The Prospects for Mathematics in a Multimedia Civilization

Philip J. Davis

I. Multimedia Mathematics

First let me explain my use of the phrase "multimedia civilization." I mean it in two senses. In my first usage, it is simply a synonym for our contemporary digital world, our click-click world, our "press 1,2, or 3 world", a world with a diminishing number of flesh-and-blood servers to talk to. This is our world, now and for the indefinite future. It is a world that in some tiny measure most of us have helped make and foster.

In my second usage, I refer to the widespread and increasing use of computers, fax, e-mail, the Internet, CD-ROMs, iPods, search engines, PowerPoint, and YouTube—in all mixtures. I mean the phrase to designate the cyberworld that embraces such terms as interface design, cybercash, cyberlaw, virtual-reality games, assisted learning , virtual medical procedures, cyberfeminism, teleimmersion, interactive literature, cinema, and animation, 3D conferencing, and spam, as well as certain nasty excrescences that are excused by the term "unforeseeable developments." The word (and combining form) "cyber" was introduced in the late 1940s by Norbert Wiener in the sense of feedback and control. Searching on the prefix "cyber" resulted in 304,000,000 hits, which, paradoxically, strikes me as a lack of control.

I personally cannot do without my word processor, my mathematical software, and yes, I must admit it, my search engines. I find I can check conjectures quickly and find phenomena accidentally. (It is also the case that I find too many trivialities!) As a writer, these tools are now indispensable for me.

Yes, the computer and all its ancillary spinoffs have become a medium, a universal forum, a method of communication, an aid both to productive work and to trouble making, from which none of us are able to escape. A mathematical engine, the computer is no longer the exclusive property of a few mathematicians and electrical engineers, as it was in the days of ENIAC et alia (late 1940s). Soon we will not be able to read anything or do any "brain work" without a screen in our lap and a mouse in our hands. And these tools, it is said, will soon be replaced by Google glasses and possibly a hyperGoogle brain. We have been seduced, we have become addicts, we have benefited, and we hardly recognize or care to admit that there is a downside.

What aspects of mathematics immersed in our cyberworld shall I consider? The logical chains from abstract hypotheses to conclusions? Other means of arriving at mathematical conclusions and suggesting actions? The semiotics of mathematics? Its applications (even to multimedia itself!)? The psychology of mathematical creation? The manner in which mathematics is done; is linked with itself and with other disciplines; is published, transmitted, disseminated, discussed, taught, supported financially, and applied? What will the job market be for its young practitioners? What will be the public's understanding and appreciation of mathematics? Ideally, I should like to consider all of these. But, of course, every topic that I've mentioned would deserve a week or more of special conferences and would result in a large book.

Poincaré's Predictions

We have now stepped into the new millennium, and inevitably this step suggests that I project forward in time. Although such projections, made in the past, have proved notoriously inadequate, I would be neglecting my duty if I did not make projections, even though it is guaranteed that they will become the objects of future humorous remarks.

Here's an example from the past. A century ago, at the Fourth International Congress of Mathematicians held at Rome in 1908, Henri Poincaré undertook such a task. In a talk entitled "The Future of Mathematics," Poincaré mentioned 10 general areas of research and some specific problems within them, which he hoped the future would resolve. What strikes me now in reading his article is not the degree to which these areas have been developed—some have—but the inevitable omission of a multiplicity of areas that we now take for granted and that were then only in utero or not even conceived. Though the historian can always find the seeds of the present in the past, particularly in the thoughts of a mathematician as great as Poincaré, I might mention as omissions from Poincaré's prescriptive vision the intensification of the...