For the second time recently, someone mentioned to me the Hardy-Littlewood rules for collaboration (and on that very site). From what I read about it, they include the following rule:

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

How is it ethical to be a co-author of a paper you have “not contributed the least bit to”?

I was flummoxed when I read that, it would be considered a serious breach of ethics in the communities I know. Is that a practice (those “rules”) specific to mathematics? Or are they just not used any more?


Generally speaking, this practice would not be acceptable under today's ethical standards.

I don't think these rules represented standard practice even in Hardy and Littlewood's day. They wrote them only to govern their own collaboration; I'm not aware that they ever even suggested that anybody else follow them. The rules are notable because they are unusual (and, as mentioned by Anonymous Mathematician, humorously exaggerated).

If your reputation matches that of Hardy and Littlewood, you may find the academic community (and your institution) willing to tolerate idiosyncracies like this. Otherwise, I wouldn't suggest trying it.

  • 1
    ACtually in mathematics is a common feature that authors are listed in the alphabetic order, regardless of their relative contribution (but I guess in most sane scenarios, rules in-out are similar to other sciences). Nov 9 '12 at 12:06
  • 2
    @Piotr: I think Nate is probably well aware of the author order for mathematical publications. :-) Perhaps you intended your comment to be on the OP? Nov 9 '12 at 16:08
  • @WillieWong It was a supplementary. The answer above may suggest that the Hardy-Littlewood is not followed. Nov 10 '12 at 16:52

I've always interpreted such remarks as meaning that the individual papers were just progress reports on their larger enterprise, to which both made irreplaceable contributions, and that they had no interest in keeping track of moment-by-moment relative contributions.

In particular, "on average", there was no misattribution or false credit.

(Further, the "not contributed the least" may easily be hyperbole, just to make the point.)

For that matter, if one is in regular correspondence with another, how to attribute ideas that develop gradually? I think their solution was entirely reasonable.

  • 19
    Exactly, I always interpreted the "contributed not the least bit" bit partly as humorous exaggeration: if one of them genuinely didn't contribute at all, they would presumably not be willing to be listed as an author, but the rule meant they didn't need to think or worry about relative contributions or try to establish a clear line for an inherently fuzzy decision. It's basically a way of acknowledging that everyone involved thinks the collaboration is valuable enough that they don't want to haggle over the details of the credit. Nov 7 '12 at 19:47

I think the context of the rule is important here. The rules taken together set up a system of trust: that the authors trust each other to contribute fully to the project, and so (as others have pointed out) they didn't have to waste time with the nitty-gritty of specific contributions.

It is not useful therefore to view this rule in isolation as a license to willy-nilly add authors without contributions.


If one takes a superficial look at the authorship issue, it would seem unethical, i.e. one author does not physically contribute to the paper. However, viewing a paper from the perspective of contributorship, which I perceive as wider than the concept of authorship (which focusses on the writing, (see for example examples from ICMJE and BMJ) a more tangible part of the research process), the original described Hardy-Littlewood case is less clear. Since both authors work intimately together, it is clearly conceivable that their joint long-term discussions form a significant background to and lead up to the final publication(s). Hence they have both contributed to the paper even if it has not been explicit. The rules for contributorship set up by the Vancouver Protocol:

  • Substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work; AND
  • Drafting the work or revising it critically for important intellectual content; AND
  • Final approval of the version to be published; AND
  • Agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

may thus not be broken. It sounds as if point two of this list is not clearly enforced but if the last point is fulfilled then it is possible to view the second and third points as implicitly covered.

Clearly the issue of ethics in what I would call a positive case such as this is not easy to deal with. The ethical rules should of course be followed in all cases but it is primarily the negative aspects that need to be scrutinized. If both authors can stand by each paper they are on, I would say all is ok. I should perhaps also mention the consortia papers that emerge from large projects such as the CERN where authorships are bound by contract rather than actual physical contribution. Again, I would see this as a positive form of division of authorship which serves its purpose and although break the Protocol rules is accepted.


As I understand it, the rule is really about uncertainty. If at the time a collaboration is established, it is expected everybody will contribute, then the credit is shared evenly regardless of how the project turned out. This is like when a group of treasure hunters agreeing to share the loot evenly before embarking on a journey. Under this interpretation, adding a new author who's done no work is not accepted, as the author must expect to contribute when he is added.


These H-L rules were but a part of the abuse of Littlewood by Hardy. Littlewood's severe depression was to a significant degree due to this sick Hardy-Littlewood so-called cooperation.

Here are but some examples: https://books.google.com/books?id=WwFMjsym9JwC&pg=PA89&lpg=PA89&dq=hardy-littlewood#v=onepage&q=hardy-littlewood&f=false (this web page doesn't let us "copy & paste"):

In 1931, Littlewood was first to lecture for Hardy-Littlewood class. Hardy came late, had to drink tea, and was pestering Littlewood about unnecessary details, against the Littlewood idea of his talk. Cartwright quoted Littlewood as saying that he was not prepared to be heckled. And Hardy and Littlewood were never seen together at these lectures after the said incident.

  • 3
    [citation needed]
    – Nobody
    Jun 13 '20 at 3:03
  • It is my opinion that Littlewood was badly abused by Hardy. It's known, however, that Littlewood was depressed for long periods of time, already in South Africa. He was very strong in about every possible way except for being, in my opinion, sensitive. The mathematical nonsense in South Africa was not helping Littlewood. Then that "cooperation" with Hardy had to be very hard on Littlewood -- this you can see from several preserved different memories.
    – Wlod AA
    Jun 13 '20 at 8:33
  • In Littlewood's Wiki, I cannot find mention of the abuse. (I understand Wiki is not 100% reliable). You'll need to come up with some reference. There is someone raised a LQP flag on this answer..
    – Nobody
    Jun 13 '20 at 8:52
  • @scaaahu, I don't care about that administrative LQP (whatever it is) or any other such ugliness. I read quite a bit, and whoever can read with open eyes will understand. I lost a lot of my books hence it's hard for me to provide that bunch of references. It's well known that Littlewood was way above Hardy mathematically. Even Hardy's anti-application posturing shows that he was not in Littlewood's class. Archimedes, Euler, Gauss, ... were fond of applications. Applications provide you with advanced mathematical environments.
    – Wlod AA
    Jun 13 '20 at 10:24
  • 2
    Thank you for the reference.
    – Nobody
    Jun 13 '20 at 10:36

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.