Mathematics and the WWW

Section 4:
Why is the Web Being Used in Mathematics?


4 March 1997

Although it is made of thin, delicate strands, the web is not easily broken.
                                                              E.B. White, Charlotte's Web


Why is the Web being used in Mathematics?

It's part of the modern communication bundle
First we all became addicted to email and many of us began transferring from other computers files that contained TeX versions of mathematics papers. At the same time we began to use computer programs with wonderful graphics capabilities, such as Maple, Mathematica, and Sketchpad. By then we were ripe for the picking. The World Wide Web came along as a means for high energy physicists to communicate, NCSA developed the elegant graphical interface Mosaic, and off we went.

Email is becoming more Webly (the new version of Eudora allows you to view attached graphics automatically in the body of a message and to format and color text more easily), and Web browsers with more email features are on the way.

Improving graphic communication is important to many mathematicians, as is access to information. The ability to publish one's own informal and formal work easily and attractively and broadly is new and exciting. (When I browse and look at what others are doing I feel good about our profession.)

Folklore had it that in 1995 over 80 percent of all the scientists who ever lived were on the Internet. Presumably, the people "networked" constitute the majority of early adopters and innovators.

Ease and simplicity
URL = uniform resource locator. Point and click. One size fits all. That's elegance -- even though it ain't perfect.


Hypertext

What is hypertext and why will it be so important?
Up until quite recently the word "hypertext" could be heard to pass the lips of very few mathematicians other than Tom Banchoff. The term was coined in 1965 by Ted Nelson and a hypertext editing system was developed in 1967 by Andy van Dam, a classmate of Ted's at a small EPADEL college.

What is hypertext? Nonlinear presentation of ideas (well, okay, that's hypermedia). Hypertext makes it possible for you to follow your own interests and needs in reading/seeing/hearing/ (soon feeling) a document -- you can look at examples (perhaps interactively), check definitions, branch to references, etc., as you wish. It quickly became apparent to me that I needed hypertext to accommodate the diverse mathematical interests and backgrounds of my audience. (Now if I can only invent hypertalk in time for the actual lecture!)

Here's a research paper in mathematics that is an example of an attractive possible communications future. It's written by Davide Cervone, who is also giving a talk at the EPADEL meeting. And here's a lovely paper by EPADEL's own Doris Schattschneider. (You need Adobe Acrobat (free) to download it.)

Here's a nice hypermedia exposition on the hypercube. Here's the new hypertextual MAA Journal of Communications in Visual Mathematics, which lists Banchoff and Cervone as its editors.

What's wrong with hypertext?
Most of us don't know how to read it yet -- we print it out, thereby rendering it linear. In general the hypertextual quality of a document may be inversely proportional to one's ability to print it out as a coherent document.

Okay, most of us don't know how to write hypertext yet either. Large hunks of text on a screen cry out to be printed. (Please send me feedback as to whether I've achieved a good balance in presenting this document -- or on anything else you wish.) It seems to me that writing successful hypertext requires a good deal of planning and thought, and that we lack clear models.

"Footnotes" are needed; you shouldn't have to jump completely from one context to another. As an example of a useful direction, just pass your cursor over the annotated version of the Math Forum home page, which uses JavaScript for this purpose.

Here's a nice, balanced discussion of hypertext: HyperContent, Hyperjunk. The Geometry Center has materials from a course on Communicating Mathematics with Hypertext.

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Gene Klotz