So welcome to the Royal Society's Centre
for the History of Science.
I'm Uta Frith, and I'm the
Chair of the Library Committee,
and therefore I feel very privileged
also to be part of the events that are
being put on,
and in fact I want to particularly thank
Felicity Henderson,
who probably is still standing outside,
for organising this really fascinating
series of events that happen on a Friday.
And of course, today's speaker,
Graham Farmelo, will be a special treat for us.
I should say that this talk will be podcast,
which has some implications for switching
mobile phones off, that sort of thing.
I'm sure you would do that anyway.
And I'll just say a very few words about Graham.
I have of course, his book here,
which maybe many of you have read
and he will talk to us about Paul Dirac.
It is very interesting that Graham trained
as a theoretical physicist himself,
so he has, of course,
extremely privileged access to the mind of Dirac.
He has been a scientist at the Science Museum.
He has now taken up a Fellowship
at Churchill College, Cambridge
and he spends his summers at
the advanced,
the Institute for Advanced Study in Princeton.
He has become a full-time writer,
because he's obviously immensely gifted as one of
the really new breed of science communicators,
whose books really win prizes,
and of course,
Graham's books have also all got wonderful awards.
So I'm now giving you to Graham Farmelo,
to speak to us about Paul Dirac
and the religion of mathematical beauty.
Thank you very much.
Well thank you for that gracious introduction,
It's a great pleasure to be here
at the Royal Society
- humbling for someone like myself
to talk in this environment.
I'd like to thank Felicity and Peter
for the introduction.
Here he is - Paul Dirac,
arguably the most illustrious scientist
elected to the Fellowship
here in the 20th century.
He is most famous for co-inventing
the most revolutionary theory
of the past 150 years
- the theory of quantum mechanics,
fundamental theory of atoms and molecules,
matter on the very small scale.
His reputation, if anything, has increased
since he did his best work in the '20s and '30s,
and now it's a by-word to hear him referred to
among theoretical physicists
as 'the theoretician's theoretician'
or the first truly modern theoretical physicist.
Around the time this picture was taken,
he was described by CP Snow
as the greatest living Englishman
- a bit of a surprise,
because hardly any English people had actually
heard of him when that was actually said.
But that was the way Dirac wanted it.
His anonymity is the price we pay
for his great modesty and taciturnity.
At the end of his life,
one thing struck me when researching
his biography:
namely, his complete obsession with
the role of mathematical beauty in physics
- the idea that if a theory is
mathematically beautiful,
then that is a candidate for a fundamental theory
of what is going on in nature
at the most fundamental level.
He was also - and this amazed his friend,
Robert Oppenheimer -
fundamentally a geometric thinker.
Oppenheimer, like most other people,
thought of Dirac as an algebraic thinker,
an algebraic practitioner of
steam-hammer power, but that is not how
Dirac saw himself at all.
He saw himself fundamentally as someone who
thought of things in geometrical,
in a spatial way.
Now what I want to do in this talk today
is to look at this abiding obsession
that he had, certainly in his old age,
with this concept of mathematical beauty,
and also take a look at his
extraordinary character.
Those of you who are physicists will know that
part of the rite of passage of any physicist
is to know at least one half-original Dirac story
- a story which illustrates his
extraordinary personality.
As every physicist knows,
Dirac was, in the words of Niels Bohr,
"the strangest man of quantum mechanics"
- someone deeply private, of very, very few words,
rectilinear in thinking, virtually,
apparently devoid of empathy with other,
other human beings, always an outsider.
Here he is - a picture taken in Cambridge
when he was in his pomp,
shortly before he was elected to the Fellowship
of the Royal Society, a year or two before,
and it's not a coincidence -
taken right next to a tree,
because he used to love climbing trees
at lunchtime, in his professorial garb,
in this suit here bought from the Co-op in Bristol
- of course, notably,
2 inches too short in every dimension.
Apart from being an outsider, there were two
characteristics that mark Dirac as different from
the theoreticians who were co-inventing
this revolutionary theory.
First of all, he was very strongly
anti-philosophical.
