Some Patterns of Research in Mathematics

We partially update Grossman’s 2005 survey of patterns in mathematical research using a sample of 401 mathematicians from MathSciNet. The mathematical landscape has changed substantially: single-paper authors have reduced from $43$ % to $32$ %, collaboration has intensified, more mathematicians have greater breadth of research areas, and the giant component of the co-authorship network has grown denser, with median Erdős number dropping from $5$ to $4$. The data reveals the profession as markedly more collaborative, particularly among younger generations, although the tail of high productivity has also grown more extreme.

💡 Research Summary

In this paper Octavio A. Agustín‑Aquino presents a partial update of Jerrold Grossman’s 2005 survey of research patterns in mathematics, using a random sample of 401 mathematicians drawn from the MathSciNet database in early 2026. The author first explains the sampling procedure: random identifiers were generated until 401 valid records were obtained, yielding an estimated total of roughly 520,000 mathematicians in the database—about twice the size reported by Grossman for 2005.

The statistical analysis focuses on several key dimensions: (1) publication productivity, (2) co‑authorship, (3) network centrality measured by Erdős numbers, and (4) disciplinary breadth as captured by MSC (Mathematics Subject Classification) codes.

Productivity: The proportion of single‑paper authors in the 2026 sample is 32.42 % (95 % CI