematicians, too, the University of Edinburgh, where we are now.
And we open it together. So that was her. And that was her last public appearance in 2040.
And before that, she taught in many places, and she taught in particular.
It's a huge college, Oxford, which you really know down the road.
And so we spent many years in Oxford, and that part of our time was spent there.
And then, of course, another button, I think it was then. Yes.
She also taught at Headington school, which is far up the road, a girls school.
I'm very pleased that Colin Bedford, sitting in the front row here with a fellow teacher of ladies all that time ago, is here for the occasion.
She taught mathematics in heading the school forever, quite a long time.
And since I've been here in Oxford this time I've been told by four different people
that their daughter was taught mathematics by my wife and altered their careers.
So you teach children any age, inspire them, you can alter their lives.
My wife has that ability.
She was a very active in the mathematical association, which involves the whole involvement of teachers teaching mathematics in schools of all kinds.
She was very active in the Mathematical Association here in Oxford.
So I think it's a it's now back in Oxford and we spent 30 years in Oxford together and she passed away a short while ago.
I think I would like to dedicate this lecture to my wife.
So I by the way, I should mention for those who you've been attending and conference on ball and who appear shortly,
it's like miraculous appearance that my wife did it in mathematics.
She worked with Mary Cartwright, the very famous woman mathematician.
And in fact, her work, which is really quite difficult stuff because I didn't really understand what you did.
It is actually turned out to be your reflection, quite closely connected with some of the things we've been hearing about.
It has done both, actually. So she did work of some mathematical importance with her.
Even in the other days I was on her own.
I got my Ph.D., went off to America in those days.
She had to give up her job and follow me. Nowadays, you wouldn't do that.
You send your husband away, say, see you, you come back. But in those days, it was customary to resign your job.
You had a full university job teaching mathematics. Yeah, before me.
And when we got married, she had to leave and go away.
It is sad, but that's how it happened.
Right. So that was my dedication to my wife. I hope you don't mind my little digression.
Now back to the main theme of my lecture.
So we looked to the past Archimedes and Euler.
Great figures. They did marvellous things. Well, how about the future?
Well, somebody in this audience here future of Archimedes.
Any Greeks here? Future Euler?
Actually, we all come from all parts of the world. Doesn't matter where you come from.
Mathematics is absolutely universal. So any way in the world you come, you can try.
So the challenge. Problem of your challenge.
Well, for player numbers like Archimedes Solar and even the new number.
Look, Archimedes Pi. Well, everybody.
And to Pi. Why not try your hand with the new number?
You will become as famous as Archimedes or Euler. You know, only one kind of immortality.
That is the immortality of ideas. Your body passes away.
But any fundamental ideas you create live on. That is real immortality.
So you want to be immortal? Don't buy medicine.
Live longer. Just work hard. Have ideas.
Now I don't want. As I pointed out here, they don't need to jump out of the bath to become famous.
That's extra bonus. But if you look around, you see, when Archimedes found Pi, he it was it being around.
Everybody knew that somehow you have a circle and you had to travel around the circle.
Its length was approximately a bit more than three times. You know, people who know practice everybody roughly speaking, see.
So we know that the shortest distance between two points in a straight line, you got in a curve configuring.
So how much longer? Well, people knew something. So Archimedes made that precise.
He said, Well, I know what it is. And he did it this way. Now you can't say this is the number.
So he was taking some material and actually formalising it, telling you what it was.
So the question is, if you wanted to do something similar to Archimedes now, what would you do?
Well, he'd look around and see what people are doing. What are the common equivalents of the people who are doing primitive agriculture now?
Well, of course, they weren't sophisticated and they might recall physicists.
And if you look around amongst your physics friends, you find that they have a number and the number is actually a name.
It's called the Fine Instructor Conference. I don't need to know anything about what the instructor called.
It is clearly something that has a name like fine structure implies something rather fine.
And it is it is a marvellous thing. Physicists love it.
And actually, whether you talk about the number which is called Alpha, well, you have to think of a letter.
The alphabet first come, first served. Well, Alpha, sometimes people write one over other.
Doesn't matter whether you have a numbers in this, each gives the other.
So they don't prefer the right one over alpha. And this number is known quite well.
Here it is. It's 137.035.
Well, you read it yourself. That number is known.
But what is it? Now, see, people now know a lot more than they did in the early days are quite more advanced.
They have pocket calculators. They don't you think they press a button?
