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Appendix B Final Report of the American Mathematical Society's Committee on Information Exchange and Publication in Mathematics I. The original charge to this committee was to ask the right questions about communications in mathematics, questions whose answers would provide the information necessary for deciding on future action by mathematics organizations. There was some indica- tion that if such questions could be pinpointed, then the NSF might be willing to help in getting the answers. It turned out that the concrete implementation of this would probably mean conducting a large survey of mathematicians, mainly in the form of question- naires. It turned out further that the NSF was not in a position to offer any help except to comment on professional survey organiza- tions which might be able to conduct such a survey. After considering this matter for many months, and after informal contact with two of the most reputable academic-type survey organ- izations (The Survey Research Center at the University of Chicago, for one), we concluded that a large survey would be a waste of energy and would Provide much more irritation to the mathematicians ' 1- questioned than it would provide sound information to the ques- tioners. Such a survey could, at most, tell what is happening now, but it is more likely to tell what people think is happening now; the results of such a survey are too easily rigged by the selection of the questions or the persons questioned; in short, the survey idea seemed a poor basis for future action. Furthermore, there have been numer- ous studies of information exchange in various sciences in recent years [see The Flow of (Behavioral) Science Information A Review ~ Reproduced by permission. 233

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234 Appendixes of the Research Library, by William J. Paisley, Institute for Com- munication Research, Stanford University, November 1965, which lists at least 29 studies between 1948 and 1965] and all these studies seem to come to much the same conclusions as we would have pre- dicted on the basis of "pure thought." The proposal to abandon the idea of a survey seems to have met with the approval of all parties involved in setting up the original charge to this committee. We therefore recommend that the American Mathematical Society set up a permanent committee to monitor problems of com- munication: that this committee should experiment with nilot projects In (hopefully) improved modes of communication if such projects are approved by the AMS and other societies concerned; and that the results of these experiments be carefully assessed after a suitable trial period. This committee should have some members representing the more applied areas of mathematics and it should work in close liaison with the other mathematical organizations, including CBMS. We have spelled out below some of the relevant ~ ~ ~ be followed up immediately. pecl~cally, we feel that the Tnform~tic~n tinter H~crriL`~H in Part II, the repository in Part III, and the Proposal for Writing Panels in Applied Mathematics in Part V are especially worthy of Present attention. areas anct some projects we think could ~ . ~ ~ . ~ . A _ ~ _ ~ ,, ~ ~ ~ ~^ ~ ~ ~ ~ ~ . ~ ~ By, ~ 1 ~ ---~ _ ~ ~ II. Prepublication services. The present methods of journal publi- cation are threatening to become unmanageable as the number of journals and the number of papers increases. The years 1950-1965 have already seen an increase of about 250 percent in the number of pages and the number of papers published. Judging from the numbers of new PhD's in mathematics, this rate of growth is not likely to decrease. Our committee did not feel that making these results available with great speed was of primary importance. Our present time lag in publication of from one to two years is much too long, but decreasing this is not a primary problem. Suggestions for avoiding the avalanche which seems to be coming should aim to make any one piece of research more readily visible to those who need it, and to make it easily accessible. After all, each mathe- matician has only a finite amount of time and energy to devote to learning new results and it is most important to help him use this time effectively. It is standard practice now to communicate results of research before publication. Many organizations have tried to formalize

