Statistics and Mathematics: Tension and Cooperation

1. INTRODUCTION. It has become a truism, at least among statisticians, that while statistics is a mathematical science, it is not a subfield of mathematics. We even have apho-risms to express some ways in which our science differs from mathematics. George Box: " All models are wrong, but some are useful. " George Cobb: " In mathematics, context obscures structure. In data analysis, context provides meaning. " David Moore: " Mathematical theorems are true; statistical methods are sometimes effective when used with skill. " That versions of these aphorisms apply whenever mathematics models phenomena in another field only emphasizes that statistics is another field. Cobb and Moore [2] discuss the implications of this fact for the teaching of statistics. Our present focus is neither the scientific distinction between mathematics and statistics nor the teaching of these subjects. We are concerned with the environment in which the fields now operate and the implications of our environment for our future prospects and for opportunities for synergy. We believe in particular that increased cooperation between the American Statistical Association (ASA) and the MAA could serve the interests of both mathematicians and statisticians. Both mathematics and statistics are of course served by other major societies, the Amer-ican Mathematical Society (AMS) and the Institute of Mathematical Statistics (IMS). These are in fact the most important societies in supporting academic research, and as such they play a large role in the culture of the two fields. The AMS is particularly significant, if only because most mathematicians are academics and most statisticians are not. Our recommendations focus on the ASA and the MAA because these groups have been more active in areas such as undergraduate education and because more statisticians are involved in the MAA than in the AMS. We begin with a simple thesis: statistics has cultural strengths that might greatly assist mathematics, while mathematics has organizational strengths that can provide shelter for academic statistics, shelter that may be essential for its survival. Better relations between these two connected fields could help both. It is mainly cultural differences that prevent closer relations. We might say that mathematics is French, while statistics is resolutely Anglo-Saxon. The French, proud of a long history and high culture, are wary of aggressive Anglo-Saxon pragmatism. In the words attributed to a French diplomat, " It works in practice , but does it work in theory? " Cultural change is never easy, …