Hopefully. So they know this. But what is it?
Well, let me give you a quotation from a physicist, a very famous physicist.
I'll show you who he was. He was called Richard Feynman.
And there's a picture of Richard Feynman. He was he got a smile on his face.
He was always making jokes, but he was one of the great physicists of the 20th century and unfortunately not dead.
And Richard Feynman said the following thing.
So I agree with you because he's very. But it is visible if I swear is not me.
Feynman swearing. So I hope I'm solved.
And I said, Where does Alpha come from? This number is it related to PI or press E?
He thinks back to Archimedes Euler, his new number.
Well, where did it come from?
It's a number that emerges from physics in some marvellous way, but nobody knows quite about much about it because nobody knows.
This is one of the great damn mysteries of physics. Now you see, it is here.
It's fireman swearing, not me. And a magic number.
Now everybody likes magic, you know, wave in the air, abracadabra.
A magic number that comes to you with no understanding by man.
Where did it come from? You might say the hand of God.
I'm just theological. Well, I didn't know what it means, but.
And we don't. And we don't know how he. That is the capitalist way he pushed his pencil.
So this is what Feynman said. It's a challenge. Can you answer his question?
What do you offer you? You know something about it, but you don't know where it comes from.
Where are you born? Where we belong. Is it part of Israeli supply?
Is it ready? Well, well, well, well, well.
I think the answer is yes. But I better not spoil your fun.
You go away. Anyway, he gets not to come back.
Give it to me. If not, I might leak the secrets privately.
So that is the great problem, is a good example of a challenge.
You look at numbers, play with numbers, but play with interesting numbers.
Play numbers that might be important. This number is not an arbitrary number is number.
It plays a very fundamental role in all of physics.
Everywhere physicists look, this pops up because think about pi.
Pi doesn't just occur in the slums of the circle.
All my physics. I know that PI occurs almost everywhere.
If you look at Gaussian distribution, you find PI. You look at this everywhere.
You look at mathematics. Pi pops up. Why? Well, God only knows.
And this number here is the same is a number that pops up everywhere you look.
You do an experiment with this, that it's there. You do another experiment, something else is there.
Same number and author was there. How does that happen?
Is magic. And magic is really the great beauty of mathematics.
It is fun, enjoyable, yet deeply serious.
We tell us things about the world we didn't understand, and even when you've done it, you stand back and admire the miracle.
So it is really mind bogglingly spectacular.
And so I think if you solve this problem, you know, we really done a lot to increase our understanding of the universe.
And so it is a challenge. And if you have any of you are one of the challenges that it is.
But it's not an easy challenge. I should tell you that this has been around for, let's say, at least 50 years of more so.
And many of you have tried to solve that problem and got nowhere.
So but that's always true of all the great problems of the past.
They've been around sometimes for hundreds of years. Think of Andrew Wiles solving Fermat's Last Theorem in this building.
I mean, the building comes off and so probably it may have been around for 5000 years.
And of course, nowadays things move much faster.
You know, 50 days now with Google and all that is equivalent to several hundred days solving things much quicker.
So you expect after 56 years, this problem would have been solved, but it hasn't.
There's a real challenge. Can you keep up the pressure of advancing mathematics by not just doing little calculations?
That's a dull theology, but solving fundamental questions which have a long history and a great importance and a great beauty.
And of course, you want when you solve this problem, you don't only want understand.
This new number, I'm sure you want to ask, is there some relationship, some analogue or Euler's formula with two fire equals one?
Does this have something to do with that? Because that was the ultimate beautiful formula, the one that I said called to be or not to be.
Well, Shakespeare was a great writer. But there are other great writers who are something else which goes beyond the Shakespearean quotation.
Well, there you see life, mathematics, literature.
Don't stop. There's always room for new things.
And so with an audience full of some young people, some not so young, I don't think there's this challenge.
Can we push the boundaries of what we know little further?
We don't do that. We're just copying our ancestors.
By the way, we had a lot of discussions, some of our meetings about modern computers.
Will the computer replace the human mind? We will.
Artificial intelligence pushes make us all redundant out of work.
People think there's a lot of serious talk these days about replacing the human brain almost entirely by artificial intelligence.
Well, fortunately, I'm a believer in that. You can't do that.
I think artificial intelligence of any kind, however sophisticated or basically has limitations, the human mind does not have those limitations.
And the human mind has evolved over several billion years.
