Tragic loss or good riddance? 
        The impending demise of traditional scholarly journals 
  
             (Preliminary version, December 30, 1993) 
  
                         Andrew M. Odlyzko  
                       AT&T Bell Laboratories 
                       amo@research.att.com 
  
  
 1. Introduction 
  
 Traditional scholarly journals will disappear in the next 10 to 20 
 years.  There is wide recognition that electronic publication will 
 significantly affect mathematics [Franks].  However, I expect that 
 changes will come much faster and will be much deeper than is usually 
 anticipated.  Further, they could occur suddenly.  It is impossible to 
 predict the date or speed of transition, but only because they will be 
 determined by sociological factors.  The technology that is necessary 
 for future systems is either already available or will be in a few 
 years.  The speed with which this technology will be adopted by the 
 mathematical community will depend on how quickly we are prepared to 
 break with traditional methods in favor of a superior but novel 
 system.  However, the pressure towards change is going to grow, and 
 will soon become irresistible. 
  
 The impending changes are caused by the confluence of two trends.  Both 
 trends have exponential growth rates (where by exponential I mean the 
 precise mathematical meaning of this word, not the current journalistic 
 usage).  One trend is in the size of the mathematical literature, which 
 is causing a crisis in the traditional approach to dissemination of 
 research results.  The other trend is the increasing power and 
 availability of electronic technology.  It offers a way to solve the 
 crisis in traditional publishing.  However, it is likely to have far 
 greater effects than just the replacement of paper journals by 
 electronic ones. 
  
 The title of this article is meant to be provocative.  I do not mean to 
 imply that the current scholarly journals were always a bad solution to 
 the problem of information dissemination.  They have served the 
 mathematical community admirably, and there are dangers in moving away 
 from them to another system, as Quinn [Quinn] argues.  At the same 
 time, they are an awkward artifact of the only technology that was 
 available several centuries ago.  I feel that a system much better 
 suited to the transmission of mathematical information is going to 
 arise, although the transition may be painful.  However, I do not think 
 we have much choice, since drastic changes are inevitable no matter 
 what our preferences are. 
  
 Most of the comments and predictions that are made here apply to other 
 scientific disciplines as well.  I will write primarily about 
 mathematics, since the data I have are clearest for this field, and I 
 am most familiar with it. 
  
  
 2. Sources of current crisis 
  
 Only some mathematicians perceive that there is a crisis in the present 
 system of journal publications.  However, librarians and publishers are 
 well aware of it.  New journals are springing up all that time, yet 
 libraries are not buying them, and are even dropping subscriptions to 
 old journals.  The blame for this is usually ascribed either to greedy 
 publishers or short-sighted administrators.  The basic underlying 
 problem, though, is the exponential growth in the mathematical 
 literature.  The number of scientific papers published annually has 
 been doubling every 10-15 years for the last two centuries [Price]. 
 That is also true of papers in mathematics alone.  The data in [MR] 
 suggest that during the post-World War 2 era, the rate in our field 
 even increased to a doubling about every 10 years.  There is some 
 evidence (private communication from Jane Kister of Mathematical 
 Reviews) that growth has slowed down in the last few years, but it is 
 still substantial.  Math. Rev. has stayed at approximately 47,000 
 reviews per year only by limiting its coverage. 
  
 The exponential growth in mathematical publishing has interesting 
 implications.  Adding up the numbers in [MR] or simply extrapolating 
 from the current figure of about 50,000 papers per year and a doubling 
 every 10 years, we come to the conclusion that about 10^6 mathematical 
 papers have ever been published.  What is much more surprising is that 
 almost half of them have been published in the last 10 years.  Even if 
 we manage to keep the number of papers down to 5*10^4 per year, we will 
 double the size of the mathematical literature in another 20 years. 
  
 Similar exponential growth rates can be seen in other indicators of the 
 size of the mathematical research enterprise.  The AMS had 1,926 
 members in 1930, 6,725 in 1960, and 25,623 in 1990, a doubling roughly 
 every 16 years.  (The number of papers published has been doubling 
 almost every 10 years, and the share of the papers written by 
 mathematicians in North America has not dropped too much recently, and 
 went up substantially in the '30's and '40's.  Does this mean that 
 mathematicians have become more productive, possibly because their jobs 
 involve less teaching and more research, or is it just that they 
 publish more, or are they publishing shorter papers?  These are 
 intriguing questions that invite further study.)  The Division of 
 Mathematical Sciences of the NSF has seen its budget grow from about $ 
 13 M in 1971 to about $ 73 M in 1991, which is about a doubling in 
 inflation-adjusted dollars.  Awards (which are roughly proportional to 
 the number of researchers supported) went from 537 to 1424, an increase 
 by a factor of 2.65.  The complaints one hears about reduced NSF 
 support, just like those about reduced library budgets, are not so much 
 about reductions in absolute or even inflation-adjusted budgets, but 
 about their growth rates not keeping up with the number and output of 
 researchers. 
  
 Exponential growth in the number of mathematicians cannot continue for 
 long.  There are already clear signs (evident in the current job market 
 and the projections one reads) that the number of jobs in North America 
 is not likely to grow at all, or at least will not grow anywhere near 
 as fast as it used to.  Still, there is scope for continuing 
 exponential growth in the mathematical literature.  Currently most 
 research mathematicians are educated and work in Europe, North America, 
 and Japan.  Continued rapid economic growth and better education in 
 countries such as China and India are likely to enlarge vastly our 
 ranks.  With world population growing towards 10^10 in the next three 
 or four decades, we might end up in the second half of the 21st century 
 with 10 times as many researchers as we have today.  Could your library 
 conceivably cope with a 10-fold increase in the literature?  Repeating 
 the point made earlier, even if we don't project more than 50 years 
 into the future, and if we somehow manage to stop the growth in the 
 quantity of mathematical papers published each year, we will still 
 double the size of the existing literature in the next 20 years.  Can 
 your library cope with that? 
  
 Mathematical (as well as general scholarly) publishing has some 
 features that sharply differentiate it from the popular fiction or 
 biography markets, say, and make rapid growth difficult to cope with. 
 Research papers are written by specialists for specialists.  Various 
 estimates have been made of how many readers a research paper usually 
 attracts.  These estimates are not too trustworthy, since there is 
 difficulty in collecting data, and also in defining what it means to 
 read a paper.  Typical estimates for the number of serious readers are 
 around 20.  (One version of an old joke has an editor tell a referee, 
 "You are probably the second and last person to read this paper," to 
 which the referee replies, "Second?  Are you sure the author has read 
 it?")  Whatever the right number is, it is small, and is unlikely to 
 grow.  This is a consequence of a simple arithmetic relationship.  If a 
 mathematician reads x papers and writes y papers per year, and those 
 numbers do not change much (although they do change some, as the 
 remarks above suggest they might) then the average paper will be read 
 by x/y mathematicians, no matter how large the total mathematical 
 community is.  (Well, I am cheating a bit, since this assumes a steady 
 state, whereas with growth in the ranks of mathematicians and papers 
 being read many years after they are published the numbers can be 
 tricky to evaluate, but the general conclusion seems right.  All the 
 numbers in this article are back-of-the-envelope type estimates.  Given 
 the exponential growth rates we are dealing with, more precise figures 
 would not change the implications of the message.) This would change if 
 we could attract more readers from outside mathematics.  However, given 

 the increasing specialization that applies in all fields, not just 
 mathematics, this is unlikely.  There are more and more exciting 
 interactions with other disciplines, but they almost always involve 
 specialists in those areas, and this does not affect the trend towards 
 a narrower focus of research, which precludes attracting a general lay 
 audience.  The trade press is different.  If the potential audience 
 doubles (either because of natural increase in population, or because 
 readers in other countries start buying translations), a popular writer 
 like LeCarre can expect to sell twice as many copies of his books. 
  
 Mathematical publishing, because of its nature, cannot benefit from the 
 economies of scale that the trade press enjoys.  As in other scientific 
 disciplines, as our numbers grow, we tend to work in narrower 
 specialties, so that the audience for our results stays constant. 
 Further, the centers in which we work (typically university mathematics 
 departments) do not grow much, so we get increasingly dispersed.  On 
 the other hand, in principle we need access to all the mathematical 
 literature.  This leads to a crisis, in which we cannot afford to pay 
 for all the paper journals we need in our work. 
  
  
 3. Technology trends 
  
 A doubling of mathematical papers published each decade corresponds to 
 an exponential growth rate of about 7 % per year.  This is fast, but 
 nowhere near as fast as the rate of growth in information processing 
 and transmission.  Microprocessors are currently doubling in speed 
 about every 18 months, corresponding to a growth rate of about 60 % per 
 year.  Equally dramatic growth figures can be cited for information 
 storage and transmission.  The point of citing these figures and those 
 below is that advances in technology have made it possible to transform 
 scholarly publishing in ways that were impossible even a couple of 
 years ago. 
  
