II.
Domain overview
Reference · livedomain:mathematics
Mathematics overview
Pure and applied mathematics spanning algebra, analysis, topology, number theory, combinatorics, probability, statistics, and numerical methods. Includes optimization, operations research, and mathematical logic. Provides the foundational language for physics, computer science, economics, and machine learning — and is increasingly relevant to formal verification and AI reasoning research.
Attributes
displayName
Mathematics
description
Pure and applied mathematics spanning algebra, analysis, topology, number
theory, combinatorics, probability, statistics, and numerical methods.
Includes optimization, operations research, and mathematical logic. Provides
the foundational language for physics, computer science, economics, and
machine learning — and is increasingly relevant to formal verification and
AI reasoning research.
Outgoing edges
contains2
- specialization:computational-mathematics·SpecializationComputational Mathematics
- specialization:statistical-methods·SpecializationStatistical Methods
Incoming edges
applies_to9
- benchmark:olympiad-bench·BenchmarkOlympiadBench
- benchmark:gsm-symbolic·BenchmarkGSM-Symbolic
- benchmark:hle·BenchmarkHumanity's Last Exam (HLE)
- benchmark:frontier-math·BenchmarkFrontierMath
- language:agda·LanguageAgda
- language:coq·LanguageCoq
- language:fortran·LanguageFortran
- language:idris·LanguageIdris
- language:lean·LanguageLean
applies_to_domain1
- workflow:experiment-design·WorkflowExperiment Design
lib_applies_to_domain80
- lib-agent:mathematics--algebraist·LibraryAgentalgebraist
- lib-agent:mathematics--bayesian-statistician·LibraryAgentbayesian-statistician
- lib-agent:mathematics--conjecture-analyst·LibraryAgentconjecture-analyst
- lib-agent:mathematics--discrete-optimization-expert·LibraryAgentdiscrete-optimization-expert
- lib-agent:mathematics--experimental-design-expert·LibraryAgentexperimental-design-expert
- lib-agent:mathematics--literature-reviewer·LibraryAgentliterature-reviewer
- lib-agent:mathematics--mathematical-modeler·LibraryAgentmathematical-modeler
- lib-agent:mathematics--mathematics-writer·LibraryAgentmathematics-writer
- lib-agent:mathematics--numerical-analyst·LibraryAgentnumerical-analyst
- lib-agent:mathematics--optimization-expert·LibraryAgentoptimization-expert
- lib-agent:mathematics--pde-expert·LibraryAgentpde-expert
- lib-agent:mathematics--proof-strategist·LibraryAgentproof-strategist
- lib-agent:mathematics--reproducibility-engineer·LibraryAgentreproducibility-engineer
- lib-agent:mathematics--statistical-modeler·LibraryAgentstatistical-modeler
- lib-agent:mathematics--symbolic-computation-expert·LibraryAgentsymbolic-computation-expert
- lib-agent:mathematics--theorem-prover-expert·LibraryAgenttheorem-prover-expert
- lib-agent:mathematics--uq-specialist·LibraryAgentuq-specialist
- lib-process:mathematics--algorithm-complexity-analysis·LibraryProcessalgorithm-complexity-analysis
- lib-process:mathematics--bayesian-inference-workflow·LibraryProcessbayesian-inference-workflow
- lib-process:mathematics--benchmark-validation·LibraryProcessbenchmark-validation
- lib-process:mathematics--conjecture-exploration·LibraryProcessconjecture-exploration
- lib-process:mathematics--convex-analysis-verification·LibraryProcessconvex-analysis-verification
- lib-process:mathematics--experimental-design-planning·LibraryProcessexperimental-design-planning
- lib-process:mathematics--hypothesis-testing-framework·LibraryProcesshypothesis-testing-framework
- lib-process:mathematics--latex-document-generation·LibraryProcesslatex-document-generation
- lib-process:mathematics--mathematical-literature-review·LibraryProcessmathematical-literature-review
- lib-process:mathematics--mathematical-notation-standardization·LibraryProcessmathematical-notation-standardization
- lib-process:mathematics--matrix-computation-optimization·LibraryProcessmatrix-computation-optimization
- lib-process:mathematics--model-formulation-workflow·LibraryProcessmodel-formulation-workflow
- lib-process:mathematics--model-validation-framework·LibraryProcessmodel-validation-framework
- lib-process:mathematics--numerical-stability-analysis·LibraryProcessnumerical-stability-analysis
- lib-process:mathematics--optimization-problem-formulation·LibraryProcessoptimization-problem-formulation
- lib-process:mathematics--pde-solver-selection·LibraryProcesspde-solver-selection
