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Question: http://mathoverflow.net/questions/56104/first-two-author-math-paper
Apart from the dubiousness of the topic, my main issue with this question is that it is unverifiable. I've voted to close, and I see that at present there are three outstanding votes to close. The comment thread is long enough to warrant a meta discussion so if anyone thinks that this question should stay open, here's your chance to persuade the rest of us.
That was roughly my thinking too, Andrew, although there may be some historian who has researched this and can offer persuasive evidence that s/he's nailed it. My downvoting suggestion was to downvote everything that's not currently in "first place". (And then there's that bothersome word "important" which threatens to derail the whole thing.)
Andrew, I'm puzzled by your notion of unverifiable and how it applies here. It seems to me that the corpus of mathematics is a definite finite object. Sure, the corpus is evolving, mostly with new stuff but also some occasional discoveries of older materials. I don't think the fact that the corpus is evolving is a valid objection since MO is evolving too. Maybe you think the corpus is too large? I don't think that the fact that the corpus is large is a valid objection since MO is a great place to pool limited observations.
Back to the question itself. I agree with Todd that the word "important" makes the question subjective and hence inappropriate for MO. However, this could be corrected with a simple edit. I also think the question should address the issue of defining the corpus of mathematics, perhaps limiting it to the relevant corpus. (In antiquity, authorship as we know it today was not a major concern so it's probably irrelevant to go that far back.) In summary, I think the question is inappropriate but salvageable.
Perhaps the underlying issue is whether the history of mathematics is off-topic for MO. My personal view here is that the history of mathematics is a perfectly fine topic for MO. However, I suspect that many find some areas of the history of mathematics to be off-topic.
Okay, this is absurd. I edited the "important" part out two hours ago. If there's a question as to what should count as a "paper", I'm happy to clarify. This question isn't any more ambiguous than any other "who first did X", like Notation for a representable functor, or Origin of symbol l for a prime different from a fixed prime. It's possible that the answer is lost in time immemorial, and then the question doesn't have a good answer, but it's no means certain.
There's no reason to vote down other answers, anymore than there's a reason on the notation questions to vote down T's answer on the "Origin of symbol l" question for suggesting that it was Weil, when it goes back to Kummer.
Francois, okay: define the "corpus of mathematics" in such a way that I can practically verify an answer to this question.
Ideally one should also clarify what it means by a published paper. Do you want to count Euclid's elements, much of which being a collection of results proven by other people, as a published paper? Or do you want to arbitrarily restrict your attention only to papers published in the Western notion of a scientific journal, which arised only after the advent of the printing press and more-or-less after the founding of learned societies, with a more modern definition of authorship? In which case, one can do worse than starting from volume 1, issue 1 of the Philosophical Transactions of the Royal Society back in 1665 and go foward until one sees a jointly authored mathematics paper (or perhaps also Hist. Acad. Sci. Berlin...)
I also voted to reopen. I think that the question is interesting, and has attracted interesting and informative answers.
I just took my first look at this question and its answers, and noticed a strange effect of the way voting plays out: the listed papers are in nearly reverse chronological order, exactly the opposite of what should be the case. (Make of that what you will; I'm not interested enough personally to endorse a course of action.)
Andrew,
You seem to be trying to argue that this question is not well defined, and hence is inappropriate. But this is a question about the history of mathematics, which is not just a subfield of mathematics, but also a subfield of history. So mathematical methodology is not necessarily appropriate here.
Of course, using historical methodology, it's perfectly possible to answer the question. Such an answer may turn out to be incorrect in the light of new evidence, and should make a case for its own validity - that the corpora it addresses are the relevant ones, etc. Both of these are perfectly normal features of the practice of history.
As Francois implies, if you think that the history of mathematics is off-topic, you should say so.
My issue with this question is that I don't have a clear definition of what constitutes a math paper. Didier Piau's answer is interesting but it is far from clear to me that a publication that old constitutes a math paper as the term is used nowadays.
Henry, I dispute the contention that "history of mathematics" is a subfield of mathematics. I did not realise that anyone thought so and so thought that the statement "History of mathematics is off-topic" was unnecessary to be said. Since you ask it, I shall say it:
I think that questions on the history of mathematics are off-topic.
While I do not think that the history of mathematics is a subfield of mathematics (I find the proposition slightly funny!) but I surely hope that questions on the history of mathematics are not off-topic.
Of course, were we somehow to be flooded with history questions, things would be degenerate into un-MO-ishness soon,
When I referred to the history of mathematics as a sub-field, of course I was being sloppy. In fact, it's a meta-field of mathematics. In any case, the link is close enough for the arXiv:math advisory committee to include History and Overview in their subject classification.
I'm just glad to have prompted Andrew to admit that his objection derives from a deeper objection to the whole topic of history of mathematics. Todd's, Qiaochu's and Daniel's comments also seem to lean in this direction. I hope we won't need to have this discussion every time a history-of-mathematics question is posted.
Daniel, the sub-optimality of MO as a way to find the answer to the question is not a factor. This is only a symptom of the fact that we have very few mathematical historians on MO. Although we're getting better every day, MO is still sub-optimal to find answers in lots of areas of mathematics. The best way to attract expert users in these areas is to have questions for them to answer!
