The History of Mathematics: Aims, Results, and Future Prospects

When talking about the status of the history of mathematics, one possible approach would be a summary of what has been published by other historians of mathematics concerning their own field.1 In the light of so many different thoughts and opinions concerning the history of mathematics, I am less interested in summarizing what others have done already than in giving my own account of what constitutes history of mathematics now and possibly in the future. This subjective element is not an expression of disrespect for the work others have done; rather it concedes the many restrictions that every account like this must suffer. I name only two. As a member of what I should call for simplicity’s sake the European culture, my opinions and judgements necessarily depend on this specific cultural back-ground; they might be different, even very different, had I been brought up in China or in India. A second restriction concerns specialization in the history of mathematics as a subject. I have worked for many years on the history of probability theory as a major field of research. Probability theory belongs to applied mathematics. Because my examples for different current forms of the history of mathematics are taken from the history of probability theory, one might well question whether they adequately represent the history of mathematics generally.