Dyson and Montgomery's fortuitous meeting over tea

Hugh Montgomery: "[Indian number theorist Daman Chowla] said, 'Have you met Dyson?' and I said, 'No,' and he said, 'I'll take you and introduce you to Dyson,' and I said 'No, no, that's OK, I don't need to meet Dyson.' This went back and forth and it ended up with Chowla dragging me across the room. I didn't really want to bother [Dyson]. I didn't think of having anything useful to say to him, but when Chowla introduced me Dyson was very cordial and asked me what I'd been working on, and so I told him that I'd been looking at the zeros of the zeta function."

It was when Montgomery mentioned the formula he had found for this distribution that Dyson's ears pricked up. At the mention of 1 - [(sin pi*u)/(pi*u)]2, Dyson said something like, 'Well, that's the density of the pair correlation of eigenvalues of random matrices in the Gaussian Unitary Ensemble.'

"I'd never heard any of these terms before," Montgomery went on. "I don't know exactly what his words were because I have heard all of these terms many times since, but he said 'pair correlation' and something resembling 'random matrices'..."

What Dyson had spotted was a connection between two apparently unconnected fields of knowledge - quantum physics and number theory. It turned out that physicists looking for ways to characterize the behaviour of atomic particles had come up with a formula that was very similar to Montgomery's description of the zeros of the Riemann zeta function.

...I asked Montgomery whether he'd done much up to that point with the mathematical entities mentioned by Dyson, known as random matrices, "I'd never seen a random matrix," he said. "I've hardly seen one since". Furthermore, for Freeman Dyson, this teatime exchange seems to have been just a momentary diversion from his own very different line of study.

"As far as I know," Montgomery said, "he didn't think about it after this five-minute conversation. I haven't spoken with him since, so I've had one conversation with him in my life. But it was quite a fruitful conversation. It was serendipity that it happened just at the right moment, because I had this result and what was needed was the connection, and he provided the connection. But it didn't alter the mathematics, it altered our understanding of what the mathematics was related to. I suppose that by now somebody [else] would have seen the connection...it's nearly thirty years ago. But it certainly was, from the standpoint of publication, instantaneous. I had the mathematics and as soon as I had it, it was just a matter of months before the connection was pointed out."

From that conversation has come a whole new approach to the Riemann Hypothesis, and the possibility that in some quite significant way the quantum universe behaves as if it is driven by the location of the Riemann zeta function zeros."

From K. Sabbagh, Dr. Riemann's Zeros (Atlantic, 2002), p.134-136


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