The "Artificial Mathematician" Objection: Exploring the (Im)possibility of Automating Mathematical Understanding

Reuben Hersh confided to us that, about forty years ago, the late Paul Cohen predicted to him that at some unspecified point in the future, mathematicians would be replaced by computers. Rather than focus on computers replacing mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being joined by “artificial mathematicians” in the proving practice—not just as a method of inquiry but as a fellow inquirer

Adoption of network technologies in the presence of converters

In many high-tech industries, the emergence of new digital technologies allows companies to develop converters to overcome technology incompatibility. In this paper, we analyze the effects of converter introduction on the adoption process of competing, incompatible technologies in the presence of network externalities. Converter introduction may accelerate, extend or reverse the technology lock-in process. We determine which conversion options are profitable for weak as well as for dominant incumbents, depending on the timing of converter introduction and the degrees of conversion. We find that the optimal strategy for weak incumbents is to introduce full one-way converters early. For dominant incumbents, the optimal conversion option is to provide two-way converters with partial compatibility for the users of the competing network at a later introduction time. We illustrate our analytical results with numerical examples.compatibility, consumer choice, converter, network externality, standards war, technology adoption,

Rotterdam’s Superdiversity from a Historical Perspective (1600–1980)

This series is the official book series of IMISCOE, the largest network of excellence on migration and diversity in the world. It comprises publications which present empirical and theoretical research on different aspects of international migration. The authors are all specialists, and the publications a rich source of information for researchers and others involved in international migration studies. The series is published under the editorial supervision of the IMISCOE Editorial Committee which includes leading scholars from all over Europe. The series, which contains more than eighty titles already, is internationally peer reviewed which ensures that the book published in this series continue to present excellent academic standards and scholarly quality. Most of the books are available open access. For information on how to submit a book proposal, please visit: http://www. imiscoe.org/publications/how-to-submit-a-book-proposal