Freeman Dyson y el teorema de Littlewood

La página Web of Stories tiene una extensa entrevista con Freeman Dyson, dividida en más de 150 videos. En particular recomiendo los de su vida académica en Cambridge y su relación con Besicovitch, Hardy y Littlewood.

En el video no. 26, discute cómo utilizó las ideas de la demostración del famoso teorema de Littlewood, sobre convergencia de series, en su construcción de ferromagnetos.

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[…] So that was the big Tauberian theorem which Littlewood proved, and this way of proving it was again a tour de force done by invoking a completely unmotivated new parameter which turned out to be the key to the proof.

And then in my existence as a physicist one of the things I did was to prove the existence of a ferromagnet in one dimension, which was something that hadn’t been done before, and I constructed this ferromagnet – this was a very “Besicovitchy”, a sort of Besicovitch construction of the ferromagnet as a hierarchical array of spins[…]

And then, in order to prove the long range order – what I proved was that the long range order is discontinuous at the transition, that it goes discontinuously from having a spontaneous magnetisation to being disordered[…] And to prove that, I used Littlewood’s trick of bringing a unmotivated new parameter – so it was a proof; although the construction was Besicovitch, the proof was Littlewood.

Anyway, so I dedicated this paper to him and it was written just, I think, sixty years after Littlewood’s proof had been published and so I dedicated it to the sixtieth anniversary of Littlewood’s proof. And I got a very nice letter from Littlewood in response, saying that as far as he knew that was the only time that a mathematician had actually celebrated the sixtieth anniversary of a proof.

Mañana o el miércoles publicaré un artículo sobre Littlewood y su teorema tauberiano.


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