I have never really been worried about
whether something was trivial or not.
Well no, that's not true, I was worried.
You know, in my early 20s let's say
people always thought that I would, you
know, be a great mathematician and be
good at various things and so on. And in
my late 20s I hadn't achieved any of the
things that people were predicting. And
so, I call it my black period. I started
to wonder you know whether it was all
nonsense, whether I was not a good
mathematician after all and so on. And
then I made a certain discovery and was
shot into international prominence as a
mathematician. When you become a
prominent mathematician in that sense it
doesn't mean that many people know your
name, it means that many mathematicians
know your name;
and there aren't many mathematicians in
the world anyway you know so it doesn't
count very much; but it suddenly released
me from feeling that I had to live up to
my promise, you know, I had lived up to my
promise. I sort of made a vow to myself
it was so nice not worrying anymore that
I thought I'm not going to worry anymore
ever again. I was going to study whatever
I thought was interesting and not worry
whether this was serious enough; and most
of the time I've kept to that vow.
(Brady: And what has that resulted in for you? What)
(has- has that made you better or more)
(successful or just happier? What's the)
(result of taking that attitude?) - Well it
made me happier, yes, it made me happier is
the only one of those different things. I,
you know, I sit in a corridor in the
mathematics department in Princeton and
I think about things and I imagine that
the young graduate students there
think, oh this guy's a loony, he did
something good once. And I don't care, I
really don't care.
I've been released from worrying about
what other people think about about me
and in a way he did do something
interesting once; you know if I may say
that. And as far as I'm concerned I'm
doing something interesting right now, I
don't mean talking to you, I'm sorry
that's really boring,
forgive me for saying that; but now I I
find some problem, I try and solve it and
I don't care whether it's a problem that
will advance my reputation or not. I mean
I really don't. I've been freed. - (Do you care about)
(advancing knowledge, advancing mathematics?)
Yes I suppose I do but less than I did
before because, you know, I'm pretty old
now and so if I advanced mathematics and
I'm not around to see the result of that
advancement then what do I care? I don't
know. I don't like thinking of my
impending death and, you know, I haven't
got all that many years left, I don't
quite know how many, but I do still like
doing mathematical things so I do. - (Do you)
(ever feel frustration that you won't see)
(where things are going to be in 50 years)
(or the next breakthrough? Do you worry about)
(the things you'll miss?) - Err no I don't
think I do.
I mean, you see, a whole series of things
have happened. You know when I was a kid,
I mean a sort of late teenager and
learnt about all these unsolved problems,
it really did seem - there were about four
of them: there was the four colour map
theorem, there was Fermat's Last Theorem, the
Riemann hypothesis, the Continuum
Hypothesis, okay. And they had all lasted
at least a hundred years and and it
looked as though they were going to last
another few hundred years. And
then they've mostly been solved, in some sense.
Continuum Hypothesis - solved in a way. Four
colour map theorem definitely solved
but
Riemann hypothesis still unsolved - I've
forgotten what the fourth one. - (Was it Fermat or?)
Fermat's solved, yes of course.
So three out of the four were solved - or
should we say two and a half out of the four
because the solution of the continuum
hypothesis is a bit different from the
others but there is a very definite sense
in which it is solved; and that may be
the only sense in which one can live
with it so to speak. But they had all
lasted at least 100 years. Now when
something lasts 100 years you're
unlikely to be in it at the beginning
and at the end of it, that demands
that you're at least a hundred and say
17 years old provided you're pretty
bright at the age of 17.
So essentially nobody is in at the
beginning and the end.
And so we're accustomed really in
mathematics to have these problems that
you don't expect to see solved in your
lifetime.
There's nothing you can do about that,
I mean you can wail and moan and say, you
know, something- I've heard people say
that if if they are granted the thing to
come back in a few hundred years you
know what's the first question you'd ask?
Some of them say 'has the so-and-so
problem been solved?' you know. But really
there's nothing you can do, you can try
desperately to solve it but if it hasn't
been solved for a hundred years you
probably aren't going to, you know, it's
only given to one person so to speak to
solve a particular one of these problems.
So we're used to it, and here's an
atmosphere of resignation you know.
There's also a thing that we don't
really know quite often whether a
problem can be solved. - (I have to ask you)
(then, if you were to- if you come back in)
(a few hundred years and get one question,)
(what's your question then?)
Yeah, interesting.
I- this is not original, I mean, I'd like
to know whether the Reimann hypothesis
had been solved and and so on, perhaps a
few more technical details about it, but
that's not an original thought with me
so- - (Do you have unfinished business? Were)
(there things you would wanted to crack)
(or do that you haven't done? I know)
(you still could do it but do you have)
(unfinished business?) - I don't know that I
have- I mean I have unfinished business
in a way, things I'd like to do, but I'm
not going to do them, I'm not going to solve
them. There's one thing I would really
like to know, yes perhaps if I hark
back to the question you asked a little
bit ago: there's a thing called the
monster group which is a beautiful very
large symmetrical thing and I would just
like to know what it's all about. You
know, why it's there. And every now and
then - I've often said, I've said for 25 or
30 years - that the one thing I'd really
like to know before I die is why the
monster group exists. I'm resigned now to
not learning it before I die - I might
just - every now and then I've taken it
out so to speak, thought about it for a
time; it's about every five years except
I haven't done it for ten. There's never been any kind
of explanation of why it's there; and
it's obviously not there just by
coincidence. It's got too many intriguing
properties for it all to be just an
accident
so- - (And what's that number again?)
196883,
that's the dimension of the space it
lives in. - (It seems so arbitrary.)
Oh no it's not arbitrary. Ooh no it's got to be
196,883, yes
47 times 59 times 71
Nine zeros on the end, so this is
approximately 8 times 10 to the 53. Okay,
that's the size of the monster. This is
pretty difficult, it's quite a difficult
thing to try and explain. - I think of them
as Christmas tree ornaments; you can hang,
you know, sometimes you see a Christmas
tree ornament which has a number of
spikes coming out of it...