You wouldn't see him discussing with Niels Bohr,
for example, the philosophical niceties
of quantum mechanics - not interested.
The other point is, he was deeply anti-religious.
His acquaintance, Wolfgang Pauli,
was once heard to say after hearing
an uncharacteristic rant from Dirac
about the concept of God,
Pauli said, "There is no God
and Dirac is his prophet."
So anti-religious and anti-philosopher.
What was most striking to people
who didn't know any physics and just came across
this remarkable man was his extreme taciturnity,
and it was that that he always said in later life
that was caused by his upbringing in Bristol.
He was born in 1902.
This picture was taken shortly before Paul Dirac
went to school - that was in 1907.
Looks like a pretty happy family.
His father is Swiss,
fled an unhappy childhood in Switzerland;
mother from Cornwall;
Dirac's elder brother, Felix,
and his sister, Betty.
Looks like a pretty ordinary family
- in fact, according to Dirac's testimony -
and I won't say that again,
but all of this comes from his own testimony -
it was an appalling childhood.
In fact, he said,
"I never had a childhood."
The reason for that
was that they never
had visitors - almost never had visitors.
In fact his father said,
"We don't need this at all."
They were driven to study the whole time,
and in particular, they had an extraordinary
linguistic regime.
Every mealtime, the family would split into two,
with Dirac and his father in the front room
and his mother and other siblings in the kitchen.
In the kitchen, they'd be speaking only English;
he would speak only French.
He's told a reporter in the 1930s that
when he was a boy, he thought that
men spoke French and women spoke English.
This was not funny to him,
because he saw every mealtime as a trial.
His father, a very strict disciplinarian -
his strategy was to speak only in French
to his children and to punish at the dinner table
any error of any kind with denying the young Dirac
his next wish.
Dirac, from a young age,
had very bad stomach problems,
often needed to be sick - like anybody else,
as a child, he needed to go to the toilet.
He would be denied those wishes.
If that sounds extreme, you go to
the Bodleian Library,
you will see that Dirac's wife
records these disasters - which of course
they would be for a child
- happening every day.
I personally don't believe that,
but that is what she said, and he told her.
One thing he never denied was that
he had a superb education -
just around the corner from their house
in Monk Road, North Bristol, where he was born,
was this school, Bishop Road School
- still stands.
And he had a very good practical education.
Go back and see the school reports -
you can see all the school inspectors said that
all the teachers were very good at
giving the children a balanced,
practical education.
From some testimonies there,
we know that Dirac was exceptionally quiet.
The only thing that would draw him into speech
would be a teacher making an error,
and his hand would shoot up
and it would be politely corrected.
Among the children he didn't speak to
were Cary Grant - Cary Grant,
who lived about 200 yards up the road.
Both Cary Grant and Paul Dirac had
an excellent education in technical drawing.
Now, this is important, because this is where -
in my judgement,
this is where Dirac got his first schooling
in the geometrical way of thinking about things.
Remember, he was doing algebra
and doing geometry at school,
in elementary fashion,
but thanks to the Great Exhibition of 1851,
the school syllabus was changed,
and this syllabus was definitely changed
that way by Sir Henry Cole,
inventor of the Christmas card,
first director of the V and A.
He and others like Lyon Playfair got
technical drawing brought in from the Continent
to chivvy up the school education for boys
- the girls were sent off and told to do
needlework.
So they were split up in those ways,
and Dirac studied technical drawing
- wait for it -
for nine consecutive years.
So he really, really had a very strong education
in depicting things geometrically
- artificial objects like this here,
but also doing the fancy tricks of cycloids
and things that I did at school
and maybe you did too.
So he was doing well at school - not brilliantly,
we're not looking at genius stuff,
but he did increasingly well at junior school
- he kept all his reports.
By 1914, opening of the First World War,
he went to another superb school -
one of the best public-funded schools
in the country -
the Merchant Venturers' Technical College.
