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Publishing a mathematical paper in a reputable journal is one way of
making mathematical knowledge accessible. People whose libraries
contain that particular journal (one among tens of thousands of
journals) read that paper, interpret the results and notation in terms
of the problem under consideration, and implement any algorithms
described. This of course leaves the work (and danger) of correctly
inferring the intention behind the content to the reader, often an
onerous, error-prone and inefficient task.
Surely it is better if the best algorithms and most useful mathematical
knowledge are already implemented in a standard, widely available
program for immediate use. At best, the mathematician user could well
use the program without knowing all the technical refinements that make
the computation possible---though in our view a basic knowledge on the
part of the user is indispensable, providing confidence that the
algorithms are not being totally umis-used. At worst, it provides a
common basis or language for communication and exchange, one which has
been carefully crafted for precision, accuracy and consistency, much
like the traditional logical formalism behind conventional
mathematics.
This appears to be what is happening today. A large portion of mathematical
knowledge is being encoded into computer algebra systems and into
numerical packages for scientific computation. How many mathematicians
would be able to write a program which could evaluate the Jacobian
elliptic functions efficiently and accurately over the complex plane?
But once it's done, then everyone can use it (assuming the right
computer with the right software with the requisite license).
It is this encoding of mathematical knowledge that we find the most
significant aspect of modern technology. The next most significant is
the exchange or communication of that encoded knowledge, for example
the act of asking on the Internet for help on a problem---by keyword search
or simply a query in the right newsgroup---is also extremely
important. There is a tendency to drown in student-type questions
(it's considered unethical to ask for outside help on assignments, for
example, but it has been known to happen on some newsgroups) but
nonetheless an important amount of research communication happens on
the Internet.
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Next: Electronic Distribution of
Up: Technology and Access
Previous: Technology and Access
omp@cecm.sfu.ca