Data on Mathematics Research Publications over Time

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). Contact Jerry Grossman for further details.

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.

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This page was last updated on May 20, 2004.
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