There, the most notorious master
was one Charles Dirac,
his father, known as 'Dedder'
- the most notorious disciplinarian in the school,
so you can imagine what it must have been like
for Felix and for Paul in that playground,
to know that their father, who was as I said,
the toughest, but also arguably the most
effective teacher there -
he was teaching modern languages.
Notice - no old-fashioned languages here
- this was a resolutely practically-minded school.
So they did French, they did German,
they did Spanish -
Charles Dirac allegedly learnt a new language
every summer.
This is where Dirac took off.
He did well at the beginning,
and two years into his school education,
he was doing extremely well.
Teachers were having real difficulties
in giving him problems that he could,
that would challenge him.
He was even given by his maths teacher
a textbook on Riemannian geometry
when he was 13 years old,
just to try and keep him occupied.
He said - and this is his own testimony
and I've no reason to disbelieve it -
that even at school, he was 13 years old,
he was going into his bedroom at home
and thinking about the nature of space and time.
This is extraordinary - not unbelievable -
remember, HG Wells was writing about
that kind of thing at that time
- but still remarkable for a boy of that age
to be thinking like that.
He was very close to his brother at that time.
This is Felix - a stouter young boy -
not nearly as clever,
not nearly as clever as Paul Dirac,
but did decently well at school.
His father bullied him,
according to Paul's account,
into not being a doctor,
which is what Felix desperately wanted to do
- I've seen the records that showed
he wanted to join the St John's Ambulance
- and he made him go and study engineering
so that he could get a job.
The Dirac brothers were the children of HG Wells
- people who wanted to get a
- not literally -
but wanted to get a job in engineering.
That was the prevailing philosophy
at the time there.
And Felix here was struggling along in his
engineering degree and his brother followed him.
Paul Dirac followed his brother into
the Merchant Venturers' College,
as it was then called,
and did a degree in engineering,
having seen, as I say,
his father bully his brother into that career.
Dirac is typically remembered,
known as the most austere of thinkers,
the most head-in-the-clouds,
nothing to do with experiment.
This is how he spent his time,
ladies and gentlemen,
as an undergraduate -
he was visiting factories,
he was building model aeroplanes,
he was building cars,
he was learning how to fill in tax forms.
And on 11 March 1919,
standing here looking like,
with a kind of - look at him - look,
he's straight into the camera there,
like James Dean - he was visiting
an automobile factory.
So let's get one thing right -
he was a very practically-minded person,
completely different, as I said,
from the image that he has among most
theoretical physicists.
A few months after this was taken,
in November 1919, Dirac had an epiphany,
and that epiphany was caused by an event
that was stage-managed by some of Britain's
leading astronomers and scientists -
partly at this institution and partly
the Royal Astronomical Society.
They arranged for Einstein to be made
a global superstar - he was already
famous among physicists,
but virtually unknown outside
- and they arranged, at a special meeting
at the Royal Astronomical Society,
to have a Newton vs Einstein,
head-to-head clash over the results of
the recent solar eclipse experiment,
which Einstein would win - and he did.
But overnight,
following an article in 'The Times',
Einstein became an international celebrity.
Eventually, as you may know,
the 'Time' magazine 'Person of the century'.
That was all launched by a campaign as cynical
or hard-bitten - whatever you want to say -
as anything you might see in the media today,
to propel an obvious genius into the place
in public life that he deserved,
after the horrors of the First World War.
Dirac started to read about this
and was entranced - this was a key event,
ladies and gentlemen,
because this is where he found his first love -
not in flesh, but in the equations of physics.
He discovered the concept of theoretical physics -
a new science, only begun in the 1850s in Germany.
He realised that there was this thing that you
could study where you could imagine your way into
the heart of nature through a combination of
mathematics and through interpreting data.
So Dirac started to aspire to this condition
of being a theoretical physicist,
while being a first-rate engineering student
whose only real flaw was his hopeless inability
as an experimenter.
He got his only really terrible report
in a placement at Rugby, at an engineering works,
where he was basically told -
'You're a very smart guy, Paul,
but don't please get a job in a factory.'
It was in Rugby that we learn,
according to Dirac's testimony,
that relations with his brother
had really got terribly bad.
