21-09-2017, 01:09 PM
The Internet has undergone a fascinating evolution in the recent past, especially since the early days of the Web, a fact well documented not only in professional journals but also in the popular press. Unprecedented in its growth, unprecedented in its heterogeneity, and unpredictable or even chaotic in the behavior of its traffic, "Internet is its own revolution," says Anthony-Michael Rutkowski, former executive director of the Internet Society. At the same time, folklore says that mathematics is at the heart of the Internet operation. After all, the argument argues, mathematics is the language of computers, and the Internet is currently connecting tens of millions of them and still doubling each year [Lo98]. However, the Internet is a new world where the reality of engineering wins over traditionally aware mathematics and requires "paradigm shifts" that favor a combination of mathematical "beauty" and high potential to contribute to the pragmatic engineering of the Internet . In this article we are going to take a look at how the Internet differs in fundamental ways from conventional voice networks, how the ® evolution of the Internet is affecting the world of mathematics in both small and large- how mathematics and to understand the network itself, what kind of math is done, and why this, in turn, turns Internet engineering into a gold mine for exciting new and challenging research opportunities in the mathematical sciences .