So evolution and no amount of clever manipulation by the scientists is going to catch up.
So they cheer you up. You're not going to be I don't have a job.
Stay with the mathematics and think not just don't don't do routine calculations.
The computer wipe that off the board very fast. That's don't think deeply think imaginatively.
Have brilliant ideas. Think of things that nobody would think of, even a computer.
Then you're ahead. So there's that left message for you. Let's encourage the future.
Don't be depressed. Just remain enjoying doing mathematics, enjoying the fun of it, and realising that the same time you can do something important.
Well, I think I've used up my time and I now. Woman comfortable chair.
If you want to stay this university. Oh, yes. No, no. Sorry.
I was on the side left. So sometimes that goal is useful.
Yes, I should have said this lecture is course called the Titchmarsh lecture.
So I should say something about Titchmarsh.
Well, actually, I shouldn't say much about Titchmarsh because I didn't want him to go for the many very few words.
It is very similar to the famous physicist Paul Dirac, who's also many, very few words, and I'll tell you stories about that.
So they spoke very little.
And so when I came to Oxford, I had to go to my old building, not this grand building here, and I had to get the keys to my office.
That was in 1961, sometime back in the Middle Ages.
And I had to go and see this march because he was the senior officer.
So I went into his office. I sat down. He gave me the key.
I said. And we did. We did. 5 minutes.
Nothing happened. I got up and walked out. He didn't he wasn't the man to wear his words.
And actually, a few years later, he died. And I. I took over his office.
But that's another story. And I tell you about Dirac since I thought I'm talking about people, few words.
Now, Paul Dirac was the most brilliant physicist of the 20th century after Einstein in the hierarchy of physics, Einstein is way up there.
Dirac is just after him and the others. That's modern physics.
I mean, if you go back, if you include Newton and so on. But and Dirac was a memorable man.
Now he had an interesting background. His name was Paul at the Maurice Dirac.
So obviously French origin and his France father, who'd come to Britain from French speaking country, came from Switzerland or Belgium.
Anyway, he was very keen that his son should learn French, so keen that he insisted that at all mealtimes you didn't get any food.
I think he spoke French. Well, if you have any experience with children, you know that he's not very productive.
So the outcome of this was that as soon as Dirac left home and he stopped speaking, his father be sort of speaking French and see he spoke almost.
I was speaking to a man of very few words, and that's true.
He was he really cut his father off completely. And he never spoke French.
I mean, trying to indoctrinate your children by force is counterproductive.
Now, I'll tell you one story and I will stop. Give you an example.
Dirac. Everybody knew he was a man of few words. One occasion he was Fellows and Jones College, Cambridge.
And he went in to lunch one day and sat down.
And a young lady sat down beside him. Hit him.
This is dreck. I've taken the bet that you will say these three words to me.
He didn't do that. He said, You lose. So you see, he was a man of few words.
So I will follow his example announcing that. I think.
Okay. And I think the company I'm sorry, is this is the hot chair.
Right, Don. Nice to meet you. A young 70 year old.
Yes. So thank you so much for this inspiring lecture.
So maybe I could ask you a question. Yes. Yes. Do you think there should be a formula for the fine structure constant or related to Euler's formula?
Yes. I'm a man of few words.
Well, it depends what you mean by a formula. So you've always had the question.
What do you mean by and former the like, you know, format.
Well in PI this isn't really a formula of a by the procedure for carrying by by going some complicated limiting process.
And I claim that this number has all the properties that you think of as PI, but it's a bit more difficult.
Yes. So it is a number with a good ancestry.
Of course, it's a it's a dimensionless number from physics. So you think there are other dimensionless numbers from physics?
Yes, I think that is sort of the same way you see in physics.
Usually you measure things in terms of units, velocities, speed, speed, distance ratio, mass,
every thing the physics depend on the units you use, you take your units metric to balance metres centimetres,
you have to rescale things, but sometimes in a ratio of two things which are the same dimensions,
then they cancel out and they have no dimensions left. So they are not pure numbers.
And by an example, if your circle radius is two pi are not that are you cancel the R and you get pi.
So pi is comes by cancelling all the dimensions and you do that with other quantities.
And this find such a constant is the example dimensionless number.
LeBron. Your number is your number. It comes from mathematics.
How it. So there's a lot of young people here from local schools, I think might be interested.
They might be interested to know how you first got interested in mathematics.
Was it an inspiring teacher, your parents, a book you read, a problem you heard about?