 There were visionaries who twenty or more years ago foresaw the 
 dramatic changes that technology could have on scientific information 
 dissemination, but their dreams took a long time to be realized.  The 
 main reason was that it took a long time for technology to provide the 
 tools that made those futuristic dreams realizable.  In those days 
 where most of computing was done in batch mode on mainframes, and the 
 few fortunate enough to have access to time-sharing systems had to 
 content themselves with printing terminals communicating at 300 bits 
 per second, electronic publishing and intensive collaborations across 
 oceans were not feasible.  With the rapid advance in technology, 
 though, we are at a stage where the needs of an electronic publishing 
 system for mathematics can be met easily.  Further, we can obtain a 
 system that will give us many additional capabilities that are 
 inherently impossible for paper journals to provide. 
  
  
 Recall that approximately 5*10^4 mathematical papers are published each 
 year.  If they were all typeset in TeX, then at a rough average of 
 5*10^4 bytes per paper, they would require 2.5*10^9 bytes, or 2.5 GB, 
 of storage.  If we include the approximately 1500 mathematics books 
 that are published each year, we find that the annual output of the 
 mathematical community requires under 4 GB of storage.  (This assumes 
 everything is in TeX.  If we use dvi files, the requirement about 
 doubles, while with PostScript it about quintuples.  On the other hand, 
 compression can reduce storage requirements by a factor of 2 or 3. 
 Given the rapid growth in the availability and cost of storage system, 
 factors of 2 or 5 mean only a difference of a couple of years.) 
  
 We can now buy a 1 GB magnetic disk for under $ 1000.  For archival 
 storage of papers, though, we can use other technologies, such optical 
 disks.  A disk with a 7 GB capacity that can be written on once costs  
 $ 200-300.  (The equipment for writing data on it is still expensive,  
 and costs $ 20,000 - 40,000, but it can be shared by many individuals  
 and even departments).  The standard CD-ROM disks, with about 0.7 GB of 
 storage capacity, cost a few dollars each to produce (with the 
 information written on it) in runs of a few thousand.  Digital tapes 
 with 250 GB capacities are also becoming available.  Thus electronic 
 storage capacity needed for dissemination of research results in 
 mathematics is trivial with today's technology. 
  
 We conclude that is it already possible to store all the current 
 mathematical publications at an annual cost much less than that of the 
 subscription to a single journal.  What about the papers published over 
 the preceding centuries?  Since there are about 10^6 of them, it would 
 require about 50 GB to store them all if they were all in TeX.  It 
 appears unlikely that anyone will undertake the project of converting 
 them all into TeX (or any other modern electronic format).  What I 
 expect to happen is that optical character recognition will eventually 
 be applied to the texts (since this will enable rapid computerized text 
 searches), while the equations will be stored as bitmaps.  To provide 
 reliable access to the text, whole papers will have to be available as 
 full bitmaps.  This dramatically increases the storage requirements. 
 However, even then, they are not prohibitive.  With current fax 
 standards (which produce copies that are not pleasant to read, but are 
 usable), a page of mathematical text requires  30 - 50 KB.  Therefore 
 all the 10^6 mathematical papers can be stored in less than 10^12 bytes 
 = 1000 GB.  This is large, but it is still less than 150 of the current 
 large optical disks.  For comparison, Wal-Mart has a database of over 
 1000 GB that is stored on magnetic disks, and is processed intensively 
 all the time. 
  
 The storage requirements of mathematical literature are likely to 
 become even more trivial in the near future.  Cable TV and phone 
 companies are getting ready to deliver movie-on-demand to the home. 
 This will require tremendous storage capacity, and is bound to 
 stimulate development of much denser and cheaper media.  There is not 
 much progress in optical disks, but magnetic hard disks are becoming 
 both larger and cheaper, and there are many promising new technologies 
 on the horizon, such as optical tape that might be able to store over 
 1000 GB on a single unit.  We can start thinking of 1000 GB storage 
 devices for personal computers becoming available in a decade or so. 
 This means that any one will be able to have the total mathematical 
 literature available right on the desktop.  Even sooner than that, 
 though, larger institutions, such as university mathematics 
 departments, will be able to make such systems available to their 
 members.  This ability will mean a dramatic change in the way we 
 operate.  For example, if you can call up any paper on your screen, and 
 after deciding that it looks interesting, print it out on the laser 
 printer on your desktop, will you need a library? 
  
 Optical disks can be shipped by parcel post at low cost.  However, it 
 is desirable to have faster communication links.  Information 
 transmission is a barrier right now.  Anyone who has to download files 
 at 2400 baud (roughly bits per second, bps) can attest how annoyingly 
 slow that is.  However, that is changing rapidly.  Most departments 
 have their machines on Ethernet networks, which operate at almost  
 10^7 bps.  Further, almost all universities now have access to the  
 Internet, which was not the case even a couple of years ago.  The  
 Internet backbone operates at 4.5*10^7 bps, and prototypes of much faster 
 systems are already in operations.  Movie-on-demand will mean wide 
 availability of networks with speed in the hundreds of megabits per 
 second.  If your local supplier can get you the movie of your choice at 
 the time of your choice for under $ 20 (as it will have to, in order 
 for the system to be economic), then sending over the 50 MB of math 
 research papers in your specialty for the last year will cost pennies. 
 Scientists might not like to depend on systems that owe their existence 
 to the demand for X-rated movies, but they will use them when they 
 become available. 
  
 There is concern in the scientific community that with the withdrawal 
 of NSF support for the Internet, the electronic data highway will 
 charge tolls that will be prohibitive for university researchers.  That 
 concern is misplaced.  It is based on a static view of the world and 
 does not take into account the increasing power and decreasing cost of 
 technology.  Yes, the commercial data highway will have tolls.  Yes, 
 the networks that the cable TV companies build may be structured 
 primarily for the broadcast delivery of movies to the home, and may not 
 have the full communication capabilities that scientists require.  The 
 point is that these networks are going to be large enough to justify 
 tremendous development efforts that will drive down the costs of all 
 communication technologies.  The tolls on the commercial data highway 
 will have to be low enough to allow transmission of movies.  Therefore 
 the cost of transmitting mathematics will be trivial.  Even if the 
 commercial data highway is not structured in an ideal way for science, 
 or is an economic flop, universities will be able to use the technology 
 that is developed and build their own cheap networks.  Just as the 
 recent progress in computers is caused much more by demand from 
 businesses running spreadsheets on PCs than from scientists modeling 
 global warming on supercomputers, so the progress in communications 
 will come primarily from commercial uses of the data highway.  Some 
 scientists and mathematicians (such as those getting atmospheric data 
 from satellites) will have to worry about the costs of communications, 
 since they will be transmitting giga- and tera-bytes of data.  The rest 
 of us can sit back and go along for the ride provided almost for free 
 by commercial demand. 
  
 Stevan Harnad (private communication) notes that even now, 
 non-scientific and non-educational uses of the Internet are a 
 significant fraction of the traffic.  The latest statistics for Usenet 
 (the decentralized system of discussion groups) collected by Brian Reid 
 of DEC show that the largest volume was generated by 
 alt.binaries.pictures.erotica, which has an estimated 240,000 readers, 
 and generated 31.4 MB of postings during one sampling period, even 
 though it is received by only about half the sites.  The second largest 
 load was 16.3 MB from alt.binaries.pictures.misc, which has 150,000 
 readers.  The third highest was 14.1 MB from 
 bionet.molbio.genbank.updates, which has 24,000 readers.  Sci.math, 
 which has an estimated 120,000 readers (the highest of any of the sci.* 
 groups, but only 39-th highest among all the groups) generated only  
 3.6 MB.  Even alt.politics.clinton generated 7.1 MB during the sampling 
 period!  This only reinforces the conclusion drawn earlier that most of 
 scientific communication can be accommodated in a tiny fraction of the 
 capacity of future networks.  (The gene bank data, like the atmospheric 
 data mentioned before, is a special case.) This is just a reflection of 
 the compact ways scholars have developed to present their results. 
  
 Not only have information storage and transmission capacities grown, 
 but the software has become much friendlier.  At the beginning most of 
 us had e-mail.  Then came anonymous ftp.  Together with the network 
 connections that are now almost universal, they provide powerful tools 
 for communication.  However, this is only the beginning.  We now have a 
 plethora of new tools, such as Archie, Gopher, WAIS, and Mosaic, which 
 allow easy access to the huge stores of information on the Internet 
 without having to learn arcane details of how it functions.  In the 
 next few years these tools are likely to evolve much further, and 
 become widely used in the day-to-day life by most mathematicians.  Here 
 I mention a few electronic document delivery systems that I have used 
 at Bell Labs.  There are similar systems in use or under development 
 elsewhere, and I mention these just because I have used them, and 
 because they appear to me to be forerunners of systems that will be 
 common soon, and will most likely become integrated with other 
 information retrieval tools.  One of these systems is Ferret(TM), and 
 it is used for internal technical documents.  All the internal 
 memoranda are digitized and stored on-line, and can be viewed on the 
 screen of one's own workstation.  In the old days, I often ordered 
 paper copies of memoranda.  After looking at the first page or so, I 
 then usually discarded the whole memo as not being of much interest. 
 Nowadays, I scan the first couple of pages on the screen, and only if 
 it looks interesting do I order a paper copy using the convenient 
 interface. 
  
