This table gives various statistics on the publication habits of mathematicians over time, organized roughly into decades. The database includes all papers included in Mathematical Reviews (MR) from its inception in 1940 through the end of 1999. (Not included are about 1500 classical older papers MR later added to its database.)
Although the basic trends are clear, the data are not 100% reliable in various ways. For example, in a few cases, MR is not able to determine who a given name string is (such as S. Wanatabe), so it lists as an author of a paper more than one unique person with that name string. This results in slightly more apparent collaboration than actually occurred. Such instances are fairly rare, however, especially in the last 20-30 years, when MR has been careful to accurately identify unique people (and, besides, collaboration was not prevalent in the early days to begin with).
All integer figures are given in thousands. Data are given both for all authors, and for authors who have collaborated. A “collaboration” is recorded for each instance of a pair of authors sharing a publication.
Cumulative data, by decade
thru 90s thru 80s thru 70s thru 60s thru 50s thru 40s
number of papers 1598 1010 572 278 109 30
number of authors 337 225 137 68 29 10
ave. authors/paper 1.45 1.35 1.27 1.20 1.14 1.10
s.d. authors/paper 1.63 1.50 1.40 1.31 1.28 0.36
fraction 1-auth papers 66% 73% 78% 84% 88% 91%
fraction 2-auth papers 26% 22% 18% 13% 11% 8%
fraction 3-auth papers 7% 4% 3% 2% 1% 1%
fraction >3-auth papers 1% 1% 1% 1% 0% 0%
ave. papers/author 6.87 6.05 5.30 4.89 4.33 3.41
s.d. papers/author 15.34 12.91 11.26 10.49 8.88 5.70
number of coll'ing authors 253 153 82 34 11 3
fraction of all authors 75% 68% 60% 49% 39% 28%
ave. coll'tors/auth 2.94 2.26 1.67 1.20 0.83 0.49
ave. coll'tions/auth 5.65 4.08 2.87 2.01 1.36 0.75
ave. coll'tors/col. auth 3.92 3.33 2.79 2.42 2.14 1.74
ave. coll'tions/col. auth 7.52 6.00 4.77 4.07 3.50 2.65
Data for each decade
90s only 80s only 70s only 60s only 50s only 40s only
number of papers 587 439 294 168 80 30
number of authors 192 144 97 51 24 10
ave. authors/paper 1.63 1.45 1.33 1.23 1.16 1.10
s.d. authors/paper 1.82 1.63 1.48 1.35 1.26 0.36
fraction 1-auth papers 54% 66% 73% 81% 87% 91%
fraction 2-auth papers 33% 27% 22% 16% 11% 8%
fraction 3-auth papers 10% 6% 4% 2% 2% 1%
fraction >3-auth papers 3% 1% 1% 1% 0% 0%
ave. papers/author 4.97 4.43 4.03 4.05 3.84 3.41
s.d. papers/author 8.31 6.91 6.15 6.60 6.73 5.70
number of coll'ing authors 155 104 62 27 9 3
fraction of all authors 81% 72% 64% 52% 41% 28%
ave. coll'tors/auth 2.84 2.16 1.62 1.18 0.84 0.49
ave. coll'tions/auth 5.14 3.66 2.62 1.90 1.34 0.75
ave. coll'tors/col. auth 3.51 2.99 2.55 2.25 2.08 1.74
ave. coll'tions/col. auth 6.35 5.06 4.11 3.64 3.31 2.65
If we look just at the papers in the late 1990s (the last 95,000 papers in our database, or about two years' worth), then we find that the mean number of authors per paper has increased to 1.71 (s.d. = 1.90), with 49% of the papers by a single author, 35% by two authors, 13% by three authors, and 3% by four or more authors, an increase in collaboration even over the 1990s as a whole.
This page was last updated on September 16, 2020.