O n the surface it seems implausible that a colonial scientist could be characterized as a mathematician by today’s standards. Yet the single aim of this note is to provide evidence that two of David Rittenhouse’s papers from 220 years ago qualify him as a modern analyst. Rittenhouse (1732–1796) had no formal education and never earned a degree. Except for a brief appointment as professor of as...

This paper complements McCarthy’s “The well designed child”, in part by putting it in a broader context, the space of possible well designed progeny, and in part by relating design features to development of mathematical competence. I first moved into AI in an attempt to understand myself, especially hoping to understand how I could do mathematics. Over the ensuing four decades, my interactions...

The aim of this paper is to improve a theorem of János Kollár by a different method. Given a Complex projective threefold X of general type, suppose the plurigenus Pk(X) ≥ 2, Kollár proved that the (11k+5)-canonical map is birational. Here we show that either the (7k +3)-canonical map or the (7k +5)-canonical map is birational and the m-canonical map is stably birational for m ≥ 13k+6. If we su...