Where Mathematics Meets the Internet

The Internet has experienced a fascinating evolution 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 heterogeneity and unpredictable or even chaotic in the behavior of its tra c 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 mathematics lies at the heart of Internet operation After all the argument goes mathematics is the language of computers and the Internet is currently connecting tens of millions of them and still doubling every year Lo 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 contributing to pragmatic Internet engineering In this article we take a look at how the Internet di ers 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 opportunities in the mathematical sciences