 RightPages(TM) is another experimental Bell Labs system that gives the 
 user access to about 60 technical journal from about 10 publishers 
 [Story].  After selecting an issue of a journal involved in the 
 experiment, the user is shown the table of contents, and by clicking on 
 an item, he or she is shown the first page of the article.  If it looks 
 interesting, a click on the appropriate icon orders a paper copy for 
 delivery to the user.  (At the moment only the first page is scanned, 
 but this is not a fundamental limitation, and is caused by the lack of 
 resources in a small-scale experiment to do more.) The RightPages 
 system is used inside Bell Labs, and also at the University of 
 California in San Francisco. 
  
 Systems like those above are meant to work with the current paper 
 journals and memoranda.  They are supposed to compensate for some of 
 deficiencies of the present system, by allowing users to sift through 
 the increasing amounts of information that are becoming available, and 
 also by giving them access to information they cannot get in their 
 local libraries.  However, while they do help to deal with the crisis 
 in scientific publishing, they can also contribute to it.  I can now 
 use the Internet to find out what books and journals the Harvard 
 libraries have.  Suppose I could also look on my screen at the articles 
 in the latest issues of the journals that Harvard has received 
 recently, and order photocopies (or even electronically digitized scans 
 that can be reproduced right away on my laser printer) of the articles 
 that interest me.  Would there be any incentive to pressure my local 
 library to order that journal?  Would there be any reason to have more 
 than one copy of the journal in the country (or the world)?  If we do 
 have only one copy, how is it going to be paid for?  Thus the arrival 
 of technological solutions to the current crisis in scholarly 
 publishing creates new problems. 
  
  
  
 4.  Electronic journals 
  
 One approach to the threat to scholarly publishers that is posed by 
 electronic access is to limit distribution to paper copies only.  Yet 
 that is not a feasible solution in the long run.  Because of the 
 publishing crisis, almost all libraries are receiving a diminishing 
 fraction of the literature that is needed by local scholars.  Hence 
 there is an absolute need to provide access to journals not on local 
 shelves.  Only those journals that can supply it conveniently will 
 survive.  Further, even if a paper journal is available, there are 
 advantages to an electronic version.  Especially valuable is the 
 ability to do rapid text searches for relevant material.  That is 
 surely why many publishers are beginning to provide electronic versions 
 of their publications.  As mathematicians become familiar with 
 electronic document distribution and learn how useful it is, they will 
 increasingly demand that all journals be available in that form. 
  
 There is no great technical difficulty in making current journals 
 available electronically.  Most of them already use computerized 
 typesetting, so it's just a matter of making their files available to 
 readers.  (Many of them, including the AMS, rely on TeX, which means 
 that little conversion is needed.)  The editorial and refereeing 
 functions can be performed just as they are today, and the standards 
 can be maintained.  In the simplest version, all that means is that 
 instead of having to go to the library to look at the latest issue of a 
 journal, one can log in remotely on a publisher's machine and look in a 
 directory for the latest papers.  With better software tools, it will 
 be unnecessary to know what machine those papers are on, as the 
 software will locate them automatically.  One can also arrange to be 
 notified via e-mail about new papers accepted by a journal. 
  
 Electronic journals have many advantages over paper ones.  Let us 
 recall that paper journals evolved in the era where printing was the 
 only practical method of wide dissemination of information.  Nobody 
 could expect Gauss to make 50 handwritten copies of his manuscripts for 
 distribution to interested colleagues.  This resulted in bulky 
 publications that are expensive to produce and maintain.  As a result, 
 a huge infrastructure has evolved of publishers to acquire and edit the 
 manuscripts, and then print and distribute the journals.  Further, 
 another large infrastructure has evolved of libraries to acquire, 
 catalog, shelve, etc., these journals, to make them accessible.  We 
 should not forget how cumbersome this system is.  Except for those 
 living near the 500 to 1000 good libraries, access to this information 
 is hard.  Even for those at institutions with good libraries, obtaining 
 the necessary information means a physical trip, often to another 
 building.  Often it requires a wait while a copy is brought back from 
 storage, or else is recalled from another borrower. 
  
 In short, traditional paper journals are not convenient. 
 Electronic publication offers a way to make all mathematical 
 literature accessible around the clock from the comfort of one's office 
 or home.  Moreover, it can make this literature accessible to 
 everyone.  One point that is made about Ginsparg's theoretical physics 
 preprint service, both by Ginsparg and other users [Ginsparg, Sci1], is 
 that it has made the latest results much more widely available, and 
 diminished the importance of various small "in" groups that were 
 exchanging preprints.  Today there are many universities around the 
 world that do not have good electronic connections.  However, that is 
 changing rapidly.  After all, it is far cheaper to hook up to the 
 Internet than it is to acquire a good mathematical library from 
 scratch.  A T1 line of 1.5*10^6 bits per second to the Internet costs 
 around $ 20 K per year, at least in the US.  On the other hand, a good 
 library has to spend well over $ 100 K per year just for mathematical 
 journal subscriptions.  Further, journal prices are going up, while the 
 cost of connections is going down. 
  
 Once many journals become available electronically, paper copies are 
 likely to disappear.  It will be a case of positive feedback operating 
 in a destructive mode.  Necessary information will be available 
 electronically, and most of it will have to be accessed electronically, 
 since the local libraries will not be able to provide copies of all 
 relevant journals.  Therefore researchers will have less incentive to 
 press for paper journal subscriptions to be maintained, which will lead 
 to diminished circulation, and therefore to higher prices and more 
 pressure from libraries to cut back on subscriptions. 
  
 While I do predict that most paper journals will disappear, I am not 
 saying that there will be no place for paper.  Display technology is 
 not moving anywhere near as fast as microprocessors or data 
 transmission, and it will be a long time before you curl up in bed with 
 a screen rather than a book.  People will wish to print papers out any 
 time they need to study them carefully.  However, that will be done on 
 their own laser printers from electronically supplied files. 
  
 Once journals move to an electronic format, reviewing publications such 
 as Math. Rev. and Zentralblatt are likely to disappear.  These journals 
 play an invaluable role in informing scholars of the latest 
 developments in mathematics.  However, just how valuable is this 
 contribution going to be in the new era in which everything is 
 available on-line?  If I can do text searches over the whole 
 mathematical literature, how important will the abstracts be? 
 Zentralblatt is almost completely devoted to author abstracts.  Do I 
 need that if I have the full text available?  Math. Rev. provides a 
 better service, since their abstracts are more often written by experts 
 who can provide an evaluation of the work, but even there, the reviews 
 are often perfunctory.  Careful surveys are going to increase in 
 importance as research publications get ever more specialized with the 
 growth of the field, but that is not what the reviewing journals 
 provide.  I feel that these publications will become superfluous, and 
 their function will be taken over by computerized searches. 
  
 How are electronic publications to be paid for?  That is a crucial 
 question that the whole information industry is struggling with, and 
 there is no clear answer.  Some form of pay-per-view is the most likely 
 answer for most situations.  It is certainly appropriate for many 
 commercial information services, as well as the entertainment 
 industry.  (Credit reporting services have been operating in this mode 
 for a long time, for example, and so have movie theaters.)  It is not 
 impossible that some system of this type will be designed for scholarly 
 publications.  There are fears among scholars about prohibitive costs 
 of such a system [Franks], but it is conceivable that a solution 
 equitable to all sides could be devised.  However, I do not think 
 pay-per-view will become the prevailing model in scholarly publishing. 
 The reason is that the value added by publishers is diminishing, and 
 there will be cheaper and better ways to provide their services. 
  
 It is widely recognized that scholarly journal publishing differs 
 significantly from the trade press.  The primary interest of authors is 
 in making their work widely available.  They practically never receive 
 any direct financial remuneration for their papers.  Their rewards come 
 from recognition their work earns in their field.  The scholarly 
 community is in the business of writing papers, giving them to 
 publishers, and then buying them back as journals and books.  Scholars 
 and publishers have developed a mutually beneficial relationship. 
 However, given the crisis in the present system, this relationship is 
 under strain, and is likely to result in the demise of traditional 
 publishers.  The main problem right now is the need to reduce costs 
 drastically. 
  
 What is the cost of producing a typical mathematical paper?  It appears 
 that the average researcher publishes two or three papers per year. 
 The total cost of employing such a person is at least $ 150 K per year 
 (this is a conservative estimate, as it is meant to include standard 
 salary, grant support, benefits, as well as all the office space, 
 libraries, and university administration costs).   Let us assign one 
 third of this cost to research activities.  If we do that, we conclude 
 that each paper costs at least $ 20 K, with the cost paid for by 
 taxpayers, students' parents, or donors to universities. 
  