Henry, your logic is backwards. My objection to this question does not derive from a deeper objection to the whole topic of history of mathematics. Rather, I see that my reason for objecting to this question would apply equally to almost any question on "history of mathematics". My stated reasons for objecting to this question is also my deeper reason for objecting to almost any question of historical nature. Therefore, I feel I can support the statement "Questions about the history of mathematics are off-topic.". As with any sweeping statement, there will be exceptions, but they will be rare. My reasons are:
I hope also that we won't need to have this discussion every time a question failing one of these two tests arises. But to claim that I have some irrational, subconscious fear of "history of mathematics" and that my vote-to-close this question is prompted by that is laughable.
Andrew,
My objection to this question does not derive from a deeper objection to the whole topic of history of mathematics. Rather, I see that my reason for objecting to this question would apply equally to almost any question on "history of mathematics".
You say 'pot-ay-to', I say 'pot-ah-to'.
But to claim that I have some irrational, subconscious fear of "history of mathematics" and that my vote-to-close this question is prompted by that is laughable.
Where did I say that you have any 'irrational, subconscious fear'? To be clear, I take no stand on whether your objection to the topic of history of mathematics is induced from your objection to this question, or whether your objection to this question is restricted from your objection to the topic of the history of mathematics.
My point is merely that arguing about the merits of a bad question in an acceptable field is different from arguing that the whole field is unacceptable. And that if the second point is the one you're really making, then we should be clear that that is what is being discussed.
- Off topic: the skills needed to answer a history of mathematics question reliably are not the same as that of a mathematical question and cannot be assumed to exist in the majority of the user base.
- Not a real question: the skills needed to verify an answer to a history of mathematics question are not the same as that of a mathematical question and similarly cannot be assumed to exist in the majority of the user base.
I'm not sure how these points apply any less to, say, many questions in applied mathematics.
I'm trying to keep an open mind here, but the issue of verification is an important one. How would one decide whether a definitive answer has been given? I think that until we can answer such questions, we're just fishing around here, hence this type of question should be community wiki.
I'm having trouble imagining a historical question that someone would ask on Math Overflow that a historian would have the special skills needed to answer it, but a mathematician would not. If somebody asked a vague question like "How did the needs of Renaissance commerce lead to the rise of symbolic algebra?" then sure, we would be hard-put to judge the accuracy of the answer. But the historical questions here have always been more specific than that.
Alexander has put into words exactly what I was trying to say. Thank you. I find that argument far more compelling than, to paraphrase, "I find it interesting" or "This authority says that they are related".
Andrew,
I find that argument far more compelling than, to paraphrase ... "This authority says that they are related".
Is this a paraphrase of my reference to the arXiv advisory committee and Gil's to the ICM? The point is not an appeal to authority, but rather to provide evidence that the history of mathematics is a part of mainstream mathematical culture, and as such of interest to working mathematicians.
The claim that mathematicians are unlikely to be able to answer history-of-mathematics questions well is just plain wrong - plenty of research mathematicians have worked on the history of mathematics. To take just one example off the top of my head, here's a paper by Cameron Gordon on the history of 3-dimensional topology.
Ha ha, very clever Gerry.
I agree wholeheartedly with KConrad's comment. (And it is not just the invention of calculus that occurred in the period between the ancient Greeks and the mid 18th century; e.g. one has the solution of the cubic by Cardano, the invention of logarithms by Napier, and the invention of analytic geometry by Descartes and Fermat, just to mention three of the best known developments in post-medieval European mathematics predating the invention of calculus.)
On a related note, along with Gil Kalai and others, I hope that interesting history of mathematics questions will continue to appear on MO.
@dan petersen: 1826 is definitely too late. See my comment about about Hist. Acad. Sci. Berlin. It was a regular periodical publishing lots of mathematical results. Euler's original paper about a PDE description of fluids, and D'Alembert's original paper writing down for the first time the linear wave equation (and solving it using the method of characteristics) were both published in it (1757 and 1749, if I remember the years right). Crelle was the first purely mathematical journal, but since the different disciplines of sciences didn't really split until the mid to late 19th century (in Cambridge, the faculty was not organized into Departments until about 1960!), early journals of "natural philosophers" tend to cover every subject under the sun, including, of course mathematics.
Dear Dan,
I don't see that it is necessary to take such a literal view of the question. If someone knows of an early case of a mathematical collaboration that resulted in work that was a book or something similar, rather than a literal paper, I'm sure they will post it; indeed, such an example has already been posted (although it turned out to involve collaboration on translation and editing rather than collaboration on new mathematics).
Regards,
Matthew
@Gil: I don't necessarily regard such concerns as game-breakers either. Nor am I disputing the accuracy of the answers I've seen (leaving aside for the moment the question of what constitutes a 'paper'). But lacking a way of settling on a definitive answer, I still think (repeating myself) that this particular case amounts to a fishing expedition and therefore should be CW. The fact that other history questions were not CW carries no weight for me.
@Alexander: with regard to "With regards to this question: I think in general we should avoid asking questions which are driven by idle curiosity." -- as a general precept, I tend to agree, but probably too high-minded to expect people to go along with very much. If I am honest, I admit to sometimes liking idle-curiosity questions, and sometimes they lead in interesting directions.
Willie: I'd say that Euclid is more analogous to a modern textbook than to a modern paper.
Dear Michael,
My understanding is that Euclid contains many original arguments, and (in that respect alone) is more than a textbook. Perhaps a research monograph is a good comparison?
Regards,
Matthew
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