Mathematics and the internet: A source of enormous confusion and great potential. Defense Technical Information

or many mathematicians and physicists, the Internet has become a popular real-world domain for the application and/or development of new theories related to the organization and behavior of large-scale, complex, and dynamic systems. In some cases, the Internet has served both as inspiration and justification for the popularization of new models and mathematics within the scientific enterprise. For example, scale-free network models of the preferential attachment type [8] have been claimed to describe the Internet’s connectivity structure, resulting in surprisingly general and strong claims about the network’s resilience to random failures of its components and its vulnerability to targeted attacks against its infrastructure [2]. These models have, as their trademark, power-law type node degree distributions that drastically distinguish them from the classical Erdős-Rényi type random graph models [13]. These “scale-free ” network models have attracted significant attention within the scientific community and have been partly responsible for launching and fueling the new field of network science [42, 4]. To date, the main role that mathematics has played in network science has been to put the physi-cists ’ largely empirical findings on solid ground