They were actually walking on different sides
of the streets to avoid each other.
We don't know the exact origin of this -
Dirac, Paul Dirac said that he speculated
that his brother was depressed,
having been pushed into the wrong career.
Dirac might not have been the most forthcoming,
loving of brothers - one doesn't know.
But whatever else one says about it,
they were effectively completely separate
human beings, not communicating at the time
that he was in Rugby.
So in 1921, we have the most successful
engineering graduate Britain produced
in the 20th century, with the value of hindsight.
This is Paul Dirac, and he was rewarded with
a certificate of unemployment.
He tried to get a job - I don't think he was
the most exciting interviewee.
Also, it has to be said,
he was being interviewed
at the worst recession this country has seen
until the one we have been in now
- we're probably still in it, actually,
except for the economists that deny it.
But that's how serious this was -
he could not get a job.
And this was the first of these instances
that I want to draw attention to here,
where Dirac had the benefit of a great,
great teacher and a kind person
who came in on his behalf
- and there are several instances like this,
you're going to hear in this talk.
His instructor in the electrical engineering lab,
David Roberts - who used to zoom around
the laboratory in his wheelchair -
saw that the feckless Dirac was doing
these ridiculous stroboscopic experiments
and said, "You don't want to do that."
He got him onto a maths degree and he was able to
freeload on that degree for two years
- that was an extremely wise
and generous thing to do,
and Dirac duly got his degree in mathematics,
so he came equipped with an engineering degree
and a maths degree.
During that maths degree, he met the teacher
he regarded as "the best teacher [he] ever had"
- the name of that teacher was Peter Fraser.
I spent about a month of my life in the course
of writing this book trying to find out things
about Peter Fraser and found nothing.
He didn't produce a single research paper.
All he did in life was to be a teacher,
but he was a brilliant teacher -
and for Dirac to say so, he must have been
damn good.
One thing we know about him,
he was obsessed with one thing -
mathematical beauty.
He taught something called projective geometry,
a type of geometry where,
about lines and planes where
there are very few equations,
in the most elementary books, at least,
and it links completely with the technical drawing
that Dirac had done at school.
In France, they're taught in the same lessons
- or they were, anyway.
Technical drawing and projective geometry
had the same origins by Monge
and people like that in France in the
previous century.
So you have that very, very strong
visual link being brought out there.
So just after this,
you have Dirac coming out now
as a very strong student,
and the person who was pushing him
to move on was his father, his hated father,
quoted from Dirac, many, many times -
loathed and detested his father.
Behind the scenes, his father was trying to
get him to Cambridge, and he did.
In 1923, shortly after his 21st birthday,
the young Paul Dirac joins up
on a PhD course here in Cambridge.
This is St John's College,
which talent-scouted him in Bristol
and got him up there.
Now, Dirac was given a supervisor by the name of
Ralph Fowler - international quality physicist,
but he was actually -
Dirac wanted to study relativity,
he was very miffed about this
- he was put onto quantum theory -
he didn't want to do that,
that was a horrible subject, he thought.
So he's here as a quantum theory student
with a very fine supervisor.
Ralph Fowler was a Henry VIII figure -
big, burly, bone-crushing handshake
- very adept at giving good problems to people
- soluble problems that they could solve.
Dirac started to stand out here.
I'm remind you - he would not have got in
as an undergraduate to Cambridge
- he didn't have Latin or Greek.
He joined this thing and stood out immediately.
Well, the first thing is - what a weird character!
He came there with a maths degree,
an engineering degree from a place whose degrees
were not even recognised - are not even recognised
still officially by Cambridge -
but brought with him a phenomenal performance
in the scholarship exam.
He stood out immediately as a first class student.
He was doing brilliantly up until March 1925 -
five papers, absolute rock-solid certainty
for a PhD.
He walked across on 8 March 1925 the quadrangle
just behind this picture here,
and all that came to an end when he went into his
pigeonhole, opened a letter from his Aunty Nell,
and that letter asked him to brace himself,
because his brother had killed himself.
