Date: Tue, 6 Aug 1996 08:57:35 -0300 (ADT) Subject: a proposal Date: Sun, 4 Aug 1996 21:24:35 -0400 From: Michael Barr Dear Colleagues: There is something that I have been thinking about for a long time that I would like to share with you. This concerns what has happened to publication in the last 50 years, although it possibly continues a trend that has been going on for a long time. I have a habit, when looking up a reference in a journal, of looking at other papers in the same journal to see what people were thinking about at the time. It is astonishing. When I look at the average paper in JPAA, I can make no sense of it in most cases. It is generally ultra-technical and has likely been shortened to the point that only an expert in the subject can read it and not always then. Go back and read a paper from the 40s. From the Annals, or from TAMS. It is amazing, but you will actually be able to read most of them. Many of the authors actually explain clearly what they are dong and why. They go into enough detail that the reader has a chance. It was a different era, of course, but it is amazing to see how technical mathematics has become in just 50 years. There are a number of reasons for this. The pressure to publish is what is ultimately responsible and that has certainly not been entirely bad. Without the possibility of electronic publication, this would even get worse. Electronic journals, like TAC, will help for size per se will no longer be an obstacle. But in the beginning, at least, TAC will not publish expository papers and will be reluctant to publish new proofs too. And given the various pressures by university administrations, untenured people will be loath to spend the time on getting the exposition clear. When I get a paper for TAC, I basically ask myself if the paper would have been publishable in JPAA. I have been an editor of JPAA since it was founded, what, 25 years ago? I hope to remain and editor until it ceases to publish, which I expect in about five years. But in the meantime, I have a fairly good idea of what it publishes and I would like to transfer this quality to TAC. Now imagine you get a paper, say, that takes a known theorem of ring theory and shows that the result depends only on some straightforward categorical property and states and proves that property using an argument that is a direct translation of the ring-theoretic argument. Here is an example: I, and no doubt many others, once observed that the theorem that a von Neumann regular ring has canonical quasi-inverses, unique subject to certain equations has an immediate categorical generalization that applies the category of finite dimensional vector spaces, but it never occurred to me to try to publish it. I assume no one else has either. I think it safe to say that such a paper is not the sort of thing that JPAA would publish. It is a shame really because that is useful insight. Perhaps equally useful is that the same fact is false for strongly von Neumann regular rings. (Actually, the property in question cannot even be stated in a category). Anyway, the point I wanted to make is that we would not want to publish it in TAC, because we must maintain credibility if we are to be in a position to take over gracefully as JPAA loses its subscribers. What we must avoid at all costs is to get a reputation as a place to send your "works of the left hand". Just a few days ago, I was reading a philosopher who imagined that a lot of mathematical publication was concerned with publishing refined proofs on known results. I don't know where he got that idea, but of course it is almost entirely wrong. There is almost no outlet for such material, especially if it is an area of 20th century mathematics, which nearly eliminates the Monthly. There is L'Enseignement Mathematiques and I once made essential use of something published there. But the very name of the journal is a guarantee that deans (and department promotion committees) are not likely to take it seriously. I happen to have sitting on my desk an M.Sc. thesis in math written about 10 years ago by a man who is now a computer scientist. He gives a surprisingly simple proof of the fact that every manifold of class at least C^2 has a simple cover. As it happened, I used this fact in a recent paper. I had to give reference to a classical proof that uses the existence of a Riemannian metric. (You then use small neighbourhoods for your cover.) I would really have liked to have an argument that I understood. But this paper is probably unpublishable, at least in respectable journals, since no matter how nice it is (and several analyst colleagues of mine agree it is very pretty and quite surprising too), the main