November 2019 – Page 2 – Libres pensées d'un mathématicien ordinaire

Les joueurs de dés, vers 1640, Georges de la Tour — Georges de la Tour – Les joueurs de dés, vers 1640.

Recently, during a coffee break, emerged a discussion about the presence of probability and statistics in top journals such as Annals of mathematics, Acta Mathematica, Inventiones Mathematicae, or Journal of the AMS. Well, the question has an interest from the point of view of the sociology and history of science. Let us use the Primary and Secondary Mathematical Subject Classification (MSC) codes of each article in order to detect Probability (60x) or Statistics (62x). Here is the data from MathSciNet/zbMath:

Annals of Mathematics published 4464 papers in total from 1938 to 2019.
Among them, 76 (1.7%) have Primary MSC 60x [PDF]
Among them, 112 (2.5%) have Primary or Secondary MSC 60x [PDF]
Moreover only 2 have Primary or Secondary MSC 62x [PDF]
Acta Mathematica published 1297 papers in total from 1938 to 2017.
Among them, 44 (3.4%) have Primary MSC 60x [PDF]
Among them, 63 (4.9%) have Primary or Secondary MSC 60x [PDF]
Moreover only 4 have Primary or Secondary MSC 62x [PDF]
Inventiones Mathematicae published 4311 papers in total from 1966 to 2019.
Among them, 52 (1.2%) have Primary MSC 60x [PDF]
Among them, 95 (2.2%) have Primary or Secondary MSC 60x [PDF]
Moreover only 2 have Primary or Secondary MSC 62x [PDF]
Journal of the AMS published 963 papers in total from 1988 to 2019.
Among them, 28 (2.9%) have Primary MSC 60x [PDF]
Among them, 49 (5.1%) have Primary or Secondary MSC 60x [PDF]
Moreover only 5 have Primary or Secondary MSC 62x [PDF]

The presence of probability is low, while the one of statistics is microscopic. A scandal.

AO(P|S). Annals of Probability (AOP) and Annals of Statistics (AOS) were founded only in 1973.

1938. Annals of Mathematics is historically American whereas Acta Mathematica is European. They started respectively in 1892 and 1882. According to MathSciNet, it seems that the first article classified 60x in these journals was published in 1938. The MSC by itself was introduced at the end of the thirties and many articles in MathSciNet are not classified before 1940 at the time of writing. Note that N. Wiener published in the twenties while A. N. Kolmogorov published in the thirties.

Why. The phenomenon has probably multiple explanations, among them we could mention for instance the possible effects of utilitarism and anti-utilitarism in the mathematical elite, in particular during the fifties and sixties, and the possible overweight of some kind of “snobish pure mathematics or mathematicians” in top journals boards. We could also see AOP and AOS as some sort of mathematical ghettos and think about self-censorship. We could moreover think about generational effects. Finally we have to keep in mind that some probability papers were published without any primary or secondary 60x code, such as for instance this one or that one.

Here is some additional data provided by MathSciNet for Annals of Mathematics:

MSC	Description	Count
	Other (includes unclassified papers before 1940)	1626
14	Algebraic geometry	319
57	Manifolds and cell complexes	298
20	Group theory and generalizations	292
11	Number theory	288
53	Differential geometry	262
46	Functional analysis	207
58	Global analysis, analysis on manifolds	203
56	Other	200
32	Several complex variables and analytic spaces	174
55	Algebraic topology	172
10	Number theory	159
22	Topological groups, Lie groups	149
30	Functions of a complex variable	135
35	Partial differential equations	126
42	Harmonic analysis on Euclidean spaces	111
37	Dynamical systems and ergodic theory	107
09	Other	100
60	Probability theory and stochastic processes	76
54	General topology	51
27	Other	47
36	Other	43
12	Field theory and polynomials	40
49	Calculus of variations and optimal control; optimization	39
17	Nonassociative rings and algebras	35
47	Operator theory	35
02	Logic and foundations	33
05	Combinatorics	32
52	Convex and discrete geometry	32
34	Ordinary differential equations	31
81	Quantum theory	26
28	Measure and integration	25
16	Associative rings and algebras	22
03	Mathematical logic and foundations	21
13	Commutative algebra	20
40	Sequences, series, summability	20
18	Category theory; homological algebra	19
83	Relativity and gravitational theory	19
31	Potential theory	18
43	Abstract harmonic analysis	17
19	K-theory	13
82	Statistical mechanics, structure of matter	13
90	Operations research, mathematical programming	12
06	Order, lattices, ordered algebraic structures	11
41	Approximations and expansions	11
15	Linear and multilinear algebra; matrix theory	10
33	Special functions	10
26	Real functions	9
48	Other	8
45	Integral equations	7
76	Fluid mechanics	7
04	Set theory	6
39	Difference and functional equations	6
70	Mechanics of particles and systems	6
00	General	3
68	Computer science	3
44	Integral transforms, operational calculus	2
62	Statistics	2
73	Mechanics of solids	2
01	History and biography	1
21	Other	1
71	Other	1
79	Other	1
80	Classical thermodynamics, heat transfer	1
84	Other	1
94	Information and communication, circuits	1

