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Life in the Fast Lane


Mathematics is more important now than it has ever been. More mathematics is being done both inside and outside of universities. Admittedly not all of it is called mathematics---among other things, it might be called robotics, or financial analysis, or operations control, or engineering, ---but when we look closely there is no doubt that we are living in the truest Golden Age for mathematics to date.
There are indications that this Golden Age is giving way to yet another due to the influence of technology. Mathematics has fundamentally affected technology, most notably computers. It is now clear that the converse will also be true. Technology, usefully falling into five major categories, has already changed mathematics dramatically, and the pace of change is accelerating. The categories are
  1. Communications (between researchers): Ordinary mail, phone, fax, e-mail, and now the Web make the synergy of group effort progressively more effective. This development is at least as much software as hardware---there is a (more or less) standard mode of communicating mathematical papers amongst ourselves, based on Donald E. Knuth's TeX program and the LaTeX set of macros, among others.

  2. Communications (via publication): Although no longer completely separable from the previous category, changes in how mathematical knowledge is formally communicated are manifold. The increased electronic distribution of papers is pressuring existing journals to adapt; as preprint distribution becomes the primary means of scholarly communication the mechanisms of peer review are in danger of being upset and the accepted importance of published results is being transformed; conference proceedings are being moved to all-electronic format for timely access and cost-effectiveness; conventional information content is being forced to make room for alternate forms which are largely digitally generated, maintained and accessed. Examples include images, videos, animations, active tools/resources, audio, etc.

    The impact upon the conventional publication industries will be dramatic and there is widespread concern for the groups who depend on those traditional means. These include publishers, authors and readers, although it is the publishers who will be most pressed to establish a viable role for themselves. Of particular concern for mathematics is the future of professional societies who depend on the revenue generated by journals.

  3. Transportation: Cheaper air travel, and the granting structure that allows mathematicians to take advantage of it, have facilitated face-to-face meetings of mathematicians with each other and with users of mathematics. This seems to be the most effective method of generating interest in various methods or problems. However, this luxury may be endangered in the face of economic changes.

  4. Communications (between professor and student): We are now seeing a steady growth of the use of video, overhead display of computer screens, in-class use of calculators or hand-held computers, e-mail, newsgroups on USENET, and the Web. These are welcome changes from the blackboard which has so long dominated the transmission of mathematics from professors to students. Furthermore, there are several embryonic virtual universities in existence right now, radically changing the confines of the traditional classroom setting. Of course, these high-tech tools are not always appropriate, but they are particularly effective for communication of computational mathematics courses.

    Given economic pressures, we can calmly predict a reduction, perhaps even a drastic reduction, in the number of graduate and senior undergraduate mathematics courses offered at different universities. The students will instead use video conferencing equipment to take ``courses" from professors at other networked universities. The facilities are in place, the demands for cost-cutting are in place, and faculty retirements are taking place.

  5.   Scientific Computation, comprising both symbolic computation and numerical computation, is at last coming into its own, both for research and teaching.

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