result is not new. What I think we need is a journal devoted to what I will call explanatory papers. This is not intended to be the same as expository, although expository papers might fit. But new proofs, better proofs, more enlightening proofs, that sort of thing. Generalizations, provided they cast new light, would be welcome, but it would not be intended primarily for new results. I even have a (very) tentative name: Mathematical Insights. If this is too pretentious, it is not cast in concrete. Of course, it would be electronic, under the same regime as TAC. It would not, however, be primarily for category theory but could cover all of mathematics. I post this on the categories bulletin board because that is the one I am on, but I would prefer it to go far and wide. (Since I wrote that someone mentioned to me that that NewAge Celestine Prophecy uses "insight". I cannot let that stop me from using it properly.) Any interest? Michael Date: Tue, 6 Aug 1996 18:56:10 -0300 (ADT) Subject: Re: a proposal Date: Tue, 6 Aug 1996 08:39:32 -0400 From: Peter Freyd I like Mike's proposal. And I would shorten the title to "Insights". When David Buchsbaum became editor of TAMS he announced that he would publish new proofs for old theorems; he would not publish new theorems for old proofs. I gather, though, that Mike is suggesting that occasionaly the later can be a genuine insight. And who, Mike, was the "philosopher"? Date: Tue, 6 Aug 1996 18:57:50 -0300 (ADT) Subject: Re: a proposal Date: Tue, 6 Aug 1996 10:57:29 -0300 (ADT) From: Wendy MacCaull Michael: I think you have an excellent idea. I believe it is important that mathematicians take some time to explain their ideas in such a way that the mathematical community can understand. I suspect that this would enrich us all and provide opportunities for cross-fertilization (I guess interdisciplinary work is the more appropriate word now). Wendy MacCaull Date: Tue, 6 Aug 1996 18:59:14 -0300 (ADT) Subject: Re: a proposal Date: Tue, 6 Aug 1996 08:35:49 -0700 From: Michael J. Healy 206-865-3123 Dear Michael, Your proposed new journal sounds interesting. Having a source that gave, in relatively brief form, the collected results from and overviews of areas of investigation would be wonderful. Often, one needs to read several books and specialized papers to get this---and that only when the material exists. For example, I would like to see some compact papers that discuss categorical logics, such as geometric logic, giving a set of axioms and rules of inference along with a grounding in the model theory and any other machinery useful to a beginner (in my case, to accelerate the learning process so I can apply it). Presently, I find I have to communicate with the people researching the area. While I enjoy doing this, I am feaful of becoming a pest. I have a question in connection with electronic journals that no one has been able to answer so far. What about archival publication? What is the guarantee that an electronic publication will be (1) citable, (2) available 50 years from now? (OK, so there are many questions!) I am citing a paper that appeared in 1943. Thanks, Mike Date: Tue, 6 Aug 1996 19:00:49 -0300 (ADT) Subject: Re: a proposal Date: Tue, 6 Aug 1996 08:58:08 -0700 From: Peter White Dear Mr. Barr Thank you for your thoghtful letter on mathematical publishing. I am not a "mathematician" in the sense that my job is to do research and find new results. I am a "mathematician" in the sense that my job is to bring more mathematics into application, and particular, into application to software. I am particularly interested in category theory for this purpose. I think this makes me a "consumer" of the papers published in mathematics journals. Since I am using category theory, the mathematics I use is not too old. The results of category theory have not been through several generations of mathematicians to refine the concepts in the same way that analysis has. This means that I do have occasion to look at recent articles published in the journals. I would say that articles that show new and better deriviations of known results would be of *primary* interest to me. I think that mathematics is just as much about coming up with proofs as it is about coming up with results. Indeed, no one believes your result until you have a proof. In fact I think a result does not really become part of the mainstream until it has been through a generation or two of refinement and the original proof (probably long) has become a short and elegant proof. Mathematics is as much about elegance as it is about results, and I feel that those who find new proofs are doing original work just as much as those who find new