Notices of the AMS July 1996 Compumatics versus Mathematics? ---------------------------------------------------------------------------- I was appalled when I read the letter written by Dr. J. J. Uhl, entitled ``Steven Krantz versus Calculus & Mathematica'' (AMS Notices, vol. 43, no. 3, March 1996, pp. 285-286). The style of the letter surprised me the most. Why is Dr. Uhl so angry? What tempted him to use such words as ``peeve ... bogus ... attacked ... infuriated ... sputter ... ''? I read a short note, ``Math for Sale'', by S. Krantz in the Notices of October 1995. It does not contain such terms, despite Dr. Uhl's qualification [of it] as ``a sarcastic personal attack''. Dr. Uhl et al. have written a textbook Calculus & Mathematica (C&M). They like it; their students like it. So, good luck, go ahead! Why be angry? I should confess right away: I did not read that text, nor did I try the software. To those who are unaware, it is worth noting that Mathematica is not mathematics; it is computer software that allows one to manipulate and visualize formulae. I have attended a demonstration of that software. In fact, the title Calculus & Mathematica is misleading because it sounds like Calculus & Mathematics, a change in just one letter which one may overlook (as I did at first). A proper unambiguous meaning of the title is ``Calculus via Compumatics''. Compumatics is mathematics that can be done by computer. There is nothing wrong or offensive in this term; it reflects a fact of life. Mathematicians use computers and computer software as a tool in mathematical research and applications. Computer scientists (programmers) use mathematical products (algorithms, iterative methods, tables of formulas) to produce software packages. Compumaticians can use both mathematics and software packages to produce new educational tools, such as computer-assisted interactive books, CM-videocassettes, CD-ROMs, etc. Here I use the abbreviation CM to stand for CompuMatics. Disclaimer. As is now common in the software market, the author of this note does not bear any responsibility for the quality of compumatical products nor for any consequences therefrom. In simple words it means the following. Once in use, a computer with its software is detached from its creators and represents a separate entity whose creators are forgotten by users. The creators, however, are usually engineers and programmers who are not mathematicians by profession. Their products naturally carry only their knowledge and experience and may present restrictions, not the best solutions, and other inconveniences for a teacher and for a student. In this note, a CM product is not evaluated nor discussed. We discuss certain aspects of the phenomenon, not its particular realizations. Compumatics can speed up and enhance the teaching process, upgrade the art of problem solving, intensify the thought processes, and downsize departments related to mathematics. For these qualities, compumatics has immediate and visible dollar value. Nobody talks about this aspect, as if it were unethical. Perhaps it is time to discuss the issue, since corridors are already full of rumors on the subject. In order not to be blamed or labeled (libeled), I have to stress that I am not passing judgment nor weighing the pros and cons of a current trend in society. I would simply like to raise some points which are now in a mist. 1. Compumatics puts the accent on computer-assisted education, similar to CAD (computer-aided design) and CAM (computer-aided manufacturing), with the difference that it introduces elements of computer automation into the human brain. We know there are wonder people who can easily multiply ten-digit numbers faster than computers. It is probably this kind of automation, on a somewhat higher level, that compumatics may introduce into the brain of some students. Whether it is good or bad, I do not know. However, if CM succeeds in addicting students, especially in high school, to the constant use of some software, it will boost computer and software sales, making profits and creating jobs, which is now the first priority. 2. With the introduction of compumatics in schools and universities, teaching mathematics as it is now can be gradually phased out with downsizing and consolidating corresponding departments, since compumatics obviously requires fewer teachers than mathematics (there are hidden costs, but these are out of sight yet). This process has already begun with the pioneering innovation of the University of Rochester (see AMS Notices, vol. 43, no. 3, March 1996, pp. 300-306). Clearly, it seems to save many tax dollars, which is another first priority nowadays. 3. Eventually, compumatics teachers will also be eliminated, since CM can be taught by a CD-ROM in a teacherless classroom. Imagine a classroom for twelve hundred students (the University of Western Ontario has such a classroom) with small screen PCs on each desk and a big-screen TV with CD-ROM at the front. The students will have great fun and enjoy unlimited freedom without the boring supervision of an instructor. Sensing an objection (``a CD-ROM cannot answer questions! ... ''), I have to disappoint opponents of compumatics. Yes, a CD-ROM can answer all questions from a student audience of any size. Proof? Very simple. To count the maximum volume of questions, suppose that future computers take questions directly from the brain, without using voice, paper, or keyboard, and transmit answers also directly to the brain of every individual student who has asked that question, this being done for all the different questions in a classroom of any number of students. Due to the finite speed of light and a finite number of students on earth, we get a finite number of questions that can be asked during a 45-hour one-semester course. Usually, it is not more than one hundred questions that are asked during a normal course. It is a trivial matter to supply a CD-ROM with a finite number of prerecorded answers or to produce a software that can gradually incorporate correct answers into a CD-ROM online with the flow of questions being actually asked by students. I am not going to argue this apocalyptic scenario. The only point I want to make is that a CD-ROM can replace all CM teachers, with seemingly great savings in public dollars. Such are the immediate economic gains from substituting compumatics for mathematics in education. At least, it seems so. There are expenditures, of course. Accountants can calculate the net savings and profits. Doctors can treat some exhausted, burnt-out students. In a decade or so, the country will see the results of such efficient and speedy education. Students, however, may render their judgment much faster. In the meantime, compumaticians will get all the funding they need. Mathematicians are unlikely to get funding. However, they can survive as their forefathers did in the last century. Of course, they would have to downsize and restructure (not downgrade) their activities. Most basic mathematical research will go underground or relocate to ``less efficient'' countries. Do we need a debate? I doubt it. I remember there was a popular explosion in favor of tele-education some ten or fifteen years ago. We were invited to a nice lecture hall with a TV for every ten seats, where we were given an excellent presentation of how fascinating it would be to have a tele-university with direct home broadcasting. Imagine a genius from Göttingen or Harvard giving a lecture worldwide for students sitting at home with a cup of good Irish coffee, taking notes or simply videorecording. ... It failed, and we do not hear about it any more. Maybe the Internet can revive the enterprise? Or compumatics with a CD-ROM in a teacherless classroom? Hey, why a classroom? [Why not] direct home broadcasting? Dreams, dreams, ... Or losing touch with reality? People need a clean, clear-cut experiment, preferably not on the scale of a country, as recommended by Dr. Uhl (`` ... in so doing we can help to renew an infrastructure that will support research mathematics and mathematics education into the next century. ... '', Notices, vol. 43, no. 3, March 1996, p. 286). Maybe the University of Rochester can turn its innovative initiative into creating compumatics faculty to promote the shining path of computer-generated science for the everlasting progress of mankind. Efim A. Galperin Universite' du Quebec a' Montreal (Received March 14, 1996)