The same for the last three years :

MSC	Description	Count
11	Number theory	29
14	Algebraic geometry	20
53	Differential geometry	17
05	Combinatorics	10
35	Partial differential equations	10
37	Dynamical systems and ergodic theory	8
20	Group theory and generalizations	6
58	Global analysis, analysis on manifolds	6
03	Mathematical logic and foundations	5
57	Manifolds and cell complexes	5
13	Commutative algebra	4
22	Topological groups, Lie groups	4
32	Several complex variables and analytic spaces	4
60	Probability theory and stochastic processes	4
42	Harmonic analysis on Euclidean spaces	3
49	Calculus of variations and optimal control; optimization	3
52	Convex and discrete geometry	3
55	Algebraic topology	3
28	Measure and integration	2
30	Functions of a complex variable	2
46	Functional analysis	2
83	Relativity and gravitational theory	2
06	Order, lattices, ordered algebraic structures	1
19	K-theory	1
43	Abstract harmonic analysis	1
47	Operator theory	1

Graphics for Annals of mathematics.Graphics for Acta Mathematica.Graphics for Inventiones Mathematicae.Graphics for Journal of the AMS.

JMPA. We could think that a journal such as Journal de mathématiques pures et appliquées, founded in 1872, is in the same time relatively prestigious, generalist, and more open to applied mathematics in general and to probability and statistics in particular. Here is the data for all MSC codes, taken from MathSciNet. We see an obvious overweight for partial differential equations. In the mean time, the situation of probability is better than before, while the presence of statistics is still microscopic.

MSC	Description	Count
35	Partial differential equations	801
58	Global analysis, analysis on manifolds	138
53	Differential geometry	136
49	Calculus of variations and optimal control; optimization	107
46	Functional analysis	86
76	Fluid mechanics	69
14	Algebraic geometry	61
60	Probability theory and stochastic processes	60
93	Systems theory; control	58
30	Functions of a complex variable	57
47	Operator theory	55
32	Several complex variables and analytic spaces	53
34	Ordinary differential equations	43
37	Dynamical systems and ergodic theory	42
42	Harmonic analysis on Euclidean spaces	35
74	Mechanics of deformable solids	34
31	Potential theory	32
81	Quantum theory	24
82	Statistical mechanics, structure of matter	23
22	Topological groups, Lie groups	21
73	Mechanics of solids	21
20	Group theory and generalizations	19
83	Relativity and gravitational theory	19
36	Other	17
11	Number theory	16
45	Integral equations	16
28	Measure and integration	15
56	Other	12
10	Number theory	11
17	Nonassociative rings and algebras	10
26	Real functions	10
54	General topology	10
65	Numerical analysis	10
78	Optics, electromagnetic theory	10
27	Other	9
33	Special functions	9
48	Other	8
50	Geometry	8
92	Biology and other natural sciences	8
05	Combinatorics	7
43	Abstract harmonic analysis	7
91	Game theory, economics, social and behavioral sciences	7
09	Other	6
55	Algebraic topology	6
02	Logic and foundations	5
12	Field theory and polynomials	5
15	Linear and multilinear algebra; matrix theory	5
41	Approximations and expansions	5
16	Associative rings and algebras	4
44	Integral transforms, operational calculus	4
52	Convex and discrete geometry	4
57	Manifolds and cell complexes	4
62	Statistics	4
70	Mechanics of particles and systems	4
40	Sequences, series, summability	3
85	Astronomy and astrophysics	3
13	Commutative algebra	2
39	Difference and functional equations	2
71	Other	2
80	Classical thermodynamics, heat transfer	2
86	Geophysics	2
90	Operations research, mathematical programming	2
94	Information and communication, circuits	2
18	Category theory; homological algebra	1
79	Other	1