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A ppenclixes 235 this system of preprints. The National Institutes of Health organ- ized nine Information Exchange Groups in various aspects of biology; each group consisted of from 100 to 1500 research person- nel, each of whom automatically received all preprints submitted by other members of his group. These groups have recently been discontinued by the NIH, though they hope other organizations will continue the system See Science, 154, 843 (18 November 1966~. One of the American Chemical Society's applied journals, Indus- trial and Engineering Chemistry, has been publishing 50-word ab- stracts of all papers being refereed and will sell copies of the manu- scripts to anyone who is interested. The AMS has considered publishing lists of titles of all forthcoming papers. The Category Information Centre has recently been organized to distribute infor- mation on the whereabouts of mathematicians interested in category theory, and on the results they prove. The actual functioning of . ~ t llS OrgaIllZatlOn IS not yet clear to us. Our committee suggests that such semiformal prepublication communication is worthwhile and should be encouraged. It is prob- ably better to have some organization handling preprints than to depend on each author's private distribution lists as at present. It is not clear what encouragement the Category Information Centre (centered in Prague) would desire, but similar centers might be organized in one or more other fields of mathematics, for example, in numerical solutions of partial differential equations, or in differential topology, or in operator theory (Hilbert space), or in set theory. Such a center might be restricted to distributing biblio- graphical information or it might actually sell copies of manu- scripts which are submitted to it. We doubt that the automatic distribution (as in NTH'S lEG'S) iS worthwhile for papers which have not yet been refereed. It is also important to be sure that all this transitory material eventually disappears. Correct bibliographical references should be made available to all participants when a pre- print is published. The experience of Industrial and Engineering Chemistry is that distributing copies of the manuscript is rather expensive, but it is conceivable that it could be automated if the demand were great enough. If such centers are set up, they will have to be reviewed periodically in some objective way to see if they are, in fact, improving the communication among mathematicians. III. Modes of publication. Publication of research articles will probably have to be changed in some manner or other eventually.

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236 A ppend ix es Our committee kept returning to the suggestion that some journal, for example the Bulletin or the Proceedings of the American Mathe- matical Society, be devoted exclusively to publication of two-page abstracts of papers, after these abstracts have been refereed by a competent mathematician who has access to the full text of the manuscript. Some central repository would collect these manuscripts. Any interested mathematician could receive a copy of the full manu- script by requesting it from this repository. It should be made extremely easy to submit such requests. In fact, eventually this might be done by punching a few buttons on an electronic console which will then produce a hard copy of the manuscript a few minutes later. However, at present the mails are probably still adequate. For example, as a privilege of his subscription, a mathe- matician might receive a number of coupons which could be torn off and mailed to the repository, thereby automatically requesting a specific article. Publication of such an abstract would count as publication, since the paper is refereed and available in full to interested readers with reasonable ease. To implement such a scheme, it would be important to raise standards of publication in all other journals. This might be easier than merely raising stan- dards a little bit. More journals could then devote much space to survey articles at a very high level, supplementing the present activities of the Bulletin. Aside from provision for such survey articles, the American Mathematical Society could drastically cut the page allotments in its present journals and might well enlist the cooperation of most other American journals. If this results in a major overflow into foreign journals, they might also be tempted to join in such a program of publication by abstract. Presumably both the by-title abstracts in the Notices and the research announcements in the Bulletin could then be eliminated; perhaps all the abstracts could go. This is an ambitious scheme, but with support from the NSF tO help temporarily in the reproduction and distribution costs, it might even work for a long enough time to determine whether it could serve the needs of mathematics. On a smaller scale, the MAA iS toying with the idea of changing the Monthly in part to a collection of abstracts. Cooperation and observation here might also be in order. An alternative to this repository scheme is the publication of a journal of abstracts with the total manuscript reduced to micro

