Bertrand Russell’s mathematical education

Abstract The influence of Bertrand Russell (F.R.S., 1909) on the foundations of mathematics has an assured place in history, but some mathematicians who look closely at this influence may well have doubts about Russell’s overall view of mathematics and how compatible that view is with their own. The British mathematician R.O. Gandy, for example, has characterized certain of Russell’s expressions as ‘absurd’ and ‘stultifying’ and as denying ‘the significance of the mathematical imagination and the value of mathematical experience’. The French mathematician Jean Dieudonne has referred to Russell as one who ‘pretends to have the reputation of being a mathematician and succeeded in doing so in the eyes of contemporaries (and even today in the eyes of a number of philosophers)’. If Russell had a response, it might be conjectured from his summaries in an 1896 notebook of his reading of French authors on foundations of geometry. Russell grouped them under two headings, ‘Fools’ and ‘Philosophers,’ the latter group containing only the note ‘None extant.’ Among the six ‘Fools’ was Auguste Calinon about whom Russell wrote ‘mere mathematician: doesn’t care what philosophers think’. We know of no evidence that Russell had pretensions to being a mathematician. However, someone who, like Russell, was ranked seventh Wrangler in the Cambridge Mathematical Tripos examinations in the late 19th century was probably entitled to believe that he had a good acquaintance with at least some mathematics. Some of the graduates of this 19th century system were among the most distinguished mathematicians of that century.