We present the emerging discipline of Mathematical Knowledge Management (MKM), which studies the possibility of computer-supporting and even automating the representation, cataloguing, retrieval, refactoring, plausibilization, change propagation and in some cases even application of mathematical knowledge. We focus on theory graph technology here, which supports modular and thus space-efficient...

I am one of a growing number of research mathematicians who are substantially engaged with school mathematics education. Such outreach has a long and honorable tradition. In this lecture, I illustrate some of the ways that I think this can be helpful, and even essential. Upon his retirement in 1990 as president of the ICMI, Jean Pierre Kahane spoke perceptively of the intimate connection betwee...

In this paper, we briefly overview how, historically, string theory led theoretical physics first to precise problems in algebraic and differential geometry, thence computational geometry the last decade or so, now, few years, data science. Using Calabi–Yau landscape — accumulated by collaboration of physicists, mathematicians computer scientists over four decades as a starting-point concrete p...

This paper is concerned with the status of 1 / 0 and ways to deal with it. These matters are treated in the setting of Komori fields, also known as non-trivial cancellation meadows. Different viewpoints on the status of 1/0 exist in mathematics and theoretical computer science. We give a simple account of how mathematicians deal with 1 / 0 in which a customary convention among mathematicians pl...