A social machine is a combination of people and computers treated as a single problem-solving entity, in which the people do the creative work and the machine does the administration. Applied to mathematics, the term covers community question-answering sites, collaborative open-conjecture blogs, and curated databases of mathematical objects, whose public records expose the backstage of research - examples, counterexamples, conjectures, acknowledged error and social glue - that a finished proof hides. Studying that record gives an empirical basis for theories of how mathematics is actually produced, and frames a design space for such systems along axes such as precise versus loose queries, human versus machine creativity, and formal versus natural-language interaction.
This arxiv paper substantively examines mathematics as an interdisciplinary field drawing on philosophy and social science to understand how mathematical knowledge is actually produced. It analyzes r…