Anxiety and abstraction in Nineteenth-Century Mathematics

Gray, Jeremy J. (2004). Anxiety and abstraction in Nineteenth-Century Mathematics. Science in Context, 17(2) pp. 23–47.

DOI: https://doi.org/10.1017/S0269889704000043

Abstract

The paper is in three parts. The first part surveys the current literature in the history of 19th Century mathematics in order to show that the question ‘Did the increasing abstraction of mathematics lead to a sense of anxiety?’ is a new and valid question. I argue that the mathematics of the 19th Century is marked by a growing appreciation of error leading to a note, hesitant at first but persistent by 1900, of anxiety. This mounting disquiet about so many aspects of mathematics after 1850 is seldom discussed. Insofar as this part of the paper is critical of present practice it retains the personal tone of the talk, but also it incorporates some of the helpful suggestions made during the discussion after the talk. The second part explores the issue of anxiety in mathematical life through an interesting account of these issues as they were perceived by one mathematician in 1911, Oscar Perron. The third and final part ventures some conclusions about the value of anxiety as a question for historians of mathematics to pursue.

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