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A ppendixes 237 fiche possibly even accompanying the journal. The Mathematics of Computation is now considering a microfiche supplement to their journal which might include the texts of tables reviewed in the journal or other extensions of the printed text. It would be inter- esting to cooperate in this experiment and assess the results after about two years. IV. Retrieval. We should take advantage of experiments in infor- mation retrieval now being tried in mathematics and other dis- ciplines and assess their relevance and value to mathematics as a whole. Among such experiments we should list the following: 1. Citation Index. This associates to each published paper all the subsequent papers which refer to it in their bibliographies. Such a citation index is being constructed at UCLA for current mathematics and another is being constructed by Tukey and others for past and present probability and statistics. 2. Permuted Index. This type of index is most easily described by the sample page (shown in Figure B1) from an index of the approximately 1500 papers appearing in the Transactions of the American Mathematical Society from Volume 86 (1956) to Volume 104 (1962~. The left-hand column gives the date and a code for the author's name (this code is translated in a separate index). The second and third columns are the standard volume and page refer- ences, and the rest consists of titles arranged alphabetically accord- ing to one word of the title. Apparently each title is indexed under each word in it except for prepositions and conjunctions. The Permuted Index for the Transactions, including a chronological list of papers and the author index is a pile of standard IBM sheets about 3/~ inch thick (if you don't squeeze too hard). Apparently the Association for Computing Machinery publishes such a permuted index to Computing Reviews at about three-year intervals. Pre- sumably Aaron Feineman at Stony Brook knows most about its ef3 activeness. 3. The MAC Technical Information project at MIT includes a combination of Permuted Index and a Citation Index stored in a computer so that the retrieval of the information (title, author or citation) is done by machine. 4. Mathematical Reviews sub ject ind ex. 5. The volume of reviews in differential topology which the AMS iS now preparing under the direction of Steenrod.

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Appendixes 239 6. Special Classification. This would index published papers not only according to title, but according to specified aspects of their contents. For example, Dorothy Bernstein, presently at Brown, maintains an index on partial differential equations which lists for each review of a paper on partial differential equations the order, number of unknowns, number of independent variables, type (elliptical, hyperbolic, linear, etc.), and type of problem (Cauchy, Dirichlet, etch. 'I'his kind of index, as well as a Permuted Index might be a by-product of the automation of record keeping in Mathematical Reviews. All such indexes should preferably be available in machine- readable form. V. The problem of communication between mathematics and other fields is deserving of more effort than it now receives. There are already special meetings on applied mathematics and applica- tions of mathematics. These meetings should be expanded and their existence should be better publicized among the users of mathematics. Next summer's meeting at Seattle on Relative Differ- ential Geometry, Generalized Abelian Integrals, etc., is one sample Another is a meeting that will take place at csu this spring on C~-Algebras. About one third of the people attending this confer ence are expected to be physicists. The AMS conferences on applied ~ . _ mathematics are more examples. It probably would be wise to en- courage such meetings not only in mathematical physics, but in mathematical economics and other applications. A second channel for communicating mathematics to researchers in other fields is the writing of expository articles or expository texts. Such expository writing must be done at a level which is sufficiently unspecialized that it can be read by nonmathematicians. This might well have a corollary advantage of producing texts which will be of use to graduate students. We propose that the president of the AMS appoint a new committee to locate areas of mathematics which would be of maximum use to physicists (e.g., Lie groups), and to organize a writing panel of mathematicians and physicists to produce suitable expository material in this area. In the above sentence "physics" and "physicists" can be changed to "economics" and "economists" or to other disciplines at the dis- cretion of the committee.

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240 A ppendixes VI. More expository books are in order inside mathematics. These probably can be successfully commissioned and should be valuable to mathematicians in fields adjacent to that of the book, as well as to graduate students. VII. In mathematics it seems clear that face-to-face communica- tion is at least as important as any other one kind. A large amount of mathematical research typically is done by discussion among a small group of mathematicians of some tentative ideas proposed by one or more members of the group. Such a small group has much more knowledge of relevant results which have been recently proved than any one researcher working alone. Therefore, we commend the great efforts expended by various mathematical organizations in organizing meetings of all kinds. and we commend the ~rnment ~1_ _ _ 1_ 1_ _ _ ~ ~ ~ ~- 5~ ~ ~4 In-1~ agencies wn~cn nave made possible travel to such meetings and to smaller conferences. Up to now, the mathematical community has not taken kindly to the telephone as a substitute for personal meet- ings and it seems unlikely that adding a visual component to the telephone will make it much more acceptable. In this context, too, some experimentation is in order. For ex- ample: Devote half of some national meeting to a more closely planned, more detailed set of lectures; for example, a series of lec- tures whose texts are available beforehand, with discussion con- ducted by formally appointed persons who are acquainted with the text. 2. Schedule discussion-only sessions where papers are submitted and abstracts included in the program. The author would be avail- able in a room for "argument." Several related papers could be scheduled in the same room with a discussion leader to chair the program. This is a possible substitute for 10-minute papers. It has been tried by the American Federation of Information Processing Societies. 3. Schedule a lecture on an important published paper by an expert in the field, not the author of the paper (in the style of the Fields Medal lecture at the International Congress). 4. Run a more extensive program in connection with the 20-minute invited papers. For example, there is to be a special ses- sion of 20-minute papers on Entire Functions at the Houston meet- ing. This will constitute a public presentation of some of the

