MSC2020 index · openai/math · 7 October 2026

OpenAI preprints by primary or secondary MSC classification

The 722 manuscripts in the openai/math repository, listed under every three-character MSC2020 class in which they have a primary or a secondary code: 200 classes in 52 of the 63 MSC areas. Each title links to the PDF.

Codes were assigned by Claude from each paper’s title and abstract in the repository’s manuscript map; they are not author-supplied. Hover over a code to see its MSC2020 description.

See also: Preprints by primary classification only

53C21 primary code 53C24 secondary code. Under each class, papers whose primary code is in the class come first.

03Mathematical logic and foundations14 preprints

03BGeneral logic1

03CModel theory5

03DComputability and recursion theory5

03ESet theory4

03FProof theory and constructive mathematics1

05Combinatorics77 preprints

05AEnumerative combinatorics2

05BDesigns and configurations8

05CGraph theory59

05DExtremal combinatorics11

05EAlgebraic combinatorics7

06Order, lattices, ordered algebraic structures12 preprints

06AOrdered sets2

06BLattices2

06EBoolean algebras (Boolean rings)8

08General algebraic systems2 preprints

08AAlgebraic structures2

11Number theory64 preprints

11AElementary number theory4

11BSequences and sets8

11CPolynomials and matrices3

11DDiophantine equations4

11FDiscontinuous groups and automorphic forms8

11GArithmetic algebraic geometry (Diophantine geometry)14

11HGeometry of numbers1

11JDiophantine approximation, transcendental number theory3

11KProbabilistic theory: distribution modulo 1; metric theory of algorithms4

11LExponential sums and character sums1

11MZeta and L-functions: analytic theory5

11NMultiplicative number theory13

11PAdditive number theory; partitions2

11RAlgebraic number theory: global fields13

11TFinite fields and commutative rings (number-theoretic aspects)1

11UConnections of number theory and logic2

11YComputational number theory3

12Field theory and polynomials5 preprints

12EGeneral field theory1

12FField extensions3

12LConnections between field theory and logic1

13Commutative algebra11 preprints

13BCommutative ring extensions and related topics4

13CTheory of modules and ideals in commutative rings3

13DHomological methods in commutative ring theory5

13FArithmetic rings and other special commutative rings2

13HLocal rings and semilocal rings4

13NDifferential algebra1

14Algebraic geometry106 preprints

14BLocal theory in algebraic geometry3

14CCycles and subschemes37

14DFamilies, fibrations in algebraic geometry19

14EBirational geometry38

14F(Co)homology theory in algebraic geometry18

14GArithmetic problems in algebraic geometry; Diophantine geometry14

14HCurves in algebraic geometry6

14JSurfaces and higher-dimensional varieties31

14KAbelian varieties and schemes7

14LAlgebraic groups4

14MSpecial varieties7

14NProjective and enumerative algebraic geometry3

14PReal algebraic and real-analytic geometry5

14QComputational aspects in algebraic geometry1

14RAffine geometry3

15Linear and multilinear algebra; matrix theory16 preprints

15ABasic linear algebra11

15BSpecial matrices5

16Associative rings and algebras18 preprints

16DModules, bimodules and ideals in associative algebras2

16EHomological methods in associative algebras4

16GRepresentation theory of associative rings and algebras4

16KDivision rings and semisimple Artin rings2

16LLocal rings and generalizations1

16NRadicals and radical properties of associative rings1

16SAssociative rings and algebras arising under various constructions9

16UConditions on elements5

17Nonassociative rings and algebras5 preprints

17BLie algebras and Lie superalgebras5

18Category theory; homological algebra7 preprints

18GHomological algebra in category theory, derived categories and functors3

18MMonoidal categories and operads2

18NHigher categories and homotopical algebra2

19K-theory10 preprints

19AGrothendieck groups and K02

19DHigher algebraic K-theory4

19EK-theory in geometry2

19KK-theory and operator algebras5

20Group theory and generalizations51 preprints

20CRepresentation theory of groups15

20DAbstract finite groups4

20EStructure and classification of infinite or finite groups14

20FSpecial aspects of infinite or finite groups21

20GLinear algebraic groups and related topics6

20JConnections of group theory with homological algebra and category theory6

20MSemigroups3

22Topological groups, Lie groups21 preprints

22DLocally compact groups and their algebras11

22ELie groups11

22FNoncompact transformation groups1

26Real functions1 preprint

26DInequalities in real analysis1

28Measure and integration18 preprints

28AClassical measure theory13

28DMeasure-theoretic ergodic theory5

30Functions of a complex variable9 preprints

30CGeometric function theory7

30FRiemann surfaces1

30LAnalysis on metric spaces2

31Potential theory6 preprints

31CGeneralizations of potential theory6

32Several complex variables and analytic spaces38 preprints

32AHolomorphic functions of several complex variables1

32EHolomorphic convexity2

32JCompact analytic spaces24

32LHolomorphic fiber spaces1

32MComplex spaces with a group of automorphisms5

32QComplex manifolds19

32SComplex singularities3

32UPluripotential theory1

34Ordinary differential equations7 preprints

34CQualitative theory for ordinary differential equations4

34LOrdinary differential operators3

34MOrdinary differential equations in the complex domain1

35Partial differential equations44 preprints

35AGeneral topics in partial differential equations3

35BQualitative properties of solutions to partial differential equations15

35CRepresentations of solutions to partial differential equations1

35DGeneralized solutions to partial differential equations3

35JElliptic equations and elliptic systems9

35LHyperbolic equations and hyperbolic systems1

35PSpectral theory and eigenvalue problems for partial differential equations4

35QPartial differential equations of mathematical physics and other areas of application21