No record of what Dirac said
- I'll just jump ahead 40 years
and say that Dirac - this is the one topic Dirac
would not discuss with his family.
He apparently was too traumatised to even
show his children a picture of his brother
when they were younger.
Dirac productivity plummeted for several months.
Right out of the blue, when Dirac returned in the
summer of 1925, his grieving family in Bristol -
Ralph Fowler got this paper and sent it,
very generously - it's the only copy of
this paper in Britain - and he sent it to
his most brilliant student, Paul Dirac.
This is the paper - it was, we now know,
the first paper on quantum mechanics.
It was the proof of Heisenberg's paper
on quantum mechanics that -
I want just to say it's very important to
recognise this was not recognised as
a masterpiece then.
Now we know it is, but then,
Dirac looked at this and Dirac said,
"Nature can't be this complicated,"
and put it aside.
If you look at the paper, it contains in there
one statement that Heisenberg made,
that if you have position and momentum
in this new scheme, where you represent
variables according to matrices, not numbers
- what a bizarre thing to do, incidentally -
then the numbers, the order in which you
multiply these things matters -
position x momentum is not the same thing as
momentum x position.
The order matters.
Heisenberg said - 'We'll clear this up.'
Dirac had seen that in his studies of
projective geometry.
He took that single thread and he wove it into
the golden tapestry that became the fundamental
equations of quantum mechanics
- his first great paper, the only paper in early
quantum mechanics you can now read,
and it still reads like a modern paper.
Thus began, ladies and gentlemen,
the longest creative streak,
longest and deepest creative streak
of any theoretical physicist in the 20th century,
apart from Einstein.
Dirac co-invented quantum mechanics
in that streak,
and in the words of the great Freeman Dyson,
Dirac's papers, unlike anyone else in the field,
they were "perfectly carved marble statues
falling from the sky".
You can still read them today.
They still look fresh, they still look accurate,
they still are written in a modern language.
I'm not going to be discussing the details
of the articles - we could spend weeks,
we could have whole summer schools on this
if we wanted to.
I want to concentrate on the themes that
I've outlined earlier on.
But I can't resist saying that he stood out.
Look at this picture.
This was a year or two after he'd got his PhD,
and he visited the centre that he was
competing with as a kind of one-man show
in Cambridge with the might of the mathematicians
and theoretical physicists in Göttingen,
led by Max Born here.
Look at Dirac here.
There's always one - not interested in talking to
the photographer - he's reading a paper.
I fantasise that he was reading about
the thing that he came into contact with
in Göttingen, that would trouble him
for the rest of his life.
One of the things that Dirac had done
a few months before was to relate
the two different types of quantum theory
that were around at the time:
the matrix theory of Heisenberg
and the wave theory of Schrödinger.
He showed how they can be switched from one
to the other.
He called that paper "my darling"
- he loved it, it was his favourite paper.
He then, three weeks later,
co-invented field theory -
the way in which the language of small
fundamental particles are now discussed.
When he did a calculation on the interaction
between an electron and a photon
- it couldn't be a simpler calculation -
he found he got infinity out for the energy
of that system.
And he wrote,
"This is obviously wrong,
but we can get rid of this."
What he'd seen there was the seeds of something,
as I said, that troubled him
for the rest of his life,
and he may just have been reading about that
in this rather evocative picture taken in
Planckstrasse in Göttingen.
The truth is - and we triumphalist physicists
like to think that there are these great people
that do all these majestic things
and they're all heroes and what-have-you
- the truth is that this subject was
being invented by many people
largely at the same time, and Dirac was,
although a pre-eminent mathematician
and an outstanding practitioner,
he was doing stuff that other people were doing
similarly at the same time.
He did - he was outstandingly good,
but he wasn't someone who you'd say
was a mighty figure - until in late 1927,
he did something that some 20 people
of Nobel stature, later of Nobel stature,
were seeking to do.
They took that ordinary quantum theory
and combined it with the special theory
of relativity to produce the first union
between those theories in describing
the electron.
