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Publication Patterns in
the Different Area
of Mathematics
Jerrold W. Grossman
Oakland University
Rochester, Michigan
AMS Annual Meeting
January 18, 2003
Baltimore, Maryland
Do publication habits vary among
the different areas of mathematics?
– applied vs. pure mathematics
– continuous vs. discrete
– math vs. physics vs. CS vs. …
What habits?
–
–
–
–
number of papers per author
number of authors per paper
fraction of joint vs. solo papers
fraction of papers with >2 authors
How many areas does a
mathematician work in?
MR CATEGORIES
Pure “discrete” mathematics:
03
05
06
08
11
12
13
14
15
16
17
18
19
20
51
52
logic, set theory
combinatorics, graph theory
ordered structures, lattices
general algebraic systems
number theory
fields, polynomials
commutative rings, algebras
algebraic geometry
linear algebra, matrix theory
associative rings, algebras
nonassociative rings, algebras
category thy, homological algebra
K-theory
group theory and generalizations
geometry
convex and discrete geometry
Pure “continuous” mathematics:
22
26
28
30
31
32
33
34
35
39
40
41
42
topological and Lie groups
real functions
measure and integration
functions of a complex variable
potential theory
several complex variables
special functions
ordinary differential equations
partial differential equations
functional equations
sequences, series
approximations and expansions
Fourier analysis
Pure “continuous” mathematics
(continued):
43
44
45
46
47
49
53
54
55
57
58
60
65
abstract harmonic analysis
integral transforms, operations
integral equations
functional analysis
operator theory
calculus of variations
differential geometry
general topology
algebraic topology
manifolds
global analysis
probability
numerical analysis
Science/engineer. (mainly physics):
70
73
76
78
80
81
82
83
85
86
92
93
particle, system mechanics
solid mechanics
fluid mechanics
optics, electomagnetics
classical thermodynamics
quantum theory
statistical mechanics
relativity, gravitational theory
astronomy, astrophysics
geophysics
biology and natural sciences
systems theory, control
Statistics:
62 statistics
Computer science:
68 computer science
94 information, commun., circuits
Operations research:
90 operations research, math prog.
Other:
00 “general”
01 history and biography
The data
all authored items from
Mathematical Reviews
(MathSciNet)
1980–1999
MR tries hard to identify authors as
people, not name strings.
220,030 authors
885,910 papers
fraction of papers by group
CS
5%
stat
5%
other
2%
discrete
20%
OR
4%
sci/eng
20%
continuous
44%
sections with the most papers
(more than 3% of the total)
81
35
62
65
60
90
58
05
68
34
11
quantum theory
PDE
statistics
numerical analysis
probability
operations research
global analysis
combinatorics
computer science
ODE
number theory
5.2%
5.2%
4.6%
4.6%
4.3%
4.3%
4.2%
3.6%
3.6%
3.2%
3.2%
46%
number of sections worked in
1
1
2
4
5
7
17
14
20
47
48
84
140
230
390
676
1069
1794
3011
5424
9528
23
21
19
17
15
13
11
9
7
5
3
18381
41399
1
47630
0
10000
20000
30000
40000
50000
(doesn’t include 90,108
people with only one paper)
60000
total number of papers per author
>100
334
51 to 100
2436
31 to 50
5328
21 to 30
7247
11 to 20
17929
10
3279
9
3844
8
4540
7
5622
6
6811
5
8997
4
12510
3
18521
2
32524
1
90108
0
20000
40000
60000
80000
100000
mean = 6.1
standard deviation = 11.6
median = 2
75%ile = 6
90%ile = 16
mean number of papers per author
(by group)
other
2.03
stat
4.05
CS
3
OR
3.12
sci/eng
3.65
continuous
5.63
discrete
5.12
0
1
2
3
4
5
6
sections with most papers per author
05
16
60
14
81
83
35
54
53
20
combinatorics
associative rings
probability
algebraic geometry
quantum theory
relativity
PDE
general topology
differential geometry
group theory
4.62
4.56
4.53
4.52
4.46
4.45
4.34
4.33
4.27
4.25
number of authors per paper
>5
1190
5
2606
4
13790
3
70094
2
261003
1
537227
0
100000
mean = 1.52
200000
300000
400000
500000
600000
standard deviation = 0.76
mean number of authors per paper
(by group)
other
1.3
stat
1.56
CS
1.75
OR
1.59
sci/eng
1.73
continuous
1.45
discrete
1.41
0
0.5
1
1.5
2
extent of collaboration
(by group)
2.7%
6%
other
17%
1.3%
stat
9%
45%
4.3%
CS
17%
52%
1.9%
OR
12%
45%
3.9%
sci/eng
16%
52%
1.2%
continuous
7%
36%
1.4%
discrete
7%
32%
2.0%
overall
10%
39%
0%
10%
joint papers
20%
30%
>2 authors
40%
50%
>3 authors
60%
sections with most authors per paper
>1 auth
53%
>2 auth
17.7%
>3 auth
4.7%
1.67
1.64
1.61
1.59
1.58
1.56
1.55
1.52
52%
50%
46%
46%
45%
45%
45%
40%
41%
16.4%
13.5%
13.7%
12.3%
11.6%
9.6%
8.7%
11.3%
9.1%
3.9%
3.2%
3.2%
2.2%
1.9%
2.0%
1.3%
2.7%
1.4%
all 1.52
39%
9.9%
2.0%
68
mean
1.77
sci 1.73
94
05
65
90
33
62
58
39
sections with fewest authors per paper
12
32
03
14
31
11
18
19
51
mean
1.30
1.30
1.30
1.31
1.32
1.32
1.33
1.33
1.34
all 1.52
>1 auth
25%
26%
24%
26%
27%
26%
28%
26%
28%
>2 auth
4.2%
3.7%
5.1%
4.4%
5.0%
5.0%
4.5%
5.7%
4.9%
>3 auth
0.5%
0.5%
0.9%
0.6%
0.3%
0.7%
0.4%
1.3%
0.7%
39%
9.9%
2.0%