Computer networking, in particular the internet, has revolutionized the mathematical sciences. The revolution started in sciences where computers were already dominant (i.e., physics and numerical mathematics). This revolution has quickly spread to fields like pure mathematics, which traditionally has shunned such technology. We now live in a world where publication of results, especially in the physical sciences, is first through online electronic preprint services, often preceding old-fashioned paper publication by a year. We have seen the development of mathematical science collaborations, like the large-scale physics laboratories, the various mathematical physics supercomputing projects, and the various distributed projects at the Santa Fe Institute, that combine many researchers, via the internet, into what are effectively single functioning research groups.
The dominant mechanism, recently, for distribution of electronic preprints have been the World Wide Web (WWW, also known as the Web). The web operates by using links between documents that can be distributed on a global basis. The links point at other documents on the WWW using a standard for referencing files on internet called the Universal Resource Locator (URL) system. Generic web browsers, like Mosaic and NetScape, allow us to skim through a large sea of data, including scientific publications, simply moving from one piece of data to a related one by clicking on a highlighted reference to it. For the last couple of years, we have seen large online papers produced with references to their data sets, diagrams, and other images. We have also seen databases containing e-mail addresses of scientists, web pages detailing research within departments, and many other applications. On a simpler level, from the days of the first-generation Internet, before the web changed it forever, scientists have been communicating their results via electronic mail. Researchers working together, but at different locations, have been able to mail each other their latest results, including their papers. Indeed, in the physical sciences, there have been online preprint archives in existence for several years, greatly predating the web-based systems used today. The ease-of-use, however, of these systems has changed greatly with the advent of web technology.
Network technology has caused a massive change in the way that science is now performed: In physics, results are published within days of being discovered. Other researchers then respond in a matter of weeks, submitting their own papers to the network. This moves the average time for a piece of research from a matter of years to a month or less. A theoretical physicist is no longer up-to-date if they have not read yesterday's list of preprints in their precise field. The ability to keep so up-to-date has greatly stimulated research, and allowed many scientists to work together, simply because collaborations are no longer long-term commitments that require large amounts of time and travel resources. Collaborations are now short-term relationships with minimal requirements in travel. The ever-increasing growth in web technology has brought us to the point where we are approaching a quantum leap in the way that scientific research is performed and organized in our society.
However, the Web as it stands has severe limitations, and is showing its age. Web browsers, with only simple document links available to them, are restricted by how they can use the data that is available to them over the network. This has been partially curtailed by the use of web servers that provide various functions for the web, from searching, to archiving, and much more. Web servers, however, are remote from the user of a web browser, restricting the form of their interaction with the user. Furthermore, to keep the communication between the browser and a server to a well-defined standard, only the URL system can be used. The URL and corresponding Hypertext Markup Language (HTML) systems were a good thing, initially, because they made it easy to combine already existing tools together when the Web was first formed. Now, however, it is greatly restricting the flow of information possible on the Web, simply because new tools come into existence every day.
The problem is that a browser needs to be setup to understand all the protocols that are sent to it. It is very different from a computer on a researcher's desk, which can easily be given a new program to handle a new data format, or way of displaying that data. This has led to the infamous ``protocol explosion'' problem: each new way of displaying and describing information on the network needs new protocols, file types, and so on, to represent it. These new protocols must be added to the browser, via extensions to the software and/or ``helper applications'' that handle the displaying of specific forms of data. There are now so many protocols around, than one must spend a lot of time adding new entries to servers to handle them, and, even worse, adding new software (helper applications) to the remote researcher's browsers. The explosion has even led to the need for information providers to present documents in many formats, with the hope that a user has the technology and software to view at least one form of them. This is obviously highly inefficient, and restricting, as one format may not have the same capabilities as another. For instance, a plain PostScript file does not have the hyperlinking capabilities as an HTML file, but an HTML file is limited when it comes to presentation quality. This problem is worst when it comes to the mathematical sciences, simply because our need for flexible forms of data is greatest. Our data is often formatted in ways that are appropriate for our own fields of study, and it is often difficult to give it to other researchers, without giving them specialized software at the same time.
Collaboration, which is surely our most important aim in a rapidly moving, multidisciplinary, research world, is greatly hampered by the protocol explosion problem. This is due to the fact that collaborators must be able to exchange data in compatible ways, and thus, to initiate a collaboration, researchers need to install pieces of software that make communication possible. Unfortunately, extensive, specialized, computer knowledge is needed to configure departmental networks, and install communication software. All the complicated configuration must be done, even before a connection to another researcher can even be initiated. Often computer-based collaboration is stymied, simply because it takes too much time and computer knowledge to install and set up the wonderful tools that are available to us.
The present state of affairs seems to be depressing--the very same technology that opens a new future for us in the mathematical sciences seems by its own success to be holding us back. However, as I shall demonstrate, technology itself comes to the rescue.