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Appendixes 241 reports and lectures given at the 1966 Summer Institute on Entire Functions. Furthermore, a second session on Entire Functions is being considered for the Houston meeting which would consist of a panel discussion with audience participation. 5. A meeting could include a set of lectures at a more expository level than present AMS lectures; for example, make them accessible to reasonably qualified graduate students. These lectures might be filmed or taped and distributed. Small, specialized meetings seem to be very successful; more of them are being proposed (by CBMS). Perhaps the various kinds should be compared: summer-long teaching-and-research-microcosms (cf. Bowdoin) versus Gordon Conference types one or two weeks long; conferences which publish their proceedings versus those which do not, etc. Are visiting lecturer programs worthwhile? CUPM and SIAM have . . ~ . . some experience In this connection. NIIII. To repeat, each of the preceding suggestions, if carried out, should be assessed after a suitable trial period. This assessment could be arrived at by a consensus (for example, no one doubts the great usefulness of small, select meetings suitably managed). How- ever, for experiments with large meetings or with modes of publi- cation some kind of formal survey will probably be in order. For example, tampering with sessions for 10-minute papers always brings an outcry at the AMS business meeting. Is this a real ground swell? A professional survey organization should be seriously con- sidered for help in such matters, both in phrasing the questions to be asked and in evaluating the significance of the answers. In any surveys that may be conducted, it will be important to tabulate separately the responses of different groups of mathe- maticians; for example, innovations should not be initiated on the basis of majority votes. For example, the following classes might be expected to respond in different ways. 1. A small group of first-rank mathematicians (to be selected by the committee, for example) 2. Productive mathematicians (five papers in the last five years, for example) 3. Mathematicians who are unproductive but not isolated 4. Mathematicians who are unproductive and isolated

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242 Appendixes 5. Mathematicians in government and industry (should research labs be classed with universities?) 6. Physicists, economists, and other users of mathematics, produc- tive in the sense of 2. 7. Editors or past editors of research journals and of technical series of advanced treatises For some purposes it may also be desirable to classify mathe- maticians according to their field of interest. For example, it is pos- sible that applied mathematics may have different needs. All this classification might best be done in advance of a survey, using Mathematical Reviews and other sources, rather than allowing each participant in the survey to classify himself. IX. Finally, a bit of philosophy. We feel that our aim should be to channel the large masses of communication, not to limit them. Papers, lectures, etc. should be more carefully titled, abstracts should be used more and should be carefully written. This is partly a call for education of mathematicians in some of the simpler devices that can help buffer the avalanche. We do not propose that the number of published papers should be restricted, because even if it can be demonstrated that the aver- age paper has almost no readers, the writing, refereeing and publish- ing of the paper is of great value to the author. Besides making him visible to the mathematical community, presentation of his paper (in person or in print) exerts a certain influence that matures a fledgling mathematician (no research is complete until it is written down) and keeps older mathematicians alive; this seems to have some enlivening effect on the author's teaching and in his par- ticipation in other mathematical activities. X. The present committee requests that it be discharged. P. R. Halmos Albert Madansky Alex Rosenberg I. Barkley Rosser J. D. Swift J. F. Traub A. S. Wightman D. Zelinsky, Chairman