Thinking·OS

← All disciplines

Formal sciences

Mathematics

A discipline is a lens, not an owner — the same idea can be viewed through many.

172 concepts417 relationships8 relation families75 bridge concepts
MathematicsFunctionSetProbability distributionHarmonic ratioDifferential equationLimitRatioProbability

Concepts viewed through this lens

These numbers describe the current Thinking OS knowledge slice, not the whole field.

Explore this lens in the graph →

Disciplines it bridges to

Each bridge is built by ideas the two fields share, the thinking patterns that recur across both, and a representative relationship that shows how they connect.

Field shape — representation health

68/100 overall · 172 concepts

The eight dimensions measure Thinking OS coverage of this field, not the quality or importance of the discipline.

  • Structural80 /100
  • Evidence77 /100
  • Foundations90 /100
  • Factual depth12 /100
  • Pedagogical50 /100
  • Cross-disciplinary100 /100
  • Provenance31 /100
  • Taxonomy100 /100

What kind of structure is this field?

Interpreted from the current atlas — how this field is represented, not a judgement of the field.

  • Representation health 68/100 — healthy representation. Strongest: cross-disciplinary, taxonomy. Thinnest: factual depth, provenance.

    structural · Measures the current Thinking OS representation, not the quality or importance of the field.

  • Its 68 representation-health is above the 64 median of 11 similarly-sized disciplines (comparable by concept count).

    structural · Measures the current Thinking OS representation, not the quality or importance of the field.

  • 22% of its concepts have a single connection (mean internal degree 2.2) — a fairly cohesive internal structure.

    structural · Measures the current Thinking OS representation, not the quality or importance of the field.

  • 54% of its relations reach into 131 other disciplines — an outward-facing field in the atlas.

    structural · Measures the current Thinking OS representation, not the quality or importance of the field.

  • 86% of its concepts carry a source, 67% a Tier A/B source; 45% of relations carry claim-level evidence.

    atlas representation · Measures the current Thinking OS representation, not the quality or importance of the field.

How this lens connects

The kinds of relationship that characterise this discipline lens in the current slice.

Kind & structure124
Teaching link110
Dependency88
Cause & effect41
Explains & models30
Analogy & transfer21
Time order2
Evidence1

Coverage matrix

How these concepts distribute across domains and concept families — real counts, not a score.

SystemsInformationMatterChangePatternsEnergyLifeScaleStructureDecisionNetworksWavesCausalityComputationEarthSpaceOptimizationNumberProbabilitySecurityThresholdsConstraintsNatural sciencesFormal sciencesEngineeringMedicine & healthSocial sciencesHumanitiesProfessionalArtsInterdisciplinary111525153011927332336661111141

Knowledge timeline

Real, sourced key dates of these concepts.

15 events
500 BCE050010001500c. 530 BCE · Pythagorean theoremc. 450 BCE · Irrational numberc. 300 BCE · Algorithmc. 300 BCE · Axiomc. 300 BCE · Golden ratioc. 300 BCE · Mathematical proofc. 300 BCE · Prime numberc. 250 BCE · Pic. 150 BCE · Trigonometryc. 820 CE · Algorithmc. 820 CE · Quadratic equation1202 · Fibonacci sequence1944 · Game theory1950 · Game theory1950 · Nash equilibrium

Ideas that connect this discipline outward

Concepts viewed through this lens that reach disciplines it does not itself carry — concept-level bridges (distinct from the discipline-to-discipline bridges below).

  • NetworkreachesAgricultureArchaeologyBiologyBusinessComplexity ScienceComputational Social ScienceComputer ScienceDecision TheoryEcologyEconomicsEngineeringEnvironmental ScienceEpidemiologyGeographyIndustrial EngineeringLogisticsManagementNeuroinformaticsNeuroscienceOperations ResearchPhysiologyPolitical SciencePublic HealthSupply Chain ManagementSystems BiologyUrban Science
  • ProbabilityreachesActuarial ScienceArtificial IntelligenceBiostatisticsComplexity ScienceComputer ScienceData ScienceDecision TheoryDiscrete MathematicsEconomicsEpistemologyEthicsFinanceInformation TheoryMachine LearningMedicinePhysical ChemistryPhysicsPublic PolicyQuantum PhysicsStatistical PhysicsThermodynamics
  • PatternreachesArtificial IntelligenceBioinformaticsComparative LiteratureComputer ScienceData StructuresDiscrete MathematicsEarth & Space SciencesGeometryHistoryLinguisticsLiteratureMolecular BiologyMusicMusic TheoryMusicologyPhilosophyPhysicsSoftware EngineeringStatisticsSystems ScienceVisual Arts
  • AlgorithmreachesArtificial IntelligenceBiochemistryBioinformaticsBiologyCell BiologyComputational BiologyComputational ComplexityData StructuresEvolutionary BiologyGeneticsHistoryInformation TheoryMachine LearningMolecular BiologyNumerical AnalysisOptimizationStatistics
  • SequencereachesAlgorithmsBiochemistryBiologyCell BiologyCognitive ScienceDesignEducationEducational ScienceEvolutionary BiologyGeneticsLogicMachine LearningSoftware EngineeringTheory of Computation
  • Mathematical modelreachesBiologyBiostatisticsBusinessCalculusClimatologyEarth & Space SciencesEconometricsEconomicsEngineeringOptimizationPhilosophy of ScienceStatisticsSystems Engineering

Mental models that recur here

Scale ×12

How a system's size changes what matters about it. Quantities rarely scale in step: doubling a length can quadruple an area and multiply a volume eightfold.

Probability ×9

A way to reason about uncertainty by assigning each possible outcome a share of the whole, between impossible (0) and certain (1).

Compounding ×7

When each step's growth is added to the base so the next step grows too — producing accelerating, exponential change rather than a steady line.

Cause and effect ×6

One thing genuinely bringing about another — as opposed to two things merely moving together. Establishing it needs a mechanism and controls, not just a pattern.

Learning journeys that use it

Why Music Moves UsHow Machines Learn

People represented in this atlas

People tagged with this lens who have a recorded contribution. Not exhaustive, and not a ranking.

Explore connections →

What this lens reveals
  • 172 concepts are viewed through this lens.
  • 75 of them bridge into other disciplines.
  • Its signature thinking pattern is “Scale” (recurs in 12 concepts).
  • The most common kind of connection here is “Kind & structure”.
  • It is most tightly linked to Physics.

Derived from the current graph structure — observations, not a judgement of the field.