 How much does it cost to publish a paper in a research journal?  Let us 
 take the figures in [AMSS].  If we assume that each paper is typeset 
 with 5*10^4 characters, and multiply that by the cost per character 
 given in [AMSS] for any given journal, and then multiply by the 
 circulation for that journal, we obtain an estimate for how much it 
 costs to publish at article in that journal.  For example, according to 
 [AMSS], Amer. J. Math.  has a circulation of 1458, and an annual 
 subscription costs $ 0.048 per 10^3 characters.  This produces an 
 estimate of $ 1458*50*0.048, or about $ 3500 for the cost of publishing 
 a single article there.  This figure includes all the editorial, 
 printing, and mailing expenses.  Doing this for the other journals 
 listed in [AMSS] for which both costs and circulation are given (but 
 excluding Bull. Amer. Math. Soc., which differs substantially in scope 
 and especially circulation from the standard research journals) 
 produces estimates for single article costs between $ 900 (for the 
 Notre Dame J. Formal Logic) and $ 8,700.  The median cost figure is 
 about $ 4,000, and is the one I will use. 
  
 The estimate of $ 4 K for the cost of publishing a paper shows that it 
 is indeed much lower than the $ 20 K cost of writing it in the first 
 place.  (The unpaid work of editors and referees is indispensable to 
 scholarly publishing, but any estimate of its monetary value would 
 surely come up with figures well below $ 4 K per article.) Thus the 
 value added by the publishers is dwarfed by that of scholars. 
  
 Is $ 4 K per article too much to pay?  That is not a question that can 
 be discussed in the abstract.  Until recently, there was not much 
 choice.  The traditional journals were the only method available for 
 transmission of research results.  The problem is that the cost per 
 article is increasing, and so is the number of articles.  Therefore 
 something will have to be done.  To put this figure into perspective, 
 let us recall that about 5*10^4 mathematical papers are published each 
 year, so the total cost of traditional mathematical journals is about  
 $ 200 M per year.  If we assume that 35 % of this cost is paid by 
 subscribers in the US (which is probably a low estimate), then we find 
 that US universities, laboratories, and individuals spend $ 70 M per 
 year for mathematical journals.  That is almost exactly the same as the 
 NSF budget for mathematical research.  If we could eliminate this cost, 
 we could potentially double the NSF budget for mathematics at no extra 
 cost to society at large.  Of course, the tradeoff is not that simple, 
 since journals are paid for from different sources than research 
 grants, and we do not have much freedom in moving public and private 
 funding around.  However, the $ 70 M figure is sufficiently large that 
 it cannot easily grow, and there will be pressure to lower it if some 
 method for doing so can be found. 
  
 To what extent can publishing costs be lowered?  Some publishers have 
 predicted that electronic publication of journals would lower the costs 
 only by around 30 %, roughly the cost of printing and mailing.  My 
 guess is that the visible costs can be lowered much further, and 
 possibly entirely eliminated.  By visible costs I mean the subscription 
 costs of the journals.  This might mean creating some additional costs 
 for the authors and their institutions, but those are not likely to be 
 large. 
  
 In my own experience as editor, I have found that papers submitted 
 electronically are much easier to handle than those on paper.  In cases 
 of electronic submission, I do all the work without help of a secretary 
 (although there is no reason that a secretary could not handle many of 
 these tasks).  Still, I find that sending out copies of the manuscripts 
 and letters to referees electronically is easier than writing out 
 instructions to the secretary, and then, after some delay, checking the 
 paperwork and signing the letters.  With more and more potential 
 referees reachable via e-mail, this is becoming increasingly 
 practical.  The main problem arises with nonstandard TeX files.  That 
 should become less of a burden in the future as authors are persuaded 
 to standardize their styles and as better software becomes available. 
 After all the reviews and revisions are done, I then send the 
 manuscript (electronically, to an increasing extent) to the journal for 
 copy editing, printing, etc.  In an electronic journal I could simply 
 place the manuscript file in a special directory or e-mail it to a list 
 of subscribers.  That is indeed how many of the electronic journals 
 that have been set up recently function.  Today some paperwork is still 
 required by publishers for authentication.  (For example, AMS insists 
 on signed letters from editors together with paper copies of 
 manuscripts that are accepted.) However, cryptography has developed the 
 technology to avoid this step, and digital signatures will become 
 common soon. 
  
 The financial costs of electronic journals should be so low that they 
 will be absorbed into general overhead expenses.  ETNA, the Electronic 
 Transactions on Numerical Analysis, published by the Kent State 
 University Library in conjunction with the Institute of Computational 
 Mathematics at Kent State University, is a new electronic journal. 
 Subscriptions to it are currently free, although the journal has 
 announced that this may change after the initial three-year trial 
 period.  Arden Ruttan, its Managing Editor, reports (private 
 communication) that so far about 90 % of the ETNA budget has gone to 
 purchasing equipment, with smaller expenditures for telephone (5%) and 
 advertising (5%).  There are neither copy editors nor secretarial 
 staff, and papers have to be submitted in LaTeX or TeX.  In general, 
 given the improving performance and decreasing cost of computers, I do 
 not think electronic journals will even need special computers. 
 Ginsparg's electronic preprint service, which will be described later, 
 uses only a small fraction of the capacity of a workstation that is 
 devoted to other purposes.  The netlib system, developed by Jack 
 Dongarra at Argonne and Eric Grosse at Bell Labs, which has been used 
 widely by the applied mathematics specialists for several years, ran 
 for a while on a Sequent multiprocessor that was donated just for that 
 purpose.  Today, although the traffic through the system has increased 
 tremendously, a fraction of a workstation handles it comfortably.  Thus 
 equipment costs in the future could be absorbed in the general overhead 
 of providing a computing environment for editors in their normal 
 professional jobs. 
  
 Electronic journals like ETNA rely currently on free links through the 
 Internet.  With communication costs going down, I expect that 
 transmission will also be covered as part of the general overhead. 
 Systems administration requires some care, as not all editors will be 
 willing and able to take care of maintaining their systems.  However, 
 with improvements in software, this is becoming much less of a problem, 
 and there are now even programs for dealing with misrouted e-mail. 
 Eric Grosse (private communication) has estimated that netlib could 
 handle all SIAM's publications needs in the next few years with the 
 half-time help of a skilled systems administrator. 
  
 Arden Ruttan (private communication) reports that the main negative 
 comments about ETNA have been about the lack of copy editing, and the 
 requirement that all manuscripts be in LaTeX or TeX.  The restriction 
 on input format is something that is likely to become less of a 
 problem, in that I expect that increasingly mathematicians will have 
 all their papers prepared in one of a few typesetting systems (which 
 may include something other than just LaTeX or TeX).  This will shift 
 some of the burden of publishing onto authors, but is not likely to be 
 particularly onerous.  I am not sure what, if anything, will happen 
 with copy editing.  Its lack results in non-uniform format and 
 substandard appearance.  At ETNA, Ruttan does extensive copy editing 
 himself, but this is clearly not something that most editors are going 
 to be willing to do.  One solution might be to give up on uniform 
 standards.  This might not be a great loss.  I have heard more than one 
 author complain betterly about the changes that a publisher made to a 
 TeX manuscript that the author devoted great efforts to.  Another 
 solution might be to force authors to prepare their manuscripts in 
 adherence to a rigid format.  Still another approach would be to have 
 professional copy editors, either at the author's institution or at the 
 editor's, who would do the job.  If this is done at the author's 
 institution, the cost might again be absorbed by the general 
 administrative overhead, as are costs of technical typists.  Even if it 
 is done at the editor's location, the cost of copy editing a file in 
 some standard input language is likely to come to less than $ 400 per 
 paper, not the $ 4,000 per paper that the present system costs.  That 
 cost might be covered by page charges to authors, say.  The final 
 appearance may not be as pleasant as with a truly professional system, 
 but it should prove adequate. 
  
 The arguments above suggest that it should be possible to have 
 electronic journals that will provide all the essential features of the 
 present paper ones at a small fraction of the cost.  Therefore, given 
 the pressure to reduce costs, the present expensive publishing 
 enterprises, commercial as well as non-profit ones, will not be able to 
 survive in anything resembling their present forms.  Contributing to 
 the general pressure to reduce costs will be the subversive influence 
 of electronic preprint distribution, which will be discussed later. 
 The transition to a paperless system is likely to be painful, though. 
 It will be painful for the employees of the publishers.  After all, 
 what I am predicting is that most of their professional skills, 
 acquired at great effort, and formerly highly valued by the scholarly 
 community, will become obsolete.  The transition will also be painful 
 for the publishers themselves, as their main business will disappear. 
 This will be a problem even for non-profit publishers like the AMS, 
 which depends on publishing revenue to support many of its activities. 
 There will be severe conflicts of interests between publishers that are 
 going out of business, but still control the copyrights to 
 publications, and the scholarly community.  It will require substantial 
 effort to devise an equitable solution.  However, I do not see any way 
 to preserve the present system, since it is too expensive already, and 
 is not able to cope with the exponential growth in production of 
 information. 
  