results. As one who applies mathematics, I need to understand the results. For the most part, this means understanding how they were derived - "where they come from". It is possible to apply a body of mathematics when you have a good understanding of most of the material but you skipped the proofs of one or two results that are too lengthy or difficult. It is also possible to understand the main principles of a theory (say integration and differentiation) and then use a large body of technical results without proof (a table of integrals or a table of solutions to differential equations). I think it is _not_ possible to use a body of mathematics by just reading the results and hoping that you understand them well enough that you will not misapply them. To apply the mathematics requires not so much a familiarity with the latest results, as it does a thoorough and deep understanding of the main results of the theory. For example, in category theory, for applications I believe one wants a thorough understanding of limits and colimits, functors and natural transformation, adjoints, toposes, sheaves, probably grothendieck topologies, and I am sure I must have left a few out. In order to understand these concepts it seems to be necessary to know about a couple of domains of application within mathematics, especially abstract algebra and vector spaces. To thoroughly understand this material would mean to have seen the proofs, step by step. Seeing two or three different proofs of the main results would be helpful. In addition, examples and applications of all the main results should be given. The examples and applications should be limited to a narrow sphere, such as basic abstract algebra. It is not useful to be given one example from algebraic geometry, another from topology on 4 manifolds, and a third from harmonic analysis on semi simple lie groups. I know very little about all three of these topics, but I find myself fully capable of understanding category theory. So I say, by all means let us have journals, monthlies, bulletin boards, whatever it takes to get publishing going that addresses new and better proofs, new insights about the connections between two theories AND new applications of the old theories. I think this would - Give students a place to publish results that are useful, but not earthshaking. - Give application people such as me the same thing. - Spread understanding of esoteric topics such as category theory. All of these would eventually lead to more results. Regards Peter White Date: Tue, 6 Aug 1996 19:01:32 -0300 (ADT) Subject: Re: a proposal Date: Tue, 6 Aug 1996 18:08:37 +0100 (BST) From: courtes The ACM publishes Computing Surveys, which contains explanatory papers on a diverse range of computing topics from image processing to unification. Date: Thu, 22 Aug 1996 22:47:25 -0300 (ADT) Subject: Re: a proposal (4 submissions) [Note from moderator: The following are further posts on Michael Barr's proposal. Since the subject is not directly within the topic of this list, further submissions will be forwarded to Michael, and posted to the list in digests like this one. Regards to all, Bob Rosebrugh] ++++++++++++++++++++++++++++ Date: Wed, 7 Aug 1996 10:11:53 -0400 (EDT) From: James Stasheff flash response I thought significiantly new proofs of known results were publishable on paper I would welcome the paper for TAC but having a journal specifically for what Barr describes is an intriguing idea Jim Stasheff jds@math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250 http://www.math.unc.edu/Faculty/jds ++++++++++++++++++++++++++++++++++++++++++++ Date: Wed, 7 Aug 1996 09:55:59 +0100 (BST) From: Adam Eppendahl I find it very irritating that so many useful pictures are drawn when a person speaks on a subject and yet so few of these pictures appear in publication. A good drawing is often like a new proof in that it represents how a person is actually using a particular idea on a daily basis. A journal that accepts new proofs might also encourage such drawings. `Journal of Mathematical Illuminations'? Adam Eppendahl +++++++++++++++++++++++++++++++++++++ >From Reinhard.Boerger@FernUni-Hagen.de Date: Thu, 8 Aug 1996 11:40:26 +0200 From: "Dr. Reinhard B/rger I like Mike`s proposal and I think it would even make sense to publish attempts of proofs that do not work in order that it prevents other people from spending much time on the same attempts. Greetings Reinhard +++++++++++++++++++++++++++++++++++++++++++ Date: Thu, 8 Aug 1996 11:57:10 -0400 From: Michael Barr There was a question raised in connection with my suggestion towards a proposal about archiving. There are a number of answers. First off, TAC is being archived by