*Concerns of Young Mathematicians* Volume 2 Issue 17 May 4, 1994 An electronically distributed digest for discussions of the issues of concern to mathematicians at the beginning of their careers. PLEASE FORWARD TO ANY POTENTIALLY INTERESTED INDIVIDUALS Please, direct submissions and questions to Curtis Bennett cbennet@andy.bgsu.edu , editor for the month of October. Next issue: Wednesday, May 10 Editor for May: Curtis Bennett cbennet@andy.bgsu.edu Editor for June: To subscribe: Send mail to Charles Yeomans at cyeomans@s.ms.uky.edu Back issues and other information are available via anonymous FTP to ftp.ms.uky.edu, in pub3/mailing.lists/ymn-list. Table of Contents Item # Title ------ ----- 1 Editor's notes 2 Mark Winstead: More employable fields 3 Todd Wilson: Questions on Discussing Research 4 Panel Responses to Discussing Research 5 Response to Questions on Joint Papers 6 Responses to Question on Refereeing 7 Curtis Bennett Graduate Enrollment Survey Response 8 Closing Credits _______________________________________________________________ Item #1 Editor's notes: We have come a long way since the Young Mathematicians Network got started. Much of what we have set out to do we have accomplished, and much remains to be accomplished. On the plus side of the margin, the AMS has passed the ethics in employment resolution, and the MAA and SIAM have started the process of passing similar resolutions. Also, while I still occasionally hear mathematicians talking about the upcoming shortage, they are almost always challenged on the matter. We also have begun to establish some useful files in archives for junior mathematicians. On the down side, we have had little success getting grant proposal files. (We have 3 NSF Postdoc files and 1 general grant proposal). I would like to say what I have found the response by the mathematical community to be very positive. When we started the YMN, I personally was afraid that it would hurt my prospects at achieving tenure or future jobs. Based on the reception the YMN has had so far, I would say this fear was groundless. I also believe the community has shown a great deal of concern for us junior mathematicians. New this issue, is something which I hope will be of use. After having been asked for discussion on issues which I feel I have little knowledge to comment on, we have contacted a "panel" of senior mathematicians who are willing to offer their answers to questions of a mathematical/ethical nature. (See Items 3 - 6.) By no means are these final answers. They are rather a starting place for discourse. In the future, I will be "filtering" questions for the panelists so that no one person is overburdened with questions. Ideally, these are topics you can discuss with colleagues at your own institutions, however, many of us do not have colleagues with whom they feel comfortable having such discussions. Curtis Bennett Bowling Green State University cbennet@andy.bgsu.edu _______________________________________________________________ Item #2 Mark Winstead: More employable fields Last month, some discussion was focused on graduate students. What I want to discuss today has some to do with graduate students, and a lot to do with curiosity. Actually, I guess discuss is not the right word. It appears apparent that of the various specialities in mathematics, those to which the general public and undergraduates can relate to or use "the cutting edge" of more readily are the ones finding favor when it comes to hiring. My evidence at this point is anecdotal; the statistics simply do not exist or are not extensive enough to point out a definite trend. Two trends that one can see do lend credence though. These are 1) Job ads which speak of "some promise of getting consulting work", or ask for applicants in areas which are more likely to get such work, such as biostatistics or simply statistics. (The reasoning for favoring such hires are the possibility of the department taking in some of the money) 2) Job ads which ask for applicants who can involve undergraduates in their research. I think that I personally probably missed out on at least one position because my field, algebraic topology, does not lend itself well to undergraduate research. I ask for the following from CoYM readers: 1) Am I correct? If so, should we, YMN, or we, AMS, or another we be doing something to guide graduate students to more employable specialities? I know one can argue that the cream of the cream will succeed anyway, but what about guiding those who aren't the cream of the crop to more employable specialities? 2) How do we determine these employable specialities? How do we avoid directing too many to a particular speciality? Should we just provide statistics to graduate students, or should those in certain specialities act by refusing to be an advisor to some for reasons of employability? (I know of one algebraic topologist who actively discourages students from choosing him as an advisor for these reasons (no, it is not someone from any university I have been affiliated with)). One can post one's responses to CoYM, or you can write to me and I will summarize the responses. I would like to get a feel for the "employable specialities" by hearing from those who know how things are going in your speciality. For example, from what I can tell, things aren't going well for algebraic topology this year, since some VERY good people still don't have a job for next year. If some of you would, please send me a short report on your field by MR #. For example, for my algebraic topology, I would send to myself 55 seemingly poor I will also summarize these reports. Of course, these reports will be extremely subjective, but should provide a snapshot of what is going on. Mark Winstead winstead@euclid.ucsd.edu _______________________________________________________________ Item #3 Todd Wilson: Questions on Discussing Research I have been reading "Concerns of Young Mathematicians" for some months now, and I haven't seen any discussion of questions I have, as a "young mathematician", on the ethics of mathematical practice. Three examples of the kind of question I have in mind are: 1. How should one discuss preliminary results or research ideas with other researchers? What about the danger of these