 I am convinced that electronic publishing that is free to readers will 
 take over in science and mathematics.  It is impossible to predict 
 accurately the date of transition.  The basic technology that makes it 
 possible is here, so it's a matter of guessing how soon the necessary 
 infrastructure of editorial systems can be developed, and how quickly 
 it will be accepted by the community.  If nothing is done, I expect 
 that traditional paper journals will become irrelevant to 
 mathematicians' needs within 10 years.  They might survive for a while 
 longer, just because of the inertia of the entire academic publishing 
 and library system, but then there might come a sudden transition, as 
 the realization spreads that this system is obsolete.  This transition 
 might be similar to the one that affected the mainframe computer 
 industry.  The experts were predicting 10 years ago that the mainframe 
 was dead.  However, there were still many jobs that only mainframes 
 could handle.  Five years ago, the mainframe was at last truly 
 obsolete, but inertia ruled, and sales of these machines were at their 
 peak.  In the last three years, however, a catastrophic decline took 
 place. 
  
 Advances in technology will also drastically affect libraries. 
 Libraries are expensive.  While mathematical journals cost the US 
 mathematical community about $ 70 M per year just in subscription 
 costs, it is likely that the costs of maintaining library collections 
 (both people and space, but excluding subscription costs) amount to a 
 comparable amount.   Right now librarians are the ones facing the 
 crisis in publishing, since they have to deal with increasing prices 
 and increasing scholarly output.  They are squeezed between publishers 
 on one hand, and scholars on the other.  Technology will solve the 
 librarians' problem, but will also eliminate most of their jobs.  Just 
 like publishers, libraries will have to shrink and change their role. 
 After all, if the entire mathematical literature is available on your 
 screen, drawn from a data storage device either on your workstation, or 
 your department's central library server, or some distant location 
 accessed over the Internet, why would you need to use the traditional 
 library?  Most functions of the traditional libraries are connected to 
 the notion that information is preserved on pieces of paper that are 
 bulky and expensive.  That paradigm is no longer appropriate, at least 
 not if we do have a system like that outlined above, where scholarly 
 information is made available for free.  A basic function of a library 
 is to decide what books and journals to obtain, to get the most 
 productive use of the limited budget.  The procurement of those 
 journals and books, and their cataloging, shelving, etc., are another 
 important function.  However, with practically unlimited storage, and 
 no cost constraint, why shouldn't your (or your department's) computer 
 have all the world's mathematical papers?  Moreover, it could have it 
 with a few clicks at appropriate icons on your machine's screen, with 
 all the data transfers taking place automatically.  Similarly, an 
 important role for libraries is to keep track of loaned material, since 
 usually there is only one physical copy of each book or journal issue. 
 With electronic data storage, though, that is not a problem, as 
 unlimited copies can be made. 
  
 Reference librarians are experts at locating information, and are 
 indispensable.  As with reviewing journals, though, there will be much 
 less need of this expertise when all information is available 
 electronically.  A dumb text search through the few tens of terabytes 
 of data that constitutes the sum of all scholarly publications can 
 frequently substitute for expert human assistance.  (While a terabyte 
 search seems outlandish right now, it won't seem so large in a few 
 years.  With proper indexing, the search problem becomes even more 
 manageable.)  Moreover, much better information-gathering software 
 programs are being developed that will make it possible to pursue 
 intelligent search strategies, further usurping the roles of expert 
 librarians.  There will always be positions for experts in information, 
 to help in navigating the oceans of data on the Net, but their roles 
 will cover only the most sophisticated skills that librarians possess. 
 There will be many fewer jobs in libraries themselves, and much less 
 space.  As one sign of what is likely to happen, the New York Times on 
 Oct. 7, 1993, reported that Time, Inc., the parent company of Time, 
 Sports Illustrated, and several other magazines, was cutting its 
 library staff from 120 to 80.  The justification for the cut was that 
 many of the functions performed by the staff, such as cutting out and 
 filing stories from various sources were being taken over by electronic 
 searches.  This is just the beginning of the trend that will see the 
 demise of the traditional library as well as the traditional journal. 
  
 The new electronic publishing system will require experts for 
 classifying information and linking it to other sources.  However, that 
 number will be small, at least in the scholarly publishing area.  It 
 should be possible for a few institutions supported by taxpayers, such 
 as the Library of Congress, or by charitable contributions, such as the 
 New York Public Library, to provide most of the services needed.  The 
 reason is that most of the work will likely be done by the unpaid 
 authors, editors, and referees.  We already have a good subject 
 classification system, and updating it would be much more the job of 
 mathematicians than other experts. 
  
 The arguments above suggest that in the future both journal publishers 
 and libraries will play a much diminished role in scholarly 
 publications.  However, this still leaves open the possibility of our 
 present journals surviving almost intact, except that instead of being 
 printed on paper, they would be electronic.  My feeling is that while 
 this might be an intermediate stage, it will not be the final one, and 
 that publications will undergo a much more dramatic change.  The reason 
 is that electronic publishing offers many more possibilities than 
 traditional paper journals. 
  
  
 5. The interactive potential of the Net 
  
 In this section I describe my vision of what future mathematical 
 publications will be like.  I start by disputing Frank Quinn's vision 
 [Quinn] of what the present system is and ought to be, and then discuss 
 some novel information dissemination systems that have certain features 
 I expect to find in future system.  Finally I present the basics of the 
 system I expect to emerge over the next decade. 
  
 Scholarly journals have evolved during the last three centuries, in the 
 world shaped by Gutenberg's invention of movable type.  This invention 
 made possible wide dissemination of scholarly publications.  However, 
 because printing, although much cheaper than hand copying, was still 
 expensive, mathematical journals were constrained into a format that 
 emphasized brevity.  Further, the standards have promoted correctness. 
 Since it took a long time to print and distribute journal issues, and 
 corrections likewise required a long time to disseminate, it made sense 
 to have a rigorous refereeing standard.  (This was not the only reason, 
 of course, but I believe it was an important one in the development of 
 our current editorial practices.) As a result, mathematical literature 
 has become reliable, in that mathematicians feel free to use results 
 published in reputable journals in their work, without necessarily 
 verifying the correctness of the proofs on their own.  Frank Quinn 
 [Quinn] argues that this feature justifies extreme caution in moving 
 away from paper journals, lest we be tempted into "blackboard-style" 
 publishing practices that are common in some fields.  I agree that 
 mathematicians should strive to preserve and enhance the reliability of 
 mathematical literature.  However, I feel that Quinn's concerns are 
 largely misplaced, and might serve to keep mathematicians from 
 developing better methods for information dissemination. 
  
 The first point that should be made is that electronic publication does 
 not in any way prevent the maintenance of present publishing 
 standards.  Electronic journals, as sketched in the previous section, 
 can follow exactly the same policies (and might even have the same 
 names) as the current paper journals.  On the other hand, paper 
 journals are no guarantee against unreliable results, since the 
 practices Quinn deplores are common in some fields, and have been 
 present for a long time.  Thus the reliability of literature in any 
 field depends primarily on the publishing norms in that field, and not 
 on the medium. 
  
 Paper journals serve several additional purposes in addition to that of 
 providing reliable results.  By having a hierarchy of journals of 
 various prestige levels, the present system serves to alert readers to 
 what the most important recent results are, and helps in making grant, 
 tenure, and similar decisions.  Here again there is no reason that 
 electronic journals could not provide the same services. 
  
 A more serious objection to Quinn's article [Quinn] (and to a large 
 extent also to [JaffeQ]) is that its picture of mathematicians whose 
 main goal is to produce formally correct proofs is unrealistic.  I 
 agree completely with Quinn that it is desirable to have correct 
 proofs.  However, it's a mistake to insist on rigor all the time, as 
 this can distract from the main task at hand, which is to produce 
 mathematical understanding.  There are many areas of mathematics today 
 that are not completely rigorous (at least so far), with the 
 classification of finite simple groups just one example.  This has been 
 true at various times in the past as well.  After all, Bishop Berkeley 
 with his "ghosts of departed quantities" jibe about infinitesimals had 
 much the better of the argument about rigor in 18-th century calculus. 
 On the other, from a historical perspective he lost the argument, since 
 the necessary rigor was eventually supplied.  In a similar vein, we 
 speak of the Riemann Mapping Theorem, even though experts agree that 
 Riemann did not have a rigorous proof of it, and that a proper proof 
 was only supplied later.  Standards have not improved all that much in 
 the intervening years.  What I do want to argue here is that the 
 present system does not do a good job of providing the expected 
 reliability, even if by reliability we mean the standards accepted in a 
 given field, and not formal correctness.  Even conscientious referees 
 often miss important points.  Furthermore, many referees are not all 
 that conscientious.  Once a paper appears, there are some additional 
 controls.  Sometimes a careful reviewer for Math. Rev. will catch a 
 mistake, but that does not happen often.  More typically, an error will 
 be pointed out by someone, and then, depending on who and what is 
 involved, there may be an erratum or retraction published, or else a 
 note will be inserted into another paper, or else the mistake will only 
 be known to the experts in the field.  If the topic is important, 
 eventually some survey will point out the deficiencies of the paper, 
 but most papers do not get this treatment.  Thus we already have 
 situations where published work has to be treated with caution.  It is 
 more reliable than that of just about any other field, but it is not as 
 reliable as Quinn's article might lead us to believe. 
  