both the Canadian Math. Soc. and some government organization. In addition to Mt. Alison U. What I would like to see is some libraries print and bind each volume. My faith that this will happen is not increased by what I heard about one university library. They are planning, for some journals, that they will receive and shelve the paper copy and then, at the end of the year, when the online volume is available, discard it! I have referred, in recent papers, to papers that appeared in 1944 and 1945 and a book (Lefschetz's Algebraic Topology) from the 30s. I do not have the same faith the librarian does that a 1990s electronic archive will still be usable in 50 years, but that problem is not one for electronic journals alone. Michael +++++++++++++++++++++++++++++++++++++++++++ Date: Fri, 16 Aug 1996 12:49:44 -0400 (EDT) From: F William Lawvere Dear Mike I am strongly in favor of your proposal. Such a journal can begin to solve a very major problem which existing institutions are scarcely addressing. We must end the standard whereby "expository" articles do not EXPLAIN. Bill Lawvere Date: Tue, 27 Aug 1996 10:21:04 -0300 (ADT) Subject: re: a proposal (3 submissions) Date: Thu, 22 Aug 1996 23:34:24 -0300 From: RJ Wood Dear Michael I am also strongly in favour of `Insights' but I think that those insights that come from our community using categorical ideas should be published in TAC. The fact is that genuine insights are far rarer than publishable technical papers. If TAC also publishes the kind of papers that you spoke of it won't put the journal below JPAA but rather {\em above} it by true scientific criteria. If TAC had a policy of dubbing certain papers as `Insight' papers it would probably confer extra prestige upon them. Why make it necessary to read yet another journal? With the change in medium we have an opportunity for reform. We have a favoured moment in history to rewrite some of the rules and tell the dean set what is important rather than waiting to receive our next set of instructions from them. We also have demography on our side. Many of us have little to lose by putting a bit on the line and that could make things a lot healthier for the next generation of category theorists. RJ +++++++++++++++++++++++++++++++++++++++++++++++++++ Date: Fri, 23 Aug 1996 15:21:01 +0100 From: "Prof R. Brown" Subject: (i) new proofs (ii) Archiving of electronic journals (i) New proofs I had a paper accepted in which the referee wrote t hat the theorem was not new, the proof was not new, but the paper should be accepted, as the originals were notorious! (ii) Archiving I am glad the idea has been put forward of paper archiving of electronic journals, in addition of course to other methods. This would help for authenticity, archiving, and for prospective authors to get a quick idea of what is in the journals. Journals on shelves have advantages over electronic media in some respects, as well as disadvantages. It could be useful to ask libraries to make a small subscription to pay for a well produced cover for a full volume, to be bound in with it, which would also confirm authenticity of the papers. Of course, electronic journals may in the end include more than can easily be put on paper, but this proposal would ensure some of the advantages of paper journals without the currently increasingly prohibitive cost (which includes keeping publishers staff and offices in good order, but based on free service by academics). For example, current technology would allow easy printing of colour where required in a paper archive of an electronic journal, and could include reference to access for further electronic facilities (e.g. animation). Ronnie Brown Prof R. Brown School of Mathematics Dean St University of Wales Bangor Gwynedd LL57 1UT UK Tel: (direct) +44 1248 382474 (office) +44 1248 382475 Fax: +44 1248 355881 email: mas010@bangor.ac.uk wwweb: http://www.bangor.ac.uk/~mas010/home.html wwweb for maths: http: //www.bangor.ac.uk/ma wwweb for `Symbolic Sculptures and Mathematics': http://www.bangor.ac.uk/~mas007/welcome.html +++++++++++++++++++++++++++++++++++ Date: Sun, 25 Aug 1996 16:52:25 -0400 (EDT) From: James Stasheff Subject: pictures In response to Eppendahl's response to Barr's sugestion of a new type or journal or at least article, fortunately drawing capabilities in xy fig or latex or... are becoming so user friendly that even I have attempted a few so hopefully more and more pictures will make it from the blackboard to the publication - electronic or print. Jim Stasheff jds@math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250 http://www.math.unc.edu/Faculty/jds May 15 - August 15: 146 Woodland Dr Lansdale PA 19446 (215)822-6707