“Free rides” in Mathematics

Jessica Carter*

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


Representations, in particular diagrammatic representations, allegedly contribute to new insights in mathematics. Here I explore the phenomenon of a “free ride” and to what extent it occurs in mathematics. A free ride, according to Shimojima (Artif Intell Rev 15: 5–27, 2001), is the property of some representations that whenever certain pieces of information have been represented then a new piece of consequential information can be read off for free. I will take Shimojima’s (informal) framework as a tool to analyse the occurrence and properties of them. I consider a number of different examples from mathematical practice that illustrate a variety of uses of free rides in mathematics. Analysing these examples I find that mathematical free rides are sometimes based on syntactic and semantic properties of diagrams.

Original languageEnglish
Pages (from-to)10475-10498
Number of pages24
Publication statusPublished - Dec 2021


  • Diagrams
  • Free rides in mathematics


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