Entering the valley of formalism: trends and changes in mathematicians' publication practice-1885 to 2015

Over the last century, there have been considerable variations in the frequency of use and types of diagrams used in mathematical publications. In order to track these changes, we developed a method enabling large-scale quantitative analysis of mathematical publications to investigate the number and types of diagrams published in three leading mathematical journals in the period from 1885 to 2015. The results show that diagrams were relatively common at the beginning of the period under investigation. However, beginning in 1910, they were almost completely unused for about four decades before reappearing in the 1950s. The diagrams from the 1950s, however, were of a different type than those used earlier in the century. We see this change in publication practice as a clear indication that the formalist ideology has influenced mathematicians' choice of representations. Although this could be seen as a minor stylistic aspect of mathematics, we argue that mathematicians' representational practice is deeply connected to their cognitive practice and to the contentual development of the discipline. These changes in publication style therefore indicate more fundamental changes in the period under consideration.

Automated summary

There have been considerable variations in the frequency and types of diagrams used in mathematical publications over the last century. Diagrams were relatively common at the beginning of the period, but were almost completely unused for about four decades before reappearing in the 1950s in a different type. This change in publication practice indicates a shift in mathematicians' choice of representations and suggests more fundamental changes during the period under consideration.