 Lack of complete reliability is only one defect of the current paper 
 journal system.  Delays in publication are the one that is best known 
 and most disliked.  There are others as well.  A major one is caused by 
 the emphasis on brevity that was encouraged by an expensive system of 
 limited capacity.  Although this is seldom said explicitly, the 
 standard for presentation in a research paper is roughly at the 
 advanced graduate student level.  If you write to be understandable to 
 undergraduates, referees and editors will complain that you are wasting 
 space describing basic steps that the reader is supposed to be able to 
 fill in.  If you write at a more advanced level, they will complain 
 that the details are too difficult to fill in.  The result is 
 exposition that is often hard to follow, especially by non-experts. 
  
 Bill Thurston [Thurston], in an article that is largely a rejoinder to 
 that of Jaffe and Quinn [JaffeQ], argues convincingly that formal 
 proofs are fundamental to the correctness of mathematics, but they are 
 a terrible way to convey mathematical understanding.  Although this is 
 seldom stated explicitly, implicitly it seems to be understood well by 
 everyone.  After all, we do have advanced seminars instead of handing 
 out copies of papers and telling everybody to read them.  The reason is 
 that the speaker is expected, by neglecting details, intonation, and 
 body language, to convey an impression of the real essence of the 
 argument, which is hard to acquire from the paper.  The medium of paper 
 journals and the standards enforced by editors and referees limit what 
 can be done. 
  
 While Thurston argues for a more intuitive exposition of mathematical 
 results, Lamport [Lamport] advocates just the opposite.  Both Lamport 
 and Thurston feel that the usual standards of mathematical presentation 
 fall far short of the rigor of formal proofs.  Lamport feels that our 
 literature would be far more reliable if proofs were more formal.  One 
 problem with this suggestion is that it would make proofs even harder 
 to understand.  Lamport's solution is to have a hierarchy of proofs, of 
 increasing levels of rigor.  However, the current system cannot 
 accommodate this, given the premium placed on brevity. 
  
 The ideal system would, as Lamport suggests, have multiple 
 presentations of the results, starting possibly with a video of the 
 author lecturing about them, and going down to a detailed formal 
 proof.  Such a system is possible with electronic publishing, given the 
 availability of almost unlimited resources (although it will be a while 
 before video presentations can be included routinely), but cannot be 
 accommodated with our paper journals. 
  
 Electronic publishing and electronic communication in general are 
 likely to have a profound impact on how mathematical research is 
 performed, beyond destroying paper journals.  It is likely to promote a 
 much more collaborative mode of research.  One mode of mathematical 
 research that is highly prized in our mythology is that of the 
 individual who goes into a study and emerges a few months or years 
 later with a great result.  Andrew Wiles' proof of Fermat's Last 
 Theorem falls into this model, and many people have expressed their 
 admiration of Wiles for devoting many years of secret work to his 
 project.  However, that is not the only mode of operation.  As an 
 example, the reviewing of the Wiles manuscript is being carried out by 
 a large team of referees who communicate via e-mail, and the 
 communication is apparently very helpful in this work.  In general, 
 team efforts have been increasing, and rapid electronic communication 
 via e-mail and fax has been instrumental in this.  Inspection of Math. 
 Rev. shows that the proportion of coauthored papers has increased 
 substantially over the last few decades.  Given the increasing 
 specialization of researchers, this is only natural.  Further, it is a 
 congenial mode of operation for many.  Laszlo Babai wrote a marvelous 
 article [Babai] that I highly recommend.  Its title is a pun.  It is an 
 account of the proof of an important recent result in computational 
 complexity, on the power of interactive proofs.  At the same time this 
 article is a description of how the proof was developed through 
 exchanges of TeX files of manuscripts and e-mail messages among a group 
 of about two dozen researchers.  There are many such interactions going 
 on, and the electronic superhighway will make them easier and more 
 popular.  (It will also create new problems, such as that of assigning 
 proper credit for a work resulting from interaction of dozens of 
 researchers.  That is another story, however.  It might seem unfamiliar 
 and hard for mathematicians, but other scientists, such as elementary 
 particle physicists, have managed to deal with it.) 
  
 The following sections examine some of the existing methods for 
 information dissemination and their relevance for scholarly 
 publications.  All have serious deficiencies, but all have promising 
 features.  The final section will present my vision of what future 
 systems will be like. 
  
  
 5.1  Netnews 
  
 The Net (the informal name for the Internet and a variety of other 
 electronic information services) provides several interesting examples 
 of information dissemination systems.  Usenet, the decentralized system 
 of discussion groups, is extremely popular, but not among serious 
 scholars.  As has been noted by many, unmoderated discussion groups, 
 such as sci.math, are at the opposite end of the spectrum from the 
 traditional scholarly journals.  They have been called a "global 
 graffiti board for trivial pursuit" [Harnad1].  They are full of arrant 
 nonsense, and uninformed commentary of the "As I recall, my high school 
 teacher said that ..." variety.  They are also beginning to attract 
 cranks.  (I was amazed that sci.math survived for many years without 
 any serious problems with crackpots, although that is unfortunately 
 changing.) Most mathematicians who try sci.math give up in disgust 
 after a few days, since only a tiny percentage of the postings (of 
 which there have been over 60,000 so far) have any real information or 
 interest.  I have continued reading it sporadically, more from a 
 sociological interest than anything else.  What I have found 
 fascinating is that although there are now cranks posting to it (and, 
 what is worse, generating long discussions), and there is plenty of 
 "flaming," as well as the nonsense alluded to above, there are 
 occasional nuggets of information that show up.  Sometimes a well-known 
 researcher like Noam Elkies or Philippe Flajolet will provide a 
 sophisticated solution to a problem that has been posted.  What is 
 perhaps even more interesting is that every once in a while some 
 totally unknown person from a medical or agricultural school, say, will 
 post an erudite message, giving a proof, a set of references, or a 
 history of a problem.  These are not the people I would think of when 
 choosing referees, yet they clearly have expert knowledge of at least 
 the topic at hand. 
  
 Reading sci.math also provides a strong demonstration of the 
 self-correcting nature of science and mathematics.  The opposite of 
 Gresham's law operates, in that good proofs tend to drive out the bad 
 ones.  For example, every few months, the Monty Hall paradox (with a 
 contestant given a choice of three doors, etc.) crops up again, as a 
 new reader brings it up.  There is typically a flurry of a few hundred 
 messages (this is Usenet, after all, and there is no centralized 
 control and no synchronization) but after a week or so the discussion 
 dies down, and everyone (or almost everyone, since there are always a 
 few crackpots) is convinced of what the right answer is. 
  
 In these days when we hear constant complaints about lack of public 
 interest in science and mathematics, it is interesting to note that 
 sci.math has an estimated 120,000 readers world wide.  This is a large 
 group of people who do have at least some interest in serious 
 mathematics. 
  
 Although the Usenet model does have some redeeming features, it is not 
 a solution to the scholarly publishing problem.  The information 
 content is far too low.  Even the specialized groups, such as 
 sci.math.num-analysis, which are at a higher level then sci.math by 
 virtue of their greater technical focus, are not adequate, as there is 
 too much discussion of elementary topics.  A somewhat better solution 
 is that of moderated discussion groups.  Dan Grayson runs the 
 sci.math.research group, which is much more interesting for 
 professional mathematicians, because of the filtering he does. 
 However, while it is a useful forum for asking technical questions or 
 picking up odd pieces of mathematical gossip or strange results, it is 
 more like a coffee hour conversation in a commons room than a serious 
 publishing venture. 
  
 There are other kinds of moderated discussion groups that engage in a 
 form of publication that is clearly useful, but would not fit into the 
 traditional paper journal mode.  For example, F. Bookstein (posting to 
 vpiej-l,  Pub-EJournals, December 2, 1993) operates a morphometrics 
 bulletin board.  Its main function is to provide technical answers to 
 questions from readers.  They are seldom novel, as one goal is to avoid 
 mathematical novelty, and provide references to existing results, or 
 combinations of known results.  However, they serve an important 
 function, saving researchers immense efforts by providing needed 
 technical advice. 
  
 There are many mailing lists that provide some of the services that 
 Bookstein's bulletin board does.  Many mathematicians are familiar with 
 the Maple and Mathematics user group mailing lists.  They consist of 
 e-mail messages from users with questions and complaints, and responses 
 to those messages from other users and the paid support staff for those 
 symbolic algebra systems.  They do not qualify for traditional paper 
 journal publications.  Too many are basic questions about simple 
 features of the system.  Most are about bugs in the current release, or 
 system incompatibilities, and nobody would want to make that part of 
 the archival record.  However, they are extremely useful, largely 
 because with electronic storage, it is possible to search the great 
 mess of them for the tidbits relevant to one's current needs.  Further, 
 they sometimes do veer into deep questions, as when a simple query 
 about solving a system of polynomial equations evolves into a 
 discussion of what is effectively computable with Groebner bases. 
  