He married those theories and came up with
what we now call the Dirac equation
- the only equation in Westminster Abbey -
you can go and check it yourself if you want,
just down the road.
This equation called by Frank Wilczek
"achingly beautiful", quite rightly.
He had achieved his aim - just like Einstein
had written the achingly beautiful equations
of general relativity,
Dirac was one of the very, very few people
who'd sought to take after
his hero
and done it.
He'd produced a wonderfully rich
mathematical structure that not only
described the electron in the way he wanted,
but explained the recently observed phenomenon
of electron spin and why the electron
has magnetism.
He was the star of the year 1928.
It was seen,
as Heisenberg said to one of his students -
"There's this English guy -
if he tackles a problem, it's not worth
going anywhere near, frankly.
Because he's so smart, it's just not worth
competing with him."
He really had arrived then, was seen as
the leading master of quantum mechanics.
It's very tempting for me now
to go into a kind of operatic aria now
about his great papers,
and there are innumerable great papers
that I could come back and talk about,
one after the other.
But I did want - I just want to mention one thing
that he squeezed out of this equation that will
have his name written in the history of
our species for however long it lasts.
He used this equation to predict the existence of
the anti-electron.
The electron has a certain mass,
it has an electrical charge.
He predicted that there should exist,
on the basis of the beauty of that equation,
a particle has identical mass
but the exact opposite electrical charge.
This was not taken seriously.
His most fervent apostles did not even
mention this in their talks -
I've seen them.
It was regarded as too wild to take any notice of.
But on 2 August 1932,
when the Los Angeles Olympics were being held,
the first example of the anti-electron
was detected at the California Institute
of Technology.
Seven months later - that's how long it took -
2 and 2 were put together to show that Anderson
had detected the first example of anti-matter.
What Dirac had done - and his friend and competitor
Heisenberg said it was probably the biggest
of all steps taken in 20th century physics -
was to open up this world of anti-matter
which, I stress again, he got from not experiment
- there were no clues -
he'd got it from mathematical thinking
that led him to this beautiful equation,
and by taking that equation seriously.
Let me just say one way of looking at this.
Dirac began his life, as I did,
in a terraced house, modest terraced house,
modest family.
Within 27 years of doing that,
he had done something special.
In cosmology, you may know that we now teach
in every classroom, right back to schools,
that the very beginning of the universe,
half of it consisted of anti-matter
- the other half of matter.
So Dirac conceived half the early universe
in his head, from those humble beginnings.
This is the scale of imagination
we're talking about.
But I would say one thing that's very striking -
I've read every single one of his papers
with great pleasure and great profit
- not one of them mentions beauty.
Not one.
He mentions it in a couple of lectures
and in one experimental paper -
yes, he was an experimentalist too -
he wrote papers on experimental physics,
which he did in Rutherford's laboratory
- he does mention it once there,
but not in his papers.
Well, here you have a Fellow of the Royal Society,
Fellow of St John's, Nobel Prize,
salary of £250,000 a year by today's money,
and I think that's pretty much
what he'd get today, isn't it?
All he wanted as a heterosexual man was a woman.
And he got one - or rather, she got him.
This was "Wigner's sister", as he called her.
He met her on 1 October 1934
and then she set about pursuing him
- it's quite clear that that is not
a sexist thing to say -
you can read the correspondence,
six-line letters from him,
24-page letters from her.
Did he write in equations?
No, no equations, but in one of them,
in one she got absolutely furious, saying,
"Well, why don't you answer
any of my questions?"
And he sent her back a table with
an enumerated list of letters,
unanswered questions and answers.
And then he did it again.
This is that extraordinary person.
She used to call him - remember,
we're talking about a serious guy here -
he's almost a religion to people in physics
- but you know what she used to call him?
"My little Mickey Mouse",
because Mickey Mouse was his favourite
film character.
Dirac had two children,
and this is a picture taken in their front garden
in Cambridge with Mary, who died recently,
and this is him reading from 'The Wizard of Oz' -
apparently being murdered now by
Andrew Lloyd Webber,
as we speak in the West End at the moment.
