Friday, 9 July 2010

soft question - Quantitatively speaking, which subject area in mathematics is currently the most research active?

Sorry to add to the noise, but here it goes. With a little script-fu (and emacs, of course!) I retrieved the data from MSC corresponding to the last ten years in each of the Primary Classifications. Annoyingly the AMS changed their subject classification scheme recently, so that the numbers I queried were interpreted as MSC2010, whereas the papers are published from the year 2000.




43465 35 Partial differential equations
38151 62 Statistics
35994 81 Quantum theory
35633 68 Computer science
34474 65 Numerical analysis
28593 05 Combinatorics
28296 90 Operations research, mathematical programming
26406 34 Ordinary differential equations
26192 60 Probability theory and stochastic processes
23879 93 Systems theory; control
22361 11 Number theory
21689 76 Fluid mechanics
20787 91 Game theory, economics, social and behavioral sciences
19440 37 Dynamical systems and ergodic theory
18425 83 Relativity and gravitational theory
17323 94 Information and communication, circuits
17247 53 Differential geometry
16465 47 Operator theory
16134 03 Mathematical logic and foundations
15408 20 Group theory and generalizations
14225 92 Biology and other natural sciences
14051 82 Statistical mechanics, structure of matter
13663 46 Functional analysis
12894 74 Mechanics of deformable solids
11241 14 Algebraic geometry
10237 49 Calculus of variations and optimal control; optimization
10215 30 Functions of a complex variable
10154 16 Associative rings and algebras
9801 01 History and biography
9781 54 General Topology
8014 42 Fourier analysis
7103 58 Global analysis, analysis on manifolds
6780 15 Linear and multilinear algebra; matrix theory
6410 70 Mechanics of particles and systems
6359 32 Several complex variables and analytic spaces
6348 57 Manifolds and cell complexes
6185 41 Approximations and expansions
5935 39 Difference and functional equations
5684 26 Real functions
5349 17 Nonassociative rings and algebras
5226 13 Commutative rings and algebras
4840 78 Optics, electromagnetic theory
4439 52 Convex and discrete geometry
4418 33 Special functions
4350 00 General
3818 06 Order, lattices, ordered algebraic structures
3511 28 Measure and integration
3295 51 Geometry
2948 22 Topological groups, Lie groups
2944 55 Algebraic topology
2538 86 Geophysics
2089 45 Integral equations
2052 18 Category theory; homological algebra
1679 80 Classical thermodynamics, heat transfer
1523 31 Potential theory
1444 43 Abstract harmonic analysis
1343 12 Field theory and polynomials
1161 40 Sequences, series, summability
1108 08 General algebraic systems
898 44 Integral transforms, operational calculus
775 19 K-theory
534 85 Astronomy and astrophysics


Usual disclaimers apply. In particular, before concluding that nobody works in astrophysics, go and check the submission statistics for astro-ph: more than 11,000 submissions in 2009 alone! Clearly the AMS does not index very widely in this area.



Let me reiterate that I do not believe for a second that this data allows one to conclude anything of value about mathematics, just perhaps about mathematicians :)



Added (incorporating Gerald Edgar's summary in the comment below)



This is the summary of "pure maths" defined as classifications 00-60, with a total of 411902 articles reviewed in the decade that has just finished. That, in case you are wondering is 55.38% of all papers reviewed.




00--08 Logic and Combinatorics 63804 15.49%
11--20 Algebra and Number Theory 80689 19.59%
22--49,60 Analysis and Probability 216252 52.50%
51--58 Geometry and Topology 51157 12.42%

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