To illustrate to what extent Hardy and Littlewood in the course of years came to be considered as the leaders of recent English mathematical research, I may report what an excellent colleague once jokingly said: `Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and Hardy-Littlewood.' The last refers to the marvellous collaboration through the years between these two equally outstanding scientists with their very different personalities. This cooperation was to lead to such great results and to the creation of entirely new methods, not least in the theory of numbers, that to the uninitiated, they almost seemed to have fused into one. To illustrate the strong feelings of independence which, as a part of the old traditions, are so characteristic of the English spirit, I should like to tell how Hardy and Littlewood, when they planned and began their far-reaching and intensive team work, still had some misgivings about it because they feared that it might encroach on their personal freedom, so vitally important to them. Therefore, as a safety measure, (it was, as usual when they work out something together, Hardy who did the writing), they amused themselves by formulating some so-called `axioms' for their mutual collaboration. There were in all four such axioms. The first of them said that, when one wrote to the other (they often preferred to exchange thoughts in writing rather than orally), it was completely indifferent whether what they wrote was right or wrong. As Hardy put it, otherwise they could not write completely as they pleased, but would have to feel a certain responsibility thereby. The second axiom was to the effect that, when one received a letter from the other, he was under no obligation whatsoever to read it, let alone to answer it, -- because, as they said, it might be that the recipient of the letter would prefer not to work at that particular time, or perhaps that he was just then interested in other problems. And they really observed this axiom to the fullest extent. When Hardy once stayed with me in Copenhagen, thick mathematical letters arrived daily from Littlewood, who was obviously very much in the mood for work, and I have seen Hardy calmly throw the letters into a corner of the room, saying: `I suppose I shall want to read them some day.' The third axiom was to the effect that, although it did not really matter if they both thought about the same detail, still, it was preferable that they should not do so. And, finally, the fourth, and perhaps most important axiom, stated that it was quite indifferent if one of them had not contributed the least bit to the contents of a paper under their common name; otherwise there would constantly arise quarrels and difficulties in that now one, and now the other, would oppose being named co-author. I think on may safely say that seldom -- or never -- was such an important and harmonious collaboration founded on such apparently negative axioms.
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