researchers following up on your idea? 2. Joint papers never have exactly equal contributions by all authors. It seems, therefore, that some authors will have something to gain, while others will have something to lose. To what extent is this true? 3. What should you do if you are refereeing a paper that contains results that you also discovered and were planning to publish, especially when the paper's results are slightly weaker than your own? How generous should an anonymous referee be? Todd Wilson Carnegie Mellon University, Pittsburgh, and Research Institute for Symbolic Computation, Linz, Austria _______________________________________________________________ Item #4 Panel Responses to Discussing Research My view is that in the long run it is much more interesting, and even more profitable, to share, rather than to protect some small piece of turf. 1. How should one discuss preliminary results or research ideas with other researchers? What about the danger of these researchers following up on your idea? Response: The vast majority of mathematicians are scrupulously ethical in such matters. They give credit where it is due, identify sources of problems, any known work previously done, any help given during discussions, etc. Most even avoid, or at least hold back on problems a student is known to be working on, and on problems that are discovered in the course of refereeing a research proposal. So the probability of getting mugged is very small. And if it does happen, then you know to be careful in dealing with THAT person in the future. A slightly different scenario arises, however, because it really is difficult to avoid working on interesting problems that you become aware of. Thus, any thing you make public should be considered fair game. So, if you are very close to solving some problem of general interest, and it is important to you to get individual credit for it, it is OK to be close mouthed for a while. However, it wouldn't be right to let others slave away for a very long time without letting them know what progress you had made. Here are some specific scenarios, and their typical resolutions: Mathematician A has made some progress an a problem, discusses it with others, then mathematician B solves it. (1) If A had most of the solution and B only supplied the final step, then A publishes, crediting the final step to B. (2) If both A and B supplied major portions of the solution, a joint paper is in order. (3) If most of the major work was B's, B publishes and credits A with the origin of the problem and perhaps some portion of the solution. The distinction between (1),(2), and (3) is determined by the parties involved. -- Charles Holland Ideally, one should be able to do as Paul Halmos advises: "Cast your bread upon the waters and see what returns." In plain English: talk to everyone about everything. The benefits accrued are worth the risk. For the most part, this is the course that I steer. However there are certain individuals whom I categorically will not trust. The unwritten rule is that if someone, especially a younger mathematician, comes to you and says "I'm working on so and so" and then asks some questions then you are supposed to leave your hands off his question. If you are a senior guy and a young person approaches you in this way and you know how to do the problem you are supposed to be very gentle. It would be extremely rude and discouraging for the senior guy to say "That's trivial and here is how you do it." Better to say "I think that there are some related ideas in thus and such a place. Have a look." The rules, if there are such, are different when a senior guy says in public "I'm working on so and so and here is where I'm stuck". That, in effect, is to be interpreted as a challenge. If some young turk comes back and says "I have an idea" then the senior guy can say "Let's write a joint paper" or "that's very nice, why don't you submit it to my journal." I'm beating all around the bush here, but the main point is that you can trust most people most of the time, and you'll benefit from being open. But you will learn quickly that there are certain individuals you should stay away from. And "Once burned, twice shy", as they say. -- Steve Krantz (Again, I would like to comment that these answers are a starting point for discussion -- ed.) _______________________________________________________________ Item #5 Response to Questions on Joint Papers 2. Joint papers never have exactly equal contributions by all authors. It seems, therefore, that some authors will have something to gain, while others will have something to lose. To what extent is this true? Response: It is hard to see how anyone loses in a joint paper. No one is forced to be a joint author. It is probably true that the contributions are never equal, in some sense, but it is also true that the paper is uniquely the product of those particular authors - it wouldn't have been the same without any one of them. Most joint-authored mathematical papers list the authors alphabetically, precisely to diffuse the question of who contributed most; and most joint authors won't discuss that question. -- W. Charles Holland Now for joint papers: read what Paul Halmos says in his memoirs. Ideally, once you've started on a joint venture everyone is a co-author until the end. It is a given that no two co-authors will make just the same contribution. What one hopes is that the whole will be greater than the sum of its parts. That is, in the best of situations each author contributes something that the others could not have. Of course situations can and will arise where it is clear that one author is contributing nothing. This can happen even with the best intentions of that errant author. The other author(s) could be leaving him in the dust. The gentlemanly (pardon the sexism) thing to do in that circumstance is for the odd man out to offer to withdraw. At the very least the odd author could work like hell to digest the material and help to write the stuff up. What typically happens is that, without anything being explicitly spoken, this one author hasn't lived up to his part of the contract and no future collaborations will occur. Of course I'm painting an ideal picture here. A lot of nasty fights have been