Geometrical foundations of asymptotic inference are described in simple cases, without the machinery of differential geometry. A primary statistical goal is to provide a deeper understanding of the ideas of Fisher and Jeffreys. The role of differential geometry in generalizing results is indicated, further applications are mentioned, and geometrical methods in nonlinear regression are related to those developed for general parametric families.

R. A. Fisher's account of the decline of inverse probability methods during the latter half of the 19th century identifies Boole, Venn and Chrystal as the key figures in this change. Careful examination of these and other writings of the period, however, reveals a different and much more complex picture. Contrary to Fisher's account, inverse methods--at least in modified form--remained theoretically respectable until the 1920's, when the work of Fisher and then Neyman caused their eclipse for the next quarter century.

This paper provides an annotated bibliography of over 100 articles containing quantitative methodology relating to the AIDS epidemic. The majority of the work describes mathematical and statistical models of the growth and extent of the epidemic, and statistical procedures to estimate key components of the disease process. Among these components, attention has focused primarily on estimating the incubation distribution. It is hoped that the bibliography will not only interest those currently active in the field but also encourage other statisticians to become involved in AIDS research efforts. The general area of AIDS research appears to be a rich source of statistical problems of considerable interest and importance.

In Martin Gardner's Mathematical Games column in the February 1960 issue of Scientific American, there appeared a simple problem that has come to be known today as the Secretary Problem, or the Marriage Problem. It has since been taken up and developed by many eminent probabilists and statisticians and has been extended and generalized in many different directions so that now one can say that it constitutes a "field" within mathematics-probability-optimization. The object of this article is partly historical (to give a fresh view of the origins of the problem, touching upon Cayley and Kepler), partly review of the field (listing the subfields of recent interest), partly serious (to answer the question posed in the title), and partly entertainment. The contents of this paper were first given as the Allen T. Craig lecture at the University of Iowa, 1988.