One thing other sciences can learn from mathematicians

April 14, 2006 11:05 AM

Hardy-Littlewood rules. Hardy's to-do lists are cool too, BTW.
posted by jeffburdges (11 comments total)

The first of them said that, when one wrote to the other, . . ., it was completely indifferent whether what they wrote was right or wrong . . .

I don't get the ,...,

What does ,..., mean?
posted by Afroblanco at 11:21 AM on April 14, 2006

It means the guy who ... typed up the page likes ... dots.
posted by Wolfdog at 11:29 AM on April 14, 2006

And as much as I like Littlewood and Hardy, wikipedia + a blurb is a pretty weak post.
posted by Wolfdog at 11:31 AM on April 14, 2006

Agreed with Wolfdog. Every mathematician who has collaborators should see that list, but nobody else is going to care much.

Attempts to raise the interest level: some other Littlewood quotes, and The Evolution of the Mathematical Research Collaboration Graph.
posted by gleuschk at 11:45 AM on April 14, 2006

I don't get it. But I didn't really understand the Hardy-Littlewood maximal function when I was studying that stuff, either, so I'm probably just out of the loop.
posted by grobstein at 11:55 AM on April 14, 2006

Oh, and the ...'s are there because whoever typed up that page left things out. Here's how it is in my copy of the Miscellany. The quote is from Harald Bohr's Collected Works, specifically from a transcript of a speech he gave at his sixtieth birthday party.

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.

posted by gleuschk at 12:00 PM on April 14, 2006

Am I missing something? What to-do lists?
posted by ijoshua at 12:02 PM on April 14, 2006

The "rules" might have been those followed by the collaborators Lennon and McCartney. Especially the axiom:
"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." Substitute the word "song" for "paper." Clearly, no Yoko Ono ever came between these guys.
posted by Faze at 12:35 PM on April 14, 2006

Littlewood's Miscellany is a hilarious book. He was confident enough to include anecdotes like this:
"Oh, you really exist!" said someone meeting Littlewood for the first time. "I had assumed you were a pseudonym that Hardy put on his weaker papers."
posted by Aknaton at 12:54 PM on April 14, 2006

Hardy's Apology [pdf of text without preface] is a fantastic little essay, as is the longer-than-the-book preface by Snow (taken from Variety of Men) that usually accompanies it. Highly recommended. Also, Inequalities (Hardy-Littlewood-Pólya) is still a fantastic reference for anyone working in basic analysis.
posted by dilettanti at 5:33 PM on April 14, 2006

Hardy's to-do lists are cool too --- Ummm where are they?
posted by BillsR100 at 2:53 PM on April 15, 2006