But this is him reading from the book,
and here he's working on a nuclear bomb,
incidentally.
He was working on the neutron flux calculations
in his back garden.
By this time, his falling-out over quantum theory
was so serious, he had come to detest that theory
- the theory of quantum field theory
that I mentioned earlier on.
He was asked at that time by Max Born,
then a refugee physicist with tenure at
the University of Edinburgh,
to give a talk on the philosophical aspects
of physics.
I would have expected Dirac to turn that down,
but in fact he accepted it,
and he gave a talk in February 1939
called 'The relation between mathematics
and physics' - ladies and gentlemen,
it is a complete masterpiece.
How many abstract mathematical variables
are in that paper? None.
You could read it to anyone.
It's got some absolutely gorgeous lines in it,
like - listen to this for a non-fussy,
non-philosophical statement -
"Mathematics is a game where mathematicians
invent the rules. Physics is a game where
the rules are given to us by nature.
What is interesting is that the rules of nature
appear to be in the same mathematical rules
as the mathematicians have concocted."
No fancy words, just complete,
devastating insight, and it goes on
for ten pages.
Absolutely amazing - you can get it on the web.
In this paper, he introduces what he calls
"the principle of mathematical beauty",
which says - it's never actually stated per se
- but the implication is very clear:
that fundamental physics advances
by successively more beautiful theories -
he has now staked his colours to the mast
of beauty as being the criterion.
He thought the thing about quantum field theory
was it was so damned ugly
- it could not be right -
and he lifted that to a criterion in physics,
one that he never turned away from.
He really hated that theory and
hated the ugliness that he saw at its heart,
that offended his aesthetic sensibilities.
After the war,
"quantum field theory was tidied up",
and they are the words used by Richard Feynman,
who with other people tidied up the quantum field
theory of the electron and made it such
that you could always calculate observables
in photons and electrons and move those infinities
away such that they're not part of
the calculation.
Dirac thought that was an abomination,
but it worked.
It won Feynman and others a Nobel Prize.
This picture here is Feynman desperately
and unsuccessfully failing to get
anything out of Dirac.
It was taken in 1962 in Warsaw.
My friend, Freeman Dyson,
who first showed that that theory
was renormalisable,
which means that that process works,
that you can take those infinities and move them
away from the field, so to speak,
so you could always have a finite prediction
- he was, as he put it -
and he described this to me many times -
he was so proud of himself.
He went up to Dirac and said,
"What do you think about the theory of
quantum electrodynamics, Dirac?"
And Dirac looked at him and he said,
"I would like it, if it were not so ugly."
And he said he felt about this big.
Dirac said, and I quote - that for him
"beauty was like a religion".
He simply could not believe that although
that theory was right to one part in a trillion,
if shown to experimenters and verified,
that that was a true, acceptable theory of nature.
It simply was unacceptable.
The year after this picture was taken,
he actually started slumming it
and writing a popular article.
He actually wrote a popular article
- or probably it was written for him -
on the history of theoretical physics
- not an academic history,
but what it focused on - yeah -
was on the concept of beauty
in theoretical physics,
and he came up with a statement,
now widely quoted and intensely irritating
to many experimenters - that it was
"more important to have beauty in one's equations
than to have them agree with experiment".
It's there, written in Dirac's own handwriting,
so to speak, along with the statement -
"God appears to be a mathematician
of a very high order."
Dirac really believed this,
and I want to say this very clearly -
if he saw a theory and it was ugly,
he would dismiss it out of hand,
as his friend Heisenberg found
when in the 1970s, a decade after this,
he sent Dirac his latest theory,
and Dirac wrote in one line -
"Dear Heisenberg, Thank you for sending
your new theory.  I have looked at it.
The equations are so ugly,
it cannot possibly be right."
When Heisenberg got that letter,
he wrote back and basically said,
"Paul, Come on…"
and Paul wrote back and said,
"I'm very serious - it makes no sense
to deal with a theory this ugly."