 All the discussion group formats mentioned above do what Quinn [Quinn] 
 regards as pernicious, namely blur the line between informal 
 communication and formal, reviewed publication.  However, where Quinn 
 sees danger, I see opportunity.  I feel that it is desirable to blur 
 this line, and I see that happening in many other forms as well. 
  
  
 5.2  FTP and automated preprint servers 
  
 To see how confining the current paper journal system is, consider 
 preprints.  Half a century ago, there were practically no preprints, 
 since there were no technical means for producing them.  Journals were 
 the primary means for information dissemination.  Today, with xerox 
 machines widely available, preprints are regarded as indispensable. 
 Even Quinn [Quinn], who warns of the dangers of rapid publication, is 
 an advocate of rapid dissemination of results through preprints.  Many 
 mathematicians feel that preprints have become the primary method of 
 communicating new results.  It has been a long time since I have heard 
 of an expert in any mathematical subject learn of a major new 
 development in his or her own area through a journal publication.  (The 
 last such instance I can recall was caused by the Great Cultural 
 Revolution in China, which interrupted the informal communication 
 methods.)  Usually the experts either receive preprints as soon as they 
 are written, or they hear of them through the grapevine, and then, when 
 the results seem especially interesting, they request preprints from 
 the author or make copies of their friends' copies. 
  
 Preprint distribution can be done, and increasingly is done, via 
 e-mail.  It is much easier to write a shell script or create an alias 
 to send 50 copies electronically than it is to make 50 xerox copies, 
 stick them in envelopes, and address them.  Still, this does lead to a 
 messy decentralized system where each author has to decide who is to 
 receive the preprints.  There are two possible enhancements to it. 
 Either one of them would be a major advance, and either one could 
 become the main method of disseminating scholarly information in the 
 space of a year or so.  Either one would be extremely subversive to the 
 present journal system, and could lead to its demise. 
  
 One enhancement to present preprint distribution is to have an 
 automated preprint server.  There are several of them already 
 operational in mathematics, such as the one at Duke that covers 
 algebraic geometry.  They have not had much impact yet.  However, this 
 could change suddenly.  An instructive example is provided by the 
 system that was set up by Paul Ginsparg at Los Alamos [Ginsparg, Sci1, 
 Sci2].  In only one year, starting about two years ago, the high energy 
 theoretical physics community switched over almost completely to a 
 uniform system of preprint distribution that is run from Ginsparg's 
 workstation (and now also from some other sites that copy the material 
 from his).  Apparently nobody in theoretical physics can afford to stay 
 out of this system, as it has become the primary means of information 
 dissemination.  Even brief interruptions of service [Sci2] bring 
 immediate heated complaints.  This system has already been extended to 
 several other fields, aside from high energy theoretical physics, and 
 the requests to help in setting up the system are a major chore for 
 Ginsparg (private communication).  The main point about this system is 
 that it is cheap.  The software is available for free, and not much 
 maintenance is required.  Physicists submit preprints electronically 
 (in a prescribed version of TeX, and in prescribed format), the system 
 automatically files them and sends out abstracts to lists of 
 (automatically maintained) subscribers, and then the entire papers can 
 be retrieved through e-mail requests. 
  
 An important observation about Ginsparg's system is that the transition 
 to it was sudden, at least by the standards of the publishing world. 
 It took under a year from the time Ginsparg wrote his program to the 
 time it became the standard and almost exclusive method for 
 distributing new results in high energy theoretical physics.  Ginsparg 
 [Ginsparg] attributes the rapid acceptance of his system to the fact 
 that his area had already switched over to a system of mass mailings of 
 preprints as the primary information dissemination scheme, and regular 
 printed journals were of secondary importance.  Mathematics is not at 
 that stage.  However, this could change rapidly.  The use of e-mail and 
 anonymous ftp for distribution of mathematics preprints is spreading. 
 Other fields have switched or are switching to the use of Ginsparg's 
 system.  I would not find it surprising if mathematicians suddenly 
 adopted Ginsparg's system. 
  
 Can Ginsparg's system coexist with paper journals?  Theoretical high 
 energy physicists are still submitting their papers to the traditional 
 journals.  However, it is not clear how long that will continue.  If I 
 have heard of an interesting result that has been published in some 
 journal, and if I can order via e-mail a preprint of the same version 
 (except possibly for the formatting) from an automated preprint server, 
 why should I bother to go to the library to look for the journal?  If I 
 don't look at the journal, why should I mind if my library cancels its 
 subscription?  If there is anything that is certain, it is that my 
 library will keep coming back each year with lists of proposed journal 
 cancellations, so the pressure to give up more and more subscriptions 
 will continue.  One solution would be for publishers to require that 
 preprint copies be deleted from preprint archives once a paper is 
 published.  I doubt if this approach can work.  It is technologically 
 hard to enforce.  How can anyone keep track of all the copies that 
 might have been squirreled away on private disks?  Even more important, 
 would scholars tolerate such requirements?  Suppose you are getting 
 extensive praise for your latest masterpiece on cohomology of 
 transcendental monoids that has been circulated in preprint form by an 
 automated archive.  A message arrives from the publisher telling you 
 that your paper has just appeared, and asking you to withdraw the 
 preprint.  You do, and instantly you start getting e-mail complaints 
 from people who had heard of it from others or had only now gotten 
 around to looking at their accumulated list of preprint announcements, 
 and who suddenly find they cannot obtain it in way they are used to. 
 You tell them to go look in the journal.  Their e-mail replies come 
 back instantly and say that their library does not subscribe to that 
 journal, or has not received it yet, or ....  Would that not tempt you 
 to resolve never again to submit your papers to any journals that had 
 such a policy? 
  
 It is not necessary to have a centralized preprint server such as 
 Ginsparg's to subvert our current publishing system.  The natural 
 evolution of anonymous ftp directories can accomplish the same result. 
 Many people are familiar with the use of ftp to transfer files.  What 
 is happening is that various departments are setting up systematic 
 directories of preprints written by their members that can be accessed 
 by ftp.  A uniform naming convention is becoming common, so that 
 preprints from the Department of Mathematics at Celestial University 
 will  be accessible at ftp.math.celestialu.edu, and will be organized 
 into directories by year or name of author.  The logic of having a 
 uniform system is so overwhelming that I am sure this convention will 
 be adopted quickly and widely.  This will be extremely dangerous to the 
 traditional journals.  Decentralized data bases that are systematic and 
 accessible with no charge can serve the same purpose as centralized 
 preprint servers.  They can be combined into a single data base by a 
 programmer that writes the simple software to keep track of changes in 
 the various departmental databases and copy new additions over the 
 network.  Alternatively, they can be accessed by various Internet 
 tools, such as Gopher, Mosaic, or their successors, which present a 
 convenient interface that hides from the user the gathering of 
 information from all over the world.  (Given the evolution of software, 
 the distinction between a centralized preprint server and a 
 decentralized database will soon be immaterial.) In either case, the 
 result would be to give the scholar immediate access from anyplace on 
 the Net to preprints.  As with preprint servers, this is likely to doom 
 traditional journals. 
  
 It is possible for a field to rely just on preprints.  Ginsparg 
 [Ginsparg] writes that in theoretical high energy physics, they have 
 long been the primary means of communicating research results.  Rob 
 Pike, a colleague working in operating systems, reports (private 
 communication) that in his area journals have become irrelevant. 
 Communication is via e-mail and electronic exchange of preprints, 
 typically through anonymous ftp.  A recent announcement of reports 
 about a new operating system resulted in over a thousand copies being 
 made via anonymous ftp in just the first week. 
  
 It is easy to argue that the experience of operating systems is not 
 relevant to mathematics, since the final product is not a paper, but 
 the software.  However, the same is increasingly true of various areas 
 of mathematics.  There have been many complains by some mathematicians 
 that their efforts were not getting proper recognition, since what they 
 were producing was software, whether for solving partial differential 
 equations or doing geometric modeling, and journal publications were 
 not the right way to evaluate their contributions.  With electronic 
 publishing, this problem can be overcome. 
  
 According to Leo Guibas (private communication), in computer graphics, 
 journals and proceedings of the SIGGRAPH conference are the primary 
 means of communication.  The reason for the reliance on paper 
 publications in this area is the lack of standardized color display 
 equipment, so that the delays in publication are tolerated.  However, 
 there are problems, such as the publication of only abstracts in 
 SIGGRAPH proceedings, which are not fully refereed, and which are too 
 short to enable researchers to fully the work. 
  
