Some Patterns of Research in Mathematics

TL;DR

This paper updates previous research on mathematical collaboration patterns, showing increased teamwork, broader research areas, and denser co-authorship networks among mathematicians, especially younger ones.

Contribution

It provides new empirical insights into evolving collaboration trends and network structures in mathematical research since 2005.

Findings

Decrease in single-author papers from 43% to 32%

Increase in collaboration and network density

Younger mathematicians exhibit more collaboration

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 Erd\H{o}s 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.