Some Reflections of a Mathematician on the Nature and the Role of Statistics

Abstract

A principal purpose of this conference, as I am given to understand, is to try to look into the future of mathematical statistics. Now, there is a saying, attributed to Niels Bohr but apparently an old Danish proverb, that it is difficult to predict, especially the future. Therefore I will not engage in this extraordinarily difficult and involved task, but will restrict myself to illustrating some points which might be relevant to the theme of the conference. First of all, it is easy to give numerous examples of research activity which started in one direction and happened to produce results in quite a different area. For example, when Sadi Carnot was working so hard on the steam engine, he was only interested in improving it. In actuality, he ended up discovering a fundamental law of nature a discovery which has led to phenomenal consequences. At my own institution, which was then the Rockefeller Institute, O. T. Avery was working with his collaborators during the last world war on an extremely applied problem concerned with pneumonia. In the process of this investigation he discovered that the carriers of genetic information were not proteins but nucleic acids. As you all know, this discovery revolutionised the whole field of genetics, although the original problem which led to it was a specific applied medical problem. So, one never knows: It is not the problem, or the name attached to it that is pertinent. What matters is the special combination of the men, the problem, the environment in fact, exactly those things which no one can possibly predict. So now I would like to speak a little bit on what statistics, with or without the adjective 'mathematical', has meant to me. Perhaps I am not quite the right person to speak about it, because my connections with statistics are somewhat tangential; nevertheless, input from the outside can sometimes be useful. My first exposure to statistics, although I did not realise then it was statistics, took place when I was 14 or 15 years of age. My class had at that time an extraordinary teacher of biology who gave us an outline of Darwin's theory and, in particular, explained how one of the claims of that theory, namely that individual characteristics are inheritable, was demolished by an experiment and a little bit of thinking. This was done by W. Johannsen, who published his results in 1909. There is a particularly vivid description of it in a book by