Well, very often people say, yes, somebody inspired me.
And, you know, teachers can be very inspiring. My wonderful teacher, she was so inspiring.
So I think I was well, I was fortunate in a way.
I didn't have to be inspired by a teacher. I was naturally inspired myself.
I mean, and I, I perfectly respectable teachers.
Later on, I got some quite good I had a good, very inspiring teacher rather late in life.
Late in life, meaning when I was 16. I mean, by that time your education's nearly finished.
So when I was 16, I was sent to a school called Manchester Grammar School because they had a very good mathematics, tricked, pretty good university.
The teacher there, it was really inspiring, very old school style person.
He'd been to Oxford, but he thought the best student would go to Cambridge.
So I was trained to go to Cambridge and he was very inspiring.
You made his work very hard. I really worked harder in that year than any time in my life, either before or since.
So he was inspiring, but I already decided the message and before that.
But at that stage he gave me excellent grace. Yes.
So any time in your life you may be inspired, maybe initially or really strong, and inspiration is very helpful.
That inspiration stayed with me. I still think about him. Yes.
You so teachers can have a big effect on your life and good teachers, you know, you can change your life in a minute.
You go and hear good teacher or good lecture and you come away.
Your life is changed and your wife is. You know what inspired her to do mathematics?
Uh, well, my wife, very complicated story, came in very poor background.
Her father works in the dockyards. Nobody. Her family went to technical school, so she found you good at mathematics.
And that was her way out of poverty. And I think what inspires you more than to rise above your roots?
So he pulled us up from nowhere. Ended up by being the best mathematician in a school the best.
Got all the prizes, the university and the, you know, doing very well.
And for me, that was. But no, no.
She pulled herself up entirely by her own existence, her own ability.
And she had the brains. And she was better than no good at English.
She failed all her command in Scotland. So.
And. But. But you always had a good mathematical brain and use it.
So it does help you have a good mathematical brain. You want to do mathematics.
But if you have a good mathematical brain, you enjoy mathematics.
And that sort of feedback, that makes you better. So.
So you're one of the world's most famous mathematicians, and you must have had many great moments, great mathematical moments.
But this is the one moment that you mathematical discovery or moment when you discovered something that stands out among all the others.
Uh, well, yes and no.
All good answers come like this. I worked on something which eventually became called index.
It doesn't matter what it is, but it's. And it wasn't a theorem, but it took me.
It has so many ramifications. Took me 20 years to develop. So it became a theory.
And so that was undoubtedly my best work.
And but it covered that two years I'm the same.
And I am still working on it now. So it takes over your life.
And so in that sense, that's the best thing I've ever done.
But so I will embrace it. It includes other somethings. So that's yes, I think if you done something like that, you you didn't even know it.
You didn't realise that you you know, you found a gold mine.
And you find a gold mine. You know, you go on digging and digging when the gold ran out.
But you so long as it's there, you keep digging. So.
Yes, so I have. Sorry, I rambled a bit.
No, no. But it happened at a precise moment in the afternoon or something.
When you suddenly saw what? Well, there have been occasions like that.
This is, of course, famous bridge story w where Hamilton, the great Irish mathematician who had flights of inspiration as he crossed the bridge.
And you wrote it down there then and now when you cross that bridge, you'll see a black saying here what Hamilton discovered.
And that's very there are many stories of mathematics which are apocryphal.
Archimedes jumping out of his bath with new photographic evidence.
Newton of Apple Tree, where there is an apple tree. But it's not quite clear.
Newton was sitting under it. So, you know, these are stories which are sort of they're really myths.
But good myth is carries a lot of importance, even if it's not actually true.
And so a lot of things are missed. But in the case of Dublin, one is fact.
In my case, I'm trying to think of anything. I've been a few cases in my life.
I remember reading that already. Poincaré, the great French mathematician, used to claim that he got good ideas getting on another bus.
Well, you know, I tried that didn't work.
But I remember very clearly once when going for a long walk.
With. I think my friend says, end of the walk.
We'd solve the problem. And in doing their work, it was a flash of inspiration.
So I remember that clearly now. It was one particular day, something we work on for quite a long time, and we went for a walk and then we walk.
We had that's it. And then we to do other a bit like that.
But within a mile of bus, it could happen anywhere. It could be a bath.
It could be this. And so you get these flashes of inspiration now where they don't know where they come from.
