The Riemann Hypothesis has been around a long
time, and I come along saying I can prove it, and of course nobody believes a word of
it – old man etc. And you can read yesterday’s Times and there’s a big article about me
which I’m rather cross about, but it says more or less ‘crazy old man thinks he’s
solved the Riemann Hypothesis ha ha ha’, but not quite as badly as that, but in Times
speak. And the point is I have solved it, so I’m certain as certain can be that I’ve
got this problem fully tied up here and moreover, unlike people searching, I wasn’t even looking
for the problem, I was trying to do something different.
That’s exactly what I was going to ask, where was that moment when you realized that
your work could, because you were looking at the…
The Fine-Structure Constant – a fundamental problem in physics.
So how did you go from that and suddenly think ‘ooh this could work with Riemann’? How
did that happen? Well it’s a complicated story, of course
I did actually say something about the Riemann Hypothesis a few years back. But what I said
then, it’s still true what I think now, which is (a). I can prove the Riemann Hypothesis
and (b). the Riemann Hypothesis is not true. Now that seems contradictory but if you know
your Godel it’s not. It means you can prove the Riemann Hypothesis with a certain set
of axioms, and with more axioms you can prove another Riemann Hypothesis, but you can’t
prove all of them all of the time. Eventually God says ‘ne plus ultra’ – you’ve reached
the end of the road, you can’t get there, the Riemann Hypothesis is out of bounds. And
that’s the real story. But on the way, I proved the Riemann Hypothesis except I proved
it upside down, people usually want to wait until they’ve got the end of the road and
look back and tell all of the Riemann Hypothesis’ they could have done. I start at the beginning
of the road, I choose the first Riemann Hypothesis I come to, the one that Riemann came to and
I solved it. Okay, what’s the great big deal? There are still many more Riemann Hypothesis
in front, the next road there’ll be another one – a more general one, and another more
general one – I’ll take them one at a time.
So that’s your plan you’re going to go for the other ones?
I think after a while I’ll hand them over to the youngsters. I’ve done the first few
, you see how it goes , just carry it on in the same way – and more or less that’s
correct – so yes, the first step is the one that counts – there’s a good French phrase
for that ‘la premiere etape qui compte’ so the first step is actually, you know, the
most dramatic step you take. So, you gave this outline of the proof in
your lecture and then are you – I assume you’re planning to sort of write this up fully or
is it already available the full proof or will this be coming over the next few weeks?
The full proof is available in the following sense – you read my short paper which is
only 5 pages. I read it this morning yes.
And you read my paper on the Fine-Structure Constant which is about 15 pages. Those between
them contain the whole proof. Okay.
Now you may not be smart enough to understand that and most people say “I don’t follow
it at all”, but it’s there, but I’m going to write another paper. But that will
be the best proof and I will say look if Riemann were here now, I would say “look – yes of
course, I knew it all the time, what’s all the fuss about?”