35RMiscellaneous topics in partial differential equations6

37Dynamical systems and ergodic theory42 preprints

37AErgodic theory17

37BTopological dynamics4

37CSmooth dynamical systems: general theory10

37DDynamical systems with hyperbolic behavior2

37ELow-dimensional dynamical systems3

37JDynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems7

37NApplications of dynamical systems11

39Difference and functional equations2 preprints

39BFunctional equations and inequalities2

40Sequences, series, summability2 preprints

40AConvergence and divergence of infinite limiting processes2

41Approximations and expansions1 preprint

41AApproximations and expansions1

42Harmonic analysis on Euclidean spaces24 preprints

42AHarmonic analysis in one variable5

42BHarmonic analysis in several variables19

42CNontrigonometric harmonic analysis1

43Abstract harmonic analysis5 preprints

43AAbstract harmonic analysis5

46Functional analysis61 preprints

46BNormed linear spaces and Banach spaces; Banach lattices24

46ELinear function spaces and their duals7

46LSelfadjoint operator algebras (C*-algebras, von Neumann (W*-) algebras, etc.)32

46MMethods of category theory in functional analysis3

47Operator theory10 preprints

47AGeneral theory of linear operators4

47BSpecial classes of linear operators3

47CIndividual linear operators as elements of algebraic systems3

47HNonlinear operators and their properties1

47LLinear spaces and algebras of operators1

49Calculus of variations and optimal control; optimization12 preprints

49JExistence theories in calculus of variations and optimal control1

49KOptimality conditions1

49QManifolds and measure-geometric topics12

51Geometry5 preprints

51FMetric geometry5

52Convex and discrete geometry34 preprints

52AGeneral convexity19

52BPolytopes and polyhedra7

52CDiscrete geometry20

53Differential geometry70 preprints

53AClassical differential geometry8

53BLocal differential geometry1

53CGlobal differential geometry50

53DSymplectic geometry, contact geometry13

53EGeometric evolution equations4

54General topology2 preprints

54CMaps and general types of topological spaces defined by maps1

54FSpecial properties of topological spaces1

55Algebraic topology22 preprints

55MClassical topics in algebraic topology2

55NHomology and cohomology theories in algebraic topology3

55PHomotopy theory16

55QHomotopy groups12

55RFiber spaces and bundles in algebraic topology1

55SOperations and obstructions in algebraic topology2

55TSpectral sequences in algebraic topology1

55UApplied homological algebra and category theory in algebraic topology3

57Manifolds and cell complexes25 preprints

57KLow-dimensional topology in specific dimensions11

57MGeneral low-dimensional topology3

57NTopological manifolds4

57PGeneralized manifolds2

57RDifferential topology10

57STopological transformation groups1

58Global analysis, analysis on manifolds9 preprints

58EVariational problems in infinite-dimensional spaces2

58JPartial differential equations on manifolds; differential operators7

60Probability theory and stochastic processes115 preprints

60BProbability theory on algebraic and topological structures18

60CCombinatorial probability10

60DGeometric probability and stochastic geometry11

60EDistribution theory6

60FLimit theorems in probability theory7

60GStochastic processes12

60HStochastic analysis1

60JMarkov processes43

60KSpecial processes64

62Statistics8 preprints

62HMultivariate analysis3

62JLinear inference, regression5

65Numerical analysis6 preprints

65CProbabilistic methods, stochastic differential equations1

65GError analysis and interval analysis3

65TNumerical methods in Fourier analysis2

68Computer science108 preprints

68NTheory of software1

68QTheory of computing81

68RDiscrete mathematics in relation to computer science14

68TArtificial intelligence3

68VComputer science support for mathematical research and practice3

68WAlgorithms in computer science42

74Mechanics of deformable solids3 preprints

74BElastic materials3

74GEquilibrium (steady-state) problems in solid mechanics1

76Fluid mechanics9 preprints

76DIncompressible viscous fluids9

80Classical thermodynamics, heat transfer2 preprints

80AThermodynamics and heat transfer2

81Quantum theory44 preprints

81PFoundations, quantum information and its processing, quantum axioms, and philosophy13

81QGeneral mathematical topics and methods in quantum theory14

81TQuantum field theory; related classical field theories10

81VApplications of quantum theory to specific physical systems15

82Statistical mechanics, structure of matter98 preprints

82BEquilibrium statistical mechanics81

82CTime-dependent statistical mechanics (dynamic and nonequilibrium)12

82DApplications of statistical mechanics to specific types of physical systems19

83Relativity and gravitational theory16 preprints

83CGeneral relativity16

90Operations research, mathematical programming16 preprints

90BOperations research and management science3

90CMathematical programming16

91Game theory, economics, finance, and other social and behavioral sciences6 preprints

91AGame theory6

92Biology and other natural sciences2 preprints

92CPhysiological, cellular and medical topics2

94Information and communication theory, circuits15 preprints

94ACommunication, information15