| The Internet has experienced a fascinating evolu- tion in the recent
past, especially since the early days of the Web, a fact well
documented not only in the trade journals but also in the popular
press. Unprecedented in its growth, unparalleled in its het-
erogeneity, and unpredictable or even chaotic in the behavior of
its traffic, "the Internet is its own revolution", as Anthony-Michael
Rutkowski, former executive director of the Internet Society, likes
to put it. At the same time, folklore has it that math- ematics
lies at the heart of Internet operation. After all, the argument
goes, mathematics is the language of computers, and the Internet
is cur- rently connecting tens of millions of them and still doubling
every year [Lo98]. Yet the Internet is a new world, one where
engineering reality wins over tradition-conscious mathematics and
requires "paradigm shifts" that favor a combination of mathematical
"beauty" and high potential for con- tributing to pragmatic Internet
engineering. In this article we take a look at how the Internet
differs in fundamental ways from the conventional voice networks,
how the (r)evolution of the Internet is impacting the world of
mathematics in the small as well as in the large both on how
mathematics is done and, for understanding the network itself, on
what sort of mathematics is done and why this, in turn, makes
Internet engineering a gold mine for new, exciting, and challenging
research opportu- nities in the mathematical sciences.
|