caused by attempted collaborations. I have even witnessed one which involved guns, lawyers, and death threats. But my experience has been almost uniformly favorable. The five percent risk is greatly counterbalanced by the 95% certainty of profitable experience. -- Steve Krantz (Again, I would like to comment that these answers are a starting point for discussion -- ed.) _______________________________________________________________ Item #6 Responses to Question on Refereeing 3. What should you do if you are refereeing a paper that contains results that you also discovered and were planning to publish, especially when the paper's results are slightly weaker than your own? How generous should an anonymous referee be? Response: Have you not yet submitted your results? Then the paper you are looking at has priority and should be accepted. However, if your more general result would substantially improve the paper, you might suggest (through the editor) making it a joint paper, in which case another anonymous referee might be brought in. Acceptance of the proposal is up to the author of the paper you are looking at. Even if your paper were already submitted, a proposal for a joint paper might be in order. Of course, sometimes the methods are so different that publication of both solutions is appropriate. -- W. Charles Holland My philosophy would be this: Case 1: The results are essentially identical, as are the proofs. Subcase a: Your paper has already been accepted by a journal. It's up to your sense of fairness. Either reject the paper on the grounds that the result is known and due to be published in .... or contact the author and offer to add his name as a co-author of your paper. Subcase b: Your paper is at a similar stage of the refereeing process. Contact the author and propose that you resubmit the work as a joint paper to be refereed by a third party. Subcase c: You have not yet submitted your work. Throw yourself on the mercy of the author. Let him know and propose a joint paper. Case 2: Your results are slightly, but only slightly stronger ... or they are the same, but you have a better proof (at least in your judgement). Subcase a as above: Reject the paper: A better result by (your name) will appear shortly in (the journal). Subcase b: Follow either subcase a or subcase c strategy Subcase c: Contact the editor. Ask him or her to contact the author and say: The referee informs me that he recently obtained similar but stronger results. He or she (i.e. you) would be happy to publish this as a joint paper with you. If the author declines the invitation, tell the editor that you recommend against publication on the grounds that you intend to submit a better paper shortly. If the editor wishes to contact another referee, the editor is of course free to do so. Case 3: Your results are significantly better. Reject the paper: Much better results in this vein have been obtained recently by (you) and will appear shortly. [Again, the editor always has the right to overrule you, seek other advice,etc.] -- Ronald Solomon, editor, Proceedings of the AMS (Again, I would like to comment that these answers are a starting point for discussion -- ed.) ______________________________________________________________ Item #7 Curtis Bennett Graduate Enrollment Survey Response Here is a summary of the responses I received to my post to the YMN about cutting graduate enrollment. For each of the respondents I took a couple of the lines outlining their position, with the exception of #6 where I made a summary. I would like to get more responses than I have in hand. As an added comment, since I am a member of the AMS Subcommittee on Employment Issues (or a name meaning the same thing), I am also passing along many of the opinions I am sent to this committee. Thus, if you want your ideas to be heard, it makes sense to let me know them. I will always respect anonymity. 1. IMHO mathematics departments should not attempt to cut back on graduate enrollment unless it's in their strategic interest. I DO think they should be honest about the market 2. Absolutely not. Why discourage people from studying such a beautiful and important subject? What should change is the pervading expectation that everyone in a PhD program is studying to be a professor. (Funding cuts might be another matter) 3. I think that, generally, enrollments should be cut. Each department will have the final say on how or whether it cuts, of course. But I think that departments generally should enroll fewer grad students. If applicants were informed about the math employment problem then enrollments would fall. But most applicants are college students, and we can't expect them to read AMS Notices. 4. I don't think any explicit decisions really need to be made here. The "free market" will probably take care of this problem by itself. To wit, undergraduate math majors will, all by themselves, choose not to pursue a ph.d. in mathematics because they will see how tough the job market is. 5. I think that it is wrong, and can lead to no good as a motive for policy. 6. (Summary) Departments need to give prospective students an honest assessment of the job market. Such warnings need to come from more than one place. Departments may also wand to reduce number of students and redirect some of their teaching load to Ph.D's. 7. I don't think we should cut grad school enrollment. I think that until women and minorities are equally represented at all levels of our profession, these groups are most likely the ones to be cut (either by being discouraged or ill-prepared early-on). _______________________________________________________________ Item #10 Closing Credits The Young Mathematicians' Network is administered by: Charles Yeomans cyeomans@s.ms.uky.edu Mark Winstead winstead@euclid.ucsd.edu Vic Perera vperera@silver.ucs.indiana.edu Franklin Mendivil mendivil@math.gatech.edu Stephen Kennedy kennedy@stolaf.edu Neil Calkin calkin@math.gatech.edu Curtis Bennett cbennet@andy.bgsu.edu Jeff Adams adams@bright.uoregon.edu Edward Aboufadel aboufade@scus1.ctstateu.edu Frank Arlinghaus frank@math.ysu.edu Matt Hudelson hudelson@math.washington.edu _______________________________________________________________ End of Journal -- Next week: The Discussion Continues