 Graphics and operating systems might not have much relevance to 
 mathematics.  However, there are fields close to mathematics that do 
 not follow the usual standard for mathematical publications. 
 Theoretical computer science has standards of rigor that are comparable 
 to those in mathematics.  There are two big annual meetings, STOC and 
 FOCS.  Papers (or, to be precise, extended abstracts of about 10 pages) 
 to these conferences are submitted about six months in advance.  A 
 program committee then selects 60 or 70 out of 200-300 submissions. 
 The full papers are then published in the proceedings, which are given 
 out at registration to all participants, and can be purchased by anyone 
 from the publishers, ACM and IEEE.  The official policy is that since 
 the committee is acting on the basis of extended abstracts only, and in 
 any case does not have time to do a thorough refereeing job, the 
 proceedings publications should be treated as preliminary, and final 
 revised versions should be submitted to refereed journals.  However, 
 there have been perennial complaints that this was not being done, and 
 that researchers were leaving the proceedings drafts as the only ones 
 on record.  Recently, however, David S. Johnson has compiled a 
 bibliography of STOC and FOCS papers, and it appears that around 60 % 
 of them do get published in a polished form in a journal.  This is 
 considerably better than the folklore would lead one to believe. 
 However, for working researchers, practically all the information 
 dissemination takes place through early preprint exchanges, and 
 interactions at these conferences.  Moreover, acceptance at these 
 conferences is regarded as more prestigious than journal publications, 
 as one can see from letters of recommendation that get written.  Thus 
 here also it is possible to have a healthy field does not depend on 
 journal publications for the information dissemination.  However, the 
 situation is not ideal.  There are frequent complaints about errors in 
 the proceedings papers, and there have been a few notorious cases where 
 the results turned out to be completely wrong.  What is lacking here, 
 as with other informal preprint systems mentioned above, is a peer 
 review system, to provide the assurance of reliability. 
  
  
 5.3  The prepublication continuum and future systems 
  
 The popularity of preprints, of Usenet groups, and of mailing lists 
 shows that they do fill an important role for scholars.  On the other 
 hand, there is also a need for reliability in the literature, to enable 
 scholars to build on the accumulated knowledge.  One way to resolve the 
 conflict is to follow Quinn's advice [Quinn] and rigidly separate 
 distribution of information, such as preprints, from publication in 
 journals.  The former would be done rapidly and informally, while the 
 latter would follow the conventional model of slow and careful 
 refereeing with even extra delays built in to help uncover problems.  I 
 feel a better solution would be to have an integrated system that would 
 combine the informal Usenet-type postings with preprints and electronic 
 journal publication.  Stevan Harnad has been advocating just such a 
 solution [Harnad1], and has coined the terms scholarly skywriting and 
 prepublication continuum to denote the process in which scholars merge 
 their informal communications with formal publications. 
  
 I will describe the system I envisage as if it were operating on a 
 single centralized database machine.  However, this is for convenience 
 only, and any working system would almost certainly involve duplicated 
 or different but coordinated systems.  At the bottom level, anyone 
 could submit a preprint to the system.  There would have to be some 
 control on submissions (after all, computers are great at generating 
 garbage, and therefore malicious users could easily exceed the capacity 
 of any storage system), but it could probably be minor.  Standards 
 similar to those at the Abstracts of the AMS might be appropriate, so 
 that proofs that the Earth is flat, or that special relativity is a 
 Zionist conspiracy would be kept out, but discussions of whether Bacon 
 wrote Shakespeare's plays might get in (since there are interesting 
 statistical approaches to this question).  There would also be digital 
 signatures and digital timestamping, to provide authentication.  The 
 precise rules for how the system would function would have to be 
 decided by experimentation.  For example, one feature of the system 
 might be that nothing that is ever submitted could be withdrawn.  This 
 is already part of Ginsparg's system, and helps enforce quality, since 
 posters submitting poorly prepared papers risk having their errors 
 exposed for ever.  On the other hand, such a rule might be felt to be 
 too inhibiting, and so might not be imposed. 
  
 Once a preprint was accepted, it would be available to anyone. 
 Depending on subject classification or keywords, notification of its 
 arrival would be sent to those subscribing to alerting services in the 
 appropriate areas.  Comments would be solicited from anyone (subject 
 again to some minor length limitations), and would be appended to the 
 original paper.  There could be provisions for anonymous comments as 
 well as signed ones.  The author would have the opportunity to submit 
 revised versions of the paper in response to the comments (or his/her 
 own further work).  All the versions of the papers, as well as all the 
 comments, would remain part of the record.  This process could continue 
 indefinitely, even a hundred years after the initial submission. 
 Author X, writing a paper that improves an earlier result Y(123) of 
 author Y, would be encouraged to submit a comment to Y(123) to that 
 effect.  Even authors who just reference Y(123) would be encouraged to 
 note that in comments on Y(123).  (Software program could do much of 
 this automatically.) This way a research paper would be a living 
 document, evolving as new comments and revisions were added.  (I will 
 avoid talking of technical details of how this could be done, but only 
 a small subset of the facilities that hypertext systems are supposed to 
 provide would be required, especially since I do not envisage any 
 requirement for real-time updates.) This process all by itself would go 
 a long way towards providing trustworthy results.  There are many 
 issues that would need to be resolved before such a system could be set 
 up.  Would anonymous comments be allowed, for example? 
  
 Grafted on top of this almost totally uncoordinated and uncontrolled 
 system there would be an editorial and refereeing structure.  This would 
 be absolutely necessary to deal with many submissions.  While 
 unsolicited comments are likely to be helpful in deciding on the 
 novelty and correctness of many papers, they will not be sufficient in 
 all cases.  What can one do about a poorly written 100-page manuscript, 
 for example?  It seems that a formal review process would be 
 indispensable.  That is also Harnad's conclusion [Harnad1, Harnad2]. 
 There would have to be editors who would then arrange for proper peer 
 review.  The editors could be appointed by learned societies, or even 
 be self-appointed.  (The self-correcting nature of science would take 
 care of the poor ones, I expect.  We do have the vanity press even now, 
 and it has not done appreciable damage.) These editors could then use 
 the comments that have accumulated to help them assess the correctness 
 and importance of the results in a submissions and to select official 
 referees.  (After all, who is better qualified to referee a paper than 
 somebody who had enough interest to look at it and comment 
 knowledgeably on it?  It is usually easy to judge someone's knowledge 
 of a subject and thoroughness of reading a manuscript from their 
 comments.)  The referee reports and evaluations would be added as 
 comments to the paper, but would be marked as such.  That way someone 
 looking for information in homological algebra, say, and who is not 
 familiar with the subject, could set his or her programs to search the 
 database only for papers that have been reviewed by an acknowledged 
 expert or a trusted editorial board.  Just as today, there would be 
 survey and expository papers, which could be treated just like all the 
 other ones.  (Continuous updating would have obvious advantages for 
 surveys and bibliographies.)  All the advantages that Quinn claims for 
 our present system in providing reliable literature could be provided 
 by the new one. 
  
 Harnad [Harnad1, Harnad2] advocates a hierarchy of groups, with 
 individuals required to pass scrutiny before being allowed to 
 participate in discussions at higher levels.  I feel this will be 
 neither necessary nor desirable, especially in mathematics.  The best 
 structure might vary from field to field.  Harnad is a psychologist, 
 and he may be reacting to the fact that the proverbial people in the 
 street all fancy themselves experts in psychology, and qualified to 
 lecture on the subject to anybody.  On the other hand, most people 
 disclaim any expertise in mathematics.  Therefore I do not expect that 
 systems in mathematics will be flooded by crank contributions.  After 
 all, what crank will be interested in discussions of crystalline 
 cohomology, or pre-homogeneous vector spaces?  There is a need to 
 provide protection against malicious abusers of the system, but beyond 
 that restrictions to specific topics might suffice.  In a few cases 
 stronger controls might be needed.  For example, Wiles' proof of 
 Fermat's Last Theorem might attract many crank or simply uninformed 
 comments that would be just a distraction.  That is not likely to be a 
 problem for the bulk of mathematical papers. 
  
 Will there be any place for paper in a system such as that sketched 
 above?  I suspect it will be very limited, if there will be any.  In 
 paper publishing nothing can be changed once it has gone to the 
 printer.  Therefore this system cannot be adapted to provide the 
 opportunities for continuous updating and correcting that is available 
 with electronic publishing.  We rely on this system because it was the 
 only one that was feasible in the past.  However, we now have better 
 alternatives, and I expect them to dominate.  Perhaps the exceptionally 
 important papers will be collected periodically (after selection by a 
 panel of experts) and printed as a mark of distinction.  If that is 
 done, then the proposed system will in many ways resemble the one 
 advocated by Quinn.  Quinn suggested a minimum six month delay between 
 submission of a paper and publication.  The scenario I am sketching 
 would provide a 10 or 20 year delay, and even greater assurance of 
 reliability!  For all practical purposes, though, it is likely that 
 traditional paper journals and libraries will cease to matter to 
 scholars. 
  
  
 Acknowledgements:  This article provides my own personal view of the 
 future of mathematical journals.  Few of the observations and 
 predictions are original, and I have freely drawn on the ideas in the 
 papers listed below.  I have benefited greatly from extensive e-mail 
 correspondence with Paul Ginsparg and Stevan Harnad.  Helpful comments 
 were also provided by Joe Buhler, Dick Palais, and Bill Thurston.  I 
 thank Carol-Ann Blackwood, Dan Grayson, Eric Grosse, Leo Guibas, Jane 
 Kister, Dan Madden, Rob Pike, and Arden Ruttan for supplying useful 
 information. 
  
  
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