| Section | P | S |
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| 00? | General | | | |
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| 01? | History and biography | | | |
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| 03 | Mathematical logic and foundations | | 67 | 2 |
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| 05 | Combinatorics | For finite fields, see 11Txx | 6 | |
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| 06 | Order, lattices, ordered algebraic structures | See also 18B35 | 19 | |
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| 08? | General algebraic systems | | | |
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| 11 | Number theory | | 11 | |
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| 12 | Field theory and polynomials | | 5 | |
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| 13 | Commutative rings and algebras | | 1 | |
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| 14? | Algebraic geometry | | | |
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| 15 | Linear and multilinear algebra; matrix theory | | 16 | 1 |
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| 16 | Associative rings and algebras | For the commutative case, see 13-xx | 13 | |
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| 17? | Nonassociative rings and algebras | | | |
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| 18 | Category theory; homological algebra | For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for algebraic topology | 9 | |
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| 19? | $K$-theory | See also 16E20, 18F25 | | |
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| 20 | Group theory and generalizations | | 7 | |
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| 22? | Topological groups, Lie groups | For transformation groups, see 54H15, 57Sxx, 58-xx. For abstract harmonic analysis, see 43-xx | | |
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| 26 | Real functions | See also 54C30 | 27 | |
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| 28 | Measure and integration | For analysis on manifolds, see 58-xx | 13 | |
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| 30? | Functions of a complex variable | For analysis on manifolds, see 58-xx | | |
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| 31? | Potential theory | For probabilistic potential theory, see 60J45 | | |
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| 32? | Several complex variables and analytic spaces | For infinite-dimensional holomorphy, see 46G20, 58B12 | | |
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| 33 | Special functions | (33-xx deals with the properties of functions as functions) For orthogonal functions, see 42Cxx; for aspects of combinatorics, see 05Axx; for number-theoretic aspects, see 11-xx; for representation theory, see 22Exx | 8 | |
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| 34? | Ordinary differential equations | | | |
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| 35? | Partial differential equations | | | |
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| 37? | Dynamical systems and ergodic theory | See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-xx | | |
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| 39? | Difference and functional equations | | | |
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| 40 | Sequences, series, summability | | 6 | |
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| 41? | Approximations and expansions | For all approximation theory in the complex domain, see 30Exx, 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42Axx, 42A10 and 42A15; for numerical approximation, see 65Dxx | | |
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| 42? | Fourier analysis | | | |
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| 43? | Abstract harmonic analysis | For other analysis on topological and Lie groups, see 22Exx | | |
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| 44? | Integral transforms, operational calculus | For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10 | | |
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| 45? | Integral equations | | | |
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| 46? | Functional analysis | For manifolds modeled on topological linear spaces, see 57N20, 58Bxx | | |
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| 47? | Operator theory | | | |
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| 49? | Calculus of variations and optimal control; optimization | See also 34H05, 34K35, 65Kxx, 90Cxx, 93-xx | | |
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| 51? | Geometry | For algebraic geometry, see 14-xx | | |
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| 52? | Convex and discrete geometry | | | |
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| 53? | Differential geometry | For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx | | |
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| 54 | General topology | For the topology of manifolds of all dimensions, see 57Nxx | 3 | |
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| 55? | Algebraic topology | | | |
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| 57? | Manifolds and cell complexes | For complex manifolds, see 32Qxx | | |
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| 58? | Global analysis, analysis on manifolds | See also 32Cxx, 32Fxx, 32Wxx, 46-xx, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15 | | |
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| 60? | Probability theory and stochastic processes | For additional applications, see 11Kxx, 62-xx, 90-xx, 91-xx,92-xx, 93-xx, 94-xx | | |
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| 62? | Statistics | | | |
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| 65? | Numerical analysis | | | |
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| 68 | Computer science | For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area | 43 | |
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| 70? | Mechanics of particles and systems | For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-xx | | |
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| 74? | Mechanics of deformable solids | | | |
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| 76? | Fluid mechanics | For general continuum mechanics, see 74Axx, or other parts of 74-xx | | |
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| 78? | Optics, electromagnetic theory | For quantum optics, see 81V80 | | |
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| 80? | Classical thermodynamics, heat transfer | For thermodynamics of solids, see 74A15 | | |
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| 81? | Quantum theory | | | |
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| 82? | Statistical mechanics, structure of matter | | | |
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| 83? | Relativity and gravitational theory | | | |
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| 85? | Astronomy and astrophysics | For celestial mechanics, see 70F15 | | |
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| 86? | Geophysics | See also 76U05, 76V05 | | |
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| 90? | Operations research, mathematical programming | | | |
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| 91? | Game theory, economics, social and behavioral sciences | | | |
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| 92? | Biology and other natural sciences | | | |
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| 93? | Systems theory; control | For optimal control, see 49-xx | | |
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| 94 | Information and communication, circuits | | 5 | |
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| 97? | Mathematics education | | | |
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