And they crack a problem for you. I think it's a sort of fundamental, difficult something we've been holding up.
And so, yes, I've had that few just not very often, you know.
But I saw it last once.
Yeah. How did these ideas, good ideas come true? He said.
I think I had one good idea, one's modesty, you know.
Now all mathematicians get stuck when they're trying to solve problems.
I feel I'm stuck almost all the time. Yes. So sort of. So what do you do when you're stuck on a problem?
Very good question. Well, after his experience helps, the first time you're stuck on a problem,
you you know, well, it can be devastating and people don't know what to do.
But with a bit of experience, you know, to do things, several things you do.
One is you leave them alone for a while. You forget about it.
Use something else. So you should have a stock of things you can do work on when this problem is stuck.
You work on that problem and that, and then maybe you come back to the person later on.
You have a half a dozen problems and you're stuck on each one.
You shuffle it round. You find you can make progress.
That's one solution. Another solution is that kind of problem.
And you talk to your friends, talk to other people, perhaps have different point of view.
See if you hit a wall, brick wall, you can bang your head against the brick wall till your head breaks.
The wall doesn't break. That's not a good way of making progress.
But it may be that that wall actually is finite.
And you go round the wall and you've got friends telling you they look, why are you banging against the wall?
Yeah, and that happens very often. You don't realise that the obstacle you're hitting is not essential.
There's a way around it and it's another point of view.
Literally perspective can tell you how to do that.
And that happened with me. I'm a gregarious mathematician.
Sorry, good. Gregarious is rather talkative, which means I like to talk to people and I do not like to sit by myself too long.
You've got to balance it in life. You are an alternate, sitting quietly and thinking and then going when talking as a very good form in your life.
Sitting by yourself quietly for a long time that leads to introversion.
Interested is not healthy, is also boring.
It's also like between being thinking hard by yourself, going out with friends, having a good drink or enjoying life and mixing those two together.
And your friends may say, Well, I got an idea about your problem. So you can combine life with that.
That's the way I've tended to work. I tend to be gregarious, talkative, interact with other friends and they give I get that way.
I learn new things. The friends teach you something, you learn something. I mean, you learn technically you just pick up points of view.
But all the rules you've faced for decades, problems that you wanted to solve somehow couldn't.
Yes. I mean, you could say that all my life I've been trying to solve some really hard problem.
And maybe today I solved it, you know, because you don't know until you've got round the wall with no whether there was a wall there.
So it's a very tricky situation. No.
I mean, all your life you're trying to do things and some big things.
You feel the life behind it and you don't quite know what they are.
And, you know, maybe in your life you find out or maybe you don't mind that.
So we always searching for the ultimate big breakthrough, whatever that big breakthrough is.
And I'm 93 and I'm still searching.
I'm not giving up. So in your in your long career, you must have met many, many famous mathematicians, too.
Does any one of them stand out particularly?
I think I bet nearly all the people in my vision of the world, my world almost I.
I met all your fields, medallists. That's a good start. Citing one. And I.
Yes, if you live long enough, you tend to meet more people.
That's a truism. I think I've met everybody.
And what is remarkable is the variety.
Mathematicians come in all shapes and sizes and be outside mathematics.
Think we are all the same. A mathematician is a peculiar character who does like mathematics.
Actually, that's not true at all. We are. We like mathematics, but we are very, very lot.
There are tall people. And so people, in fact, we will be.
And of course, significantly, those who work this kind of mathematical work and that kind of mathematics,
those who work this way or that way, we are a very good, broad cross-section of humanity.
And so that is the diversity of people is actually a very healthy sign.
Mathematics, I think I saw I don't know when I started this one thing going, I keep going.
What was the question? Well. Was there anybody in particular that you remember standing out in some way?
Well, let me say I've met many mathematicians who are obviously Steve said to me in some direction, I think Amanda was much better than me.
In an analysis I let me and I met Jean-Pierre said he was much better than me and number theory and
I met many people who obviously tremendously impressive in the sheer ability to solve our problems.
Doug Milner for example, another man position and I made each one of these I met, I said, Well,
I can't possibly compete with these guys on that score because they're just better than me.
They've got a brain that is very good for this. My brain is of, you know, inferior subsets or different.
So, yes, I've met a lot of people who I consider robots.
Six In Britain, the example of physics is a genius.
So the people who are really good. But every genius had his weak points.
Well, it's Maurice by definition. A genius is somebody is so focussed on doing something that he doesn't notice something else.
