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...
Saw this tweet by Matt Parker. It got me a little teary. Rest in piece John Conway.