By 1969, his tenure as the Lucasian Chair
in Cambridge was up, and he moved to
the physics department ranked 83rd in America.
This was at the Florida State University,
where he became the apostle of
mathematical beauty.
He gave some 600 talks all over the world,
actually - right down to Australia,
right across America
- if you look at those talks and the
transcriptions of them, he hardly ever fails
to mention the importance of beauty.
He also lightened up as a human being.
Contrary to the ascetic, etiolated person
that we've been reading about
in previous works of Dirac,
this was someone who used to read John Le Carré,
used to go to classical concerts very regularly
- Mozart, Beethoven -
read Tolstoy's 'War and Peace',
even met, on one occasion, Marlon Brando.
It was not a successful meeting.
He even acquired a television at one point,
because his favourite artist on television
was Cher, and in order to avoid
a mental argument with his wife,
he bought a television so that he could watch her
and Elton John and Sting,
his favourite artists at the time
- so much for Dirac the ascetic.
By the time he was 80,
he felt deeply disillusioned,
because he knew that other people regarded him
as a silly old fuddy-duddy - I'm caricaturing,
but that is an accurate caricature -
someone basically whose rejection of
the modern field theory,
the theory that he created
- they thought this was absolutely absurd.
And when he got back into his home in Florida
from his last visit to Britain in 1982 -
he was 80 years old
- there was a letter from John Wheeler,
Feynman's supervisor, on his doormat
and it's a very touching and generous letter.
I just want to read two lines from it -
"I write to tell you what I'm not sure you divine
- how many of the younger generation as well as
the older one look up to you as a hero,
as a model of how to do things right,
of a passion for rectitude, underlined,
as well as beauty.
May your influence keep on growing."
Well, Dirac was right - people did see him as
a bit of a fuddy-duddy, but they knew that
he was a class act.
And one of the people who knew that
was the greatest mathematical physicist
of our time, Edward Witten,
who met him that summer
- and this is a picture which Edward has
very kindly allowed me to use here,
of him talking to Dirac.
Edward doesn't remember much
of that conversation, except to hear
the great old man execrating
quantum field theory
- the theory that he had - this is Dirac -
co-invented, and I believe he advised Witten -
"Do something different.
Just move on from this awful, awful theory."
Two years after this picture, Dirac died -
spared the prospect of losing his mind,
something that terrified him -
and his very last lecture,
written effectively or dictated on his deathbed,
was about the abomination of quantum field theory.
You can go and visit his grave now
in Roselawn, Tallahassee, buried with his wife,
a dog - not her actual dog,
but the stone dog up there at the top.
We just ought to reflect that Dirac
is one of the truly great thinkers
this country has produced,
and like all people of great and
truly great achievement,
he is posthumously productive.
Still, not just his basic equations of
quantum mechanics,
but his thinking about the way you do
theoretical physics;
his thinking about the magnetic monopole,
something I haven't mentioned,
which people are still,
theoretical physicists are still looking for,
a fundamental in their theories;
in the technical work he did on quantum
field theory, desperately trying to find
what was wrong with it,
still being used today -
you go and Google 'Dirac' in the modern papers
and you still see his name coming up
every single week.
I would say - I know I'm biased,
but I would say that Dirac should be  [INAUDIBLE]
better than any of those people
in quantum mechanics,
although he was so modest he never claimed to
have invented the subject himself.
What he left more than anything
is this legacy of appreciating beauty
and not relying on
'here today, gone tomorrow'
experimental data, but having faith in theories
that might superficially look wrong,
but had greater potential in the longer term,
which is, as you'd know,
the fundamental philosophy that gives
string theory such encouragement,
that although there's not experimental support
for it directly, it has so much
mathematical beauty and richness
that they're minded to keep on the faith
to persevere with it.
They say that Dirac never changed
from when he was a little boy
to when he was an old man
- you look at his signature -
it seemingly never changed.
But in aesthetic terms,
I think that's completely wrong.
He began his life anti-religious
and anti-philosophical,
and he ended his life,
with his thinking on beauty,
as a religious philosopher.
Thank you very much.