Uh, they never knew Ramanujan, but he had his weaknesses too.
Yes. So, I mean, if the one was genius who knew everything very depressing.
I mean, I think was there was one person like that. It was Archimedes.
And fortunately for me, he lived a long time ago and I write his metal.
So I feel, you know, I can. But he would be if I'd been around in Archimedes time, he would have been a daunting figure.
And so but nowadays there are great mathematicians of all kinds and there's lots of them,
and they're all better than me in some particular niche, but they're not all better or in all directions.
So that's what friends. Yeah, but it's, it is interesting that I mean, the same thing is true.
If you're a musician you're very much better at Panenka Jettisons while the musician.
But he's better the the oboe, the violin. And so, you know, there's no single musician who is equally good across the entire slate.
Oh, no, no, no writer. A poet who equally good writing in a large tragedy is more comedies.
Shakespeare got pretty close. And, you know, so people get close.
So this is the real Archimedes Newton.
So they're all very big figures. And in my time, I've got to know quite a lot of mathematicians.
Oh, really? Yes. And it's nice to have them because you get you you learn them, uh, both.
Both the skills and limitations of the human mind. So, uh, well, that's what we do in life.
We learn to live with our limitations and take advantage of our assets.
So as well as being a great mathematician, you became president of the Royal Society.
That was a very different job to do, talking to governments and so on.
So was was that a sort of shock to do that? Did mathematics help you in the in the job?
Well, I'll come clean. I'll tell you exactly.
I was approached. By then President Ross.
I'd say we council decided we'd like to. Oh, but you didn't express it.
I was horrified. It was a good one. I'm not.
I'm not. I had no idea. Reverend Rossetti, you're a real scientist.
And so he said, Well, I'll think about it. So I went back and thought about this.
Talk to my wife, you know, should I take on this job? I'm not I'm not mad.
I'm a scientist, an ordinary mathematician. And I really was very unsure.
And finally, after a lot of hard thinking, I said, perhaps it's my duty to think of my party.
I was influenced by the fact that I'd had all my life.
Fortunately, very early on, I had jobs which allowed me to do my research, which involved a lot of teaching my youth.
But then later on, less and less. And I was really a free man to spend my time doing mathematics.
And I thought, I know. And I by this time I was aged 60.
I thought I'd done my mathematics. Perhaps now it's time for me to repay to society in some other way.
Maybe I. Maybe my days as a creative might be finished. So I take on the job.
They took on the job. There's good sense of public duty because once you take it on, you learn the job.
I learned that running mobilisation, which has its problems and Rosaria was a very old organisation,
had very distinguished people to scientists, but they'd always sometimes mess this up.
And I came to the young radical. I was 60, but so young radical.
And I made a lot of changes. I changed roles.
I mean, in lots of ways. I can tell you privately later on. And I'm glad to see that subsequent presidents that carried on the tradition.
But old institution, you know, lives on in past.
But they had to change the times. I felt the role wasn't changing fast enough.
So I gave you a kick in the pants. That was my contribution.
And after you had done that, did you find it difficult to get back to doing mathematics?
Well, first of all, I didn't do it own. I was simultaneously master of Trinity College, Cambridge.
So I had a double whammy. And so I thought, that's fine.
I'm fully engaged in public service so that that my job as a mathematician, I'm now, you know, good for my duties.
And then I will go in the scrap heap and die quietly.
Unfortunately, things didn't work out like that. When I finished all of this stuff, I said goodbye to all these duties.
Well, what were they going to do? I couldn't possibly keep up with all the young guys who would be doing mathematics in my absence.
So where would I get a new idea? Unfortunately, this is where good fortune strikes you.
I got a letter from my friend Michael Berry, who's a very good physicist.
And when we collaborated, he had John Roberts here. And he said to me, I've come across this following problem in physics.
It is mathematical. It should have solution.
And so he gave me this problem and I found a very good man.
I looked at it worked. Is good problem a solve?
Interesting. I look at it as I looked at it. So what is it, first of all?
Is it true? It is not true. If it's true, it probably state then it is not true.
I looked at it. Nobody done it. There was this beautiful problem sitting around and nobody had done it.
So I was given this free problem. And since and that was my time.
This was 20 years ago. And so over the next ten years or more, I worked on that problem off and on in different ways.
And that's grown and grown. And now that's the centre of my work.
And so it came from responding to a question from a colleague who thought I might be interested and nobody else could contribute.