The same for the last three years:

MSC	Description	Count
35	Partial differential equations	154
49	Calculus of variations and optimal control; optimization	25
53	Differential geometry	19
14	Algebraic geometry	16
93	Systems theory; control	16
58	Global analysis, analysis on manifolds	12
42	Harmonic analysis on Euclidean spaces	8
37	Dynamical systems and ergodic theory	7
60	Probability theory and stochastic processes	7
76	Fluid mechanics	7
31	Potential theory	6
32	Several complex variables and analytic spaces	6
34	Ordinary differential equations	5
46	Functional analysis	5
81	Quantum theory	5
11	Number theory	4
47	Operator theory	4
74	Mechanics of deformable solids	4
28	Measure and integration	2
30	Functions of a complex variable	2
43	Abstract harmonic analysis	2
82	Statistical mechanics, structure of matter	2
83	Relativity and gravitational theory	2
92	Biology and other natural sciences	2
05	Combinatorics	1
12	Field theory and polynomials	1
15	Linear and multilinear algebra; matrix theory	1
20	Group theory and generalizations	1
26	Real functions	1
45	Integral equations	1
65	Numerical analysis	1
70	Mechanics of particles and systems	1
78	Optics, electromagnetic theory	1
86	Geophysics	1
91	Game theory, economics, social and behavioral sciences	1
94	Information and communication, circuits	1

CPAM. Finally, here is the same data for Communication on Pure and Applied Mathematics. This journal, established in 1948, is truly open to applied mathematics in general and to probability theory in particular. However, the presence of statistics is still extremely low.

MSC	Description	Count
35	Partial differential equations	898
76	Fluid mechanics	234
58	Global analysis, analysis on manifolds	182
60	Probability theory and stochastic processes	177
53	Differential geometry	97
65	Numerical analysis	92
82	Statistical mechanics, structure of matter	92
34	Ordinary differential equations	85
47	Operator theory	65
49	Calculus of variations and optimal control; optimization	64
37	Dynamical systems and ergodic theory	58
78	Optics, electromagnetic theory	58
20	Group theory and generalizations	49
46	Functional analysis	48
81	Quantum theory	43
10	Number theory	39
73	Mechanics of solids	37
30	Functions of a complex variable	29
36	Other	25
32	Several complex variables and analytic spaces	24
57	Manifolds and cell complexes	24
11	Number theory	23
74	Mechanics of deformable solids	23
94	Information and communication, circuits	22
42	Harmonic analysis on Euclidean spaces	20
03	Mathematical logic and foundations	15
31	Potential theory	15
45	Integral equations	15
62	Statistics	15
14	Algebraic geometry	14
55	Algebraic topology	14
70	Mechanics of particles and systems	14
83	Relativity and gravitational theory	14
92	Biology and other natural sciences	14
01	History and biography	13
15	Linear and multilinear algebra; matrix theory	13
52	Convex and discrete geometry	13
44	Integral transforms, operational calculus	12
22	Topological groups, Lie groups	11
26	Real functions	9
80	Classical thermodynamics, heat transfer	9
85	Astronomy and astrophysics	8
86	Geophysics	8
05	Combinatorics	7
43	Abstract harmonic analysis	7
12	Field theory and polynomials	6
28	Measure and integration	6
90	Operations research, mathematical programming	6
00	General	5
39	Difference and functional equations	5
68	Computer science	5
93	Systems theory; control	5
41	Approximations and expansions	4
91	Game theory, economics, social and behavioral sciences	4
02	Logic and foundations	3
17	Nonassociative rings and algebras	3
33	Special functions	3
09	Other	2
16	Associative rings and algebras	2
27	Other	2
40	Sequences, series, summability	2
54	General topology	2
69	Other	2
19	K-theory	1
51	Geometry	1

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Month: November 2019

Annals of mathematics : probability and statistics