Some Patterns of Research in Mathematics

TL;DR

This study provides a partial update to Grossman’s 2005 patterns of mathematical research by sampling $401$ MathSciNet authors, revealing a larger, more collaborative mathematical community with a denser coauthorship network and a lower median Erdős distance ($4$) than two decades prior. It documents a substantial rise in average coauthors ($8.52$) and broader disciplinary breadth (up to $18$ MSC areas for some authors), suggesting stronger interdisciplinary integration. The work highlights shifts in productivity tails and collaboration dynamics, including a drop in single-paper authors to $32.42\%$ and a sustained importance of cross-disciplinary researchers in maintaining rapid network connectivity. Overall, the findings indicate that younger generations participate more in collaborations and that the mathematical research landscape has grown both in size and interconnectedness, aligning with Erdős-inspired network centrality and broader MSC engagement.

Abstract

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.