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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

OCR for page 233

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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OCR for page 233

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

OCR for page 233

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