- lib-process:mathematics--proof-writing-assistance·LibraryProcessproof-writing-assistance
- lib-process:mathematics--reproducible-computation-setup·LibraryProcessreproducible-computation-setup
- lib-process:mathematics--sensitivity-analysis-optimization·LibraryProcesssensitivity-analysis-optimization
- lib-process:mathematics--statistical-model-selection·LibraryProcessstatistical-model-selection
- lib-process:mathematics--symbolic-integration-differentiation·LibraryProcesssymbolic-integration-differentiation
- lib-process:mathematics--symbolic-simplification·LibraryProcesssymbolic-simplification
- lib-process:mathematics--theorem-proof-verification·LibraryProcesstheorem-proof-verification
- lib-process:mathematics--uncertainty-quantification·LibraryProcessuncertainty-quantification
- lib-skill:mathematics--arxiv-search-interface·LibrarySkillarxiv-search-interface
- lib-skill:mathematics--benchmark-suite-manager·LibrarySkillbenchmark-suite-manager
- lib-skill:mathematics--combinatorial-enumeration·LibrarySkillcombinatorial-enumeration
- lib-skill:mathematics--computational-environment-manager·LibrarySkillcomputational-environment-manager
- lib-skill:mathematics--convex-optimization-solver·LibrarySkillconvex-optimization-solver
- lib-skill:mathematics--coq-proof-assistant·LibrarySkillcoq-proof-assistant
- lib-skill:mathematics--counterexample-generator·LibrarySkillcounterexample-generator
- lib-skill:mathematics--derivative-free-optimization·LibrarySkillderivative-free-optimization
- lib-skill:mathematics--diagram-generator·LibrarySkilldiagram-generator
- lib-skill:mathematics--floating-point-analysis·LibrarySkillfloating-point-analysis
- lib-skill:mathematics--graph-algorithm-library·LibrarySkillgraph-algorithm-library
- lib-skill:mathematics--interpolation-approximation·LibrarySkillinterpolation-approximation
- lib-skill:mathematics--isabelle-hol-interface·LibrarySkillisabelle-hol-interface
- lib-skill:mathematics--latex-math-formatter·LibrarySkilllatex-math-formatter
- lib-skill:mathematics--lean-proof-assistant·LibrarySkilllean-proof-assistant
- lib-skill:mathematics--math-notation-validator·LibrarySkillmath-notation-validator
- lib-skill:mathematics--mathematica-wolfram-interface·LibrarySkillmathematica-wolfram-interface
- lib-skill:mathematics--mathscinet-interface·LibrarySkillmathscinet-interface
- lib-skill:mathematics--maxima-cas-interface·LibrarySkillmaxima-cas-interface
- lib-skill:mathematics--mcmc-diagnostics·LibrarySkillmcmc-diagnostics
- lib-skill:mathematics--mixed-integer-optimization·LibrarySkillmixed-integer-optimization
- lib-skill:mathematics--monte-carlo-simulation·LibrarySkillmonte-carlo-simulation
- lib-skill:mathematics--multiple-testing-correction·LibrarySkillmultiple-testing-correction
- lib-skill:mathematics--nonlinear-optimization-solver·LibrarySkillnonlinear-optimization-solver
- lib-skill:mathematics--numerical-linear-algebra-toolkit·LibrarySkillnumerical-linear-algebra-toolkit
- lib-skill:mathematics--ode-solver-library·LibrarySkillode-solver-library
- lib-skill:mathematics--pde-solver-library·LibrarySkillpde-solver-library
- lib-skill:mathematics--polynomial-chaos-expansion·LibrarySkillpolynomial-chaos-expansion
- lib-skill:mathematics--power-sample-size-calculator·LibrarySkillpower-sample-size-calculator
- lib-skill:mathematics--proof-structure-analyzer·LibrarySkillproof-structure-analyzer
- lib-skill:mathematics--pymc-probabilistic-programming·LibrarySkillpymc-probabilistic-programming
- lib-skill:mathematics--robust-statistics-toolkit·LibrarySkillrobust-statistics-toolkit
- lib-skill:mathematics--sage-math-interface·LibrarySkillsage-math-interface
- lib-skill:mathematics--sensitivity-analysis-toolkit·LibrarySkillsensitivity-analysis-toolkit
- lib-skill:mathematics--sensitivity-analysis-uq·LibrarySkillsensitivity-analysis-uq
- lib-skill:mathematics--special-functions-library·LibrarySkillspecial-functions-library
- lib-skill:mathematics--stan-bayesian-modeling·LibrarySkillstan-bayesian-modeling
- lib-skill:mathematics--sympy-computer-algebra·LibrarySkillsympy-computer-algebra
- lib-skill:mathematics--zbmath-interface·LibrarySkillzbmath-interface
specializes3
- specialization:mathematics·SpecializationMathematics
- specialization:computational-mathematics·SpecializationComputational Mathematics
- specialization:statistical-methods·SpecializationStatistical Methods