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Topic: Amount of mathematics knowledge
Replies: 1   Last Post: Jun 24, 1995 12:39 AM

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Chih-Han sah

Posts: 75
Registered: 12/3/04
Amount of mathematics knowledge
Posted: Jun 23, 1995 8:27 AM
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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 "non-essential" 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 math-physicist (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 Chi-Tien 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 B-2 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 Chi-Tien Hsu's post.


Han Sah, sah@math.sunysb.edu





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