And yes, that was a gift from God or a gift from Michael Berry.
I mean, God works through an evil, so God has me down.
But now he's a project, he's a problem. And he got mine a very you ask me question and that's how it works.
Yes, that's really true. And I went to Michael Berry, various birthday parties and things, and told him I'd solve this problem.
And it kept me going for 20 years. So you think older people can do mathematics as well as younger people?
Absolutely. I think one of my complaints is that, well, I'll tell you a secret.
Sorry, I have a son, my youngest son.
Some say I told my son good ideas. He said that, look, we all know that mathematicians have their best ideas before they're 40.
You want to get a feel of middle you yet under 40, you're over 80.
It's quite impossible that you have a good idea. If think you've got a good idea, you deluding yourself.
How do I disprove that?
Well, I have been systematically trying to do try to persuade my son that I'm over 80 and I'm not 89, that you can do good stuff.
He's slowly coming around. Maybe I. Maybe I'm right, but not sure yet.
So trying to persuade people that you can good do good work when you're old is extremely hard.
They think you're deleting yourself. And the thought has me alone.
If you look back in history, you'll find that all of great mathematicians or physicists in the later years Einstein then without doubt,
the greatest physicist of the 20th century and famous.
But halfway through his life and done all his fundamental work, people are doing new things.
And he didn't believe in them. He stuck his old roots in the past.
Now he's currently up with the Times. He's passé.
He's old man. You know, he's not keeping up. And so you passed aside, Einstein.
And I think I know a bit about it. I've looked at it.
I think I was right. It was wrong. But they didn't believe him because the old man seems to have drank when he was young.
He had brilliant ideas and was a great man. Nobel Prize five year old one.
He had crazy ideas. So you've gone crazy. Oh, man.
And I think they're actually right. They were wrong.
So is he disregarding what happens with elderly people if they realise they can't keep up the youngsters by running?
You can't keep running the same rate and your 4850 ranks.
But you may have wisdom. You may have instinct.
You may be able to. And you say, well, if I get to contribute now, it's not going to be some trivial calculation.
Anybody can do that. I got to contribute something great.
So you radio stakes, you aim high, and then you tell people, I'm thinking about how you solve the part of the universe.
They say, Oh, you're crazy. But sometimes they're right.
And that's the way old people make big advances.
And the Chinese, like the old people, there's one thing, you know, if you go to China and there was talk before China,
the only thing I like about China or the Orient, they give respect to elderly people.
This is America country for the young, you know, kind of the country with the old.
That's why a lot of Chinese retired to China, because, you know, I think the older and older you get more and more respect.
So finally you disappear under the clouds.
And so I try to end with perhaps I could press you a bit on on something you raised in your lecture about artificial intelligence.
Yes, I remember many years ago, nobody thought that a computer would be able to play good chess.
And now my smartphone can beat me. I trust very easily.
And now computers can check the proofs of theorems and maybe they'll be able to find theorems.
So do you think mathematicians will become redundant now?
No, absolutely not. But for example, chess.
Well, okay. Computer can beat you at chess. But what?
Are you ready? Chess itself. I see.
I mean, we admit the chess society and computers is good getting better, but we lay down the rules.
They just copied us. Okay, that's chess. Remote advancing. Now, you could do much more complicated things.
The same principle. They don't have the imagination do something entirely new, or they have the capacity to do what we do, do much better.
They have the capacity to invent new rules because now computers now will bend new rules, but they will invent rather dull rules.
We won't have the really imaginative ones that go way beyond.
They won't be like Einstein or our Shakespeare or that they will not be like that, because that requires a creative human mind.
And I think the artificial intelligence community has got anywhere near that.
They delude themselves. They are the ones who tell you exist.
So I think and I know the very brilliant man I know by the code, Demis Hassabis,
who runs DeepMind, is the big get the system, which is supported by Google.
And we've done not only report chess but people at go we use a much more difficult game and the is aiming.
I know the Japanese a very brilliant man and he said to me what he's trying to do is to develop machines that
have emotions and you've got a machine as an emotion in principle to be able to tell you this is a good,
beautiful theorem or not.
But I think even that misses the point because we don't understand our own emotions well enough to create a machine that will do something similar.
So I think I'm a firm believer in that the human mind will always be ahead of anything else that's created by machinery.
Well, that's an optimistic note to end with. Thank you very much.
It's been great. I began.