The Mathematics Survey project seeks to encourage development of infrastructure for communicating mathematical knowledge, at or near the research level, freely over the web. A five page article to appear in the Notices of the AMS. This site was originally created by Jim Pitman and David Aldous. Anyone interested in participating in the project to contact the founders via email to x@y where x = mathsurv and y = stat.berkeley.edu
Open Access Electronic Survey Journals
Survey articles are an intrinsically worthwhile way to communicate mathematical knowledge. But there are few existing venues where survey articles in mathematics can be published with open access via the web. In 2004 Jim Pitman and David Aldous founded the journal Probability Surveys devoted to survey papers in probability. Volumes 1 and 2 are complete and Volume 3 (2006) is growing. Jim Pitman and David Aldous are in the process of launching a companion journal Statistics Surveys. Another journal participating in the project is Ensaios Matemáticos published by the Sociedade Brasiliera de Matemática. The more mathematicians who found sister survey journals in mathematics, supported by a variety of organizations, the better off we shall all become.
The Encyclopedia Layer
For any mathematical topic there ought to be a place on the web where you can find a brief description (encyclopedia entry) of the topic, together with annotated links to survey papers, research papers etc. Today, only a few such sites exist, created independently by different individuals. For instance:
- The Mathematical Atlas created by Dave Rusin, provides a guide to the top level of the Mathematics Subject Classification (MSC 2000);
- The Number Theory and Physics Archive created by Matthew Watkins, provides a guide to research literature which links number theory and physics.
- The site Perfectly Random Sampling with Markov Chains created by David Wilson is one of a small number of high quality sites devoted to specialized subjects.
To provide access to various subject sites, companion Mathematics Survey journals, and other online resources in mathematics, including subscription services such as:
as well as free services such as:
Mathematical Publication Today
Textbooks and monographs on one side, and peer-reviewed research journals on the other side, are the most familiar categories of mathematical publication. They have not changed in essence for 50 or 100 years, and likely will not change much in the near future - the transition of journals from paper to electronic format facilitates physical access without changing the roles of authors, referees and editors and (as yet) without resolving contentious issues of price. But cyberspace provides opportunity for a much broader spectrum of types of publication. One can already find online, for instance:
- unreviewed preprints
- peer-reviewed research papers
- peer-reviewed survey papers
- monographs and polished lecture notes
- lectures recorded by slide presentations, scribe notes, and videos
- literature databases
- retroactive digitization of old print literature
- descriptions by individuals or groups of their ongoing research activities
- encyclopedias at an elementary level.
There are three unsatisfactory features of its structure.
Cost of journals: Commercial publishers impose ever-increasing subscription costs on their ejournals, thereby restricting access, with negligible compensating advantages.
Fragmentation: The totality of mathematical material in cyberspace is at present neither well linked together nor intelligently searchable. Seeking a readable account of Topic X, one could use a search engine like Google or MathSciNet. But Google treats a mathematics page as just another page on the Web, having no conception of the logical interrelationships of mathematics. The new Google Scholar service restricts the search to the scholarly literature, accessing the content of many copyrighted books and journals as well arXiv and other open access sources. But it is not easy to restrict such a search to expository material. MathSciNet and Zentralblatt MATH enable basic searches like "find papers by author A in subject S". But there is no resource currently available for a search like "find a survey on topic X accessible to a first year graduate student". Designing a system which can respond to such queries seems to require more human intervention. As another instance, when you post your lecture notes on subject S, you currently have no systematic way of providing links to your material which make it easily accessible to someone searching for material on subject S.
Compartmentalization: Research progress continually increases the gap between research frontiers and first-year-graduate-textbook level material, and the gaps between different disciplines. Monographs help fill these gaps, but we see an increasing need for survey papers. At present, writing of expository survey papers carries insufficient prestige, and such papers are often scattered in hard-to-find conference proceedings and expensive handbooks. Writing high-quality surveys should be encouraged, to help organize mathematical knowledge in accessible form, and to facilitate interdisciplinary work.
Going forward, Mathematics Survey will contain mathematical information that is more easily accessible to non-scholars. It is hoped that statistical analyses written with the general public in mind as oppsed to scholarly literature will encourage greater interest in the field of mathematics.