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Amount of mathematics knowledge
Posted:
Jun 23, 1995 8:27 AM


Mathematicians usually measures the amount of mathematical knowledge by a rough count of the pages published in mathematical journals. Of course, this requires one to view books and manuscripts before professional journals became the norm. Mathematical journals are typically restricted to those which are considered as "research journals". There is a long article by Andrew Odlyzko concerning the future of journal publication. One of the old postings (not by me) mentioned that a "Mr. Odlyzko" ..... Odlyzko is a world class number theorist (among others) who had been working in ATT research lab. (the old Bell Lab) for many, many years. He and other mathematicians used a rough count of the type I mentioned and showed the exponential growth (going backwards) on the number of pages of journals articles. The statement about over half of the math. knowledge (or something close to this) were recorded in the last 100 years is in the right ballpark. One can, of course, carry out an endless debate on whether this is a "meaningful" way of measuring the amount of knowledge. The point Odlyzko was trying to make is that there may soon come a day when the entire journal publication enterprise will undergo a cataclysmic change. The technology is already available (in terms of hardware and software). He was alerting the community that unless we think about the problem, there can be a serious problem in terms of "knowledge loss". The "essential" stuff becomes indistinguishable from the "nonessential" or even "incorrect" stuff. Odlyzko did not suggest solutions, he identifies the problem on the basis of his extensive knowledge of pure mathematics and technology. Nevertheless, it should be mentioned that these recent developments in mathematics are not disjoint from the early works. Unlike most experimentally based sciences, "old" mathematics does not become "useless". A respected mathphysicist (Eliot Lieb) had noted (unfortunately, his draft of a letter to the NYTimes was not published) that one of the most remarkable facts about the Fermat Last Theorem is that the work done on that problem over the past 350 or so years can still be read by mathematicians with profit. In no other scientific fields is there anything that comes close. Namely, technologically advances most often renders previous works "obsolete". Mathematics should not be so treated. In many ways, mathematics is closer to "art" than to "science". However, as ChiTien Hsu posted, mathematics is at the foundation of all science and engineering...... By comparison with many of the "big sciences", research in "pure mathematics" costs a drop in a bucket. The current fasion of "science bashing" may have the unfortunate side effect of drying up that "drop" in the bucket. The federal expenditure in terms of supporting "pure math" per year is something less than one half of a B2 bomber. By the time one look at how this "pork barrel" is divided up, one sees that the push for "applied research" is overwhelming the "basic research". The idea that "basic research" in mathematics is no longer needed is indeed a very shorted sighted view of the role of mathematics. No, mathematics should not be divorced from technology. However, it should not made to be so dependent on technology that "it goes down with the ship" when the current technology gets overtaken by advances. The difficulty rests with a "proper" balance. This is the essence, in my opinion, of the important message from ChiTien Hsu's post.
Han Sah, sah@math.sunysb.edu



