Thinking·OS

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Integer is a Rational number. Activate to inspect this relation.Natural number is a Integer. Activate to inspect this relation.Prime number is a Natural number. Activate to inspect this relation.Divisor applies to Integer. Activate to inspect this relation.Prime number depends on Divisor. Activate to inspect this relation.Divisibility applies to Integer. Activate to inspect this relation.Fundamental theorem of arithmetic depends on Prime number. Activate to inspect this relation.Modular arithmetic applies to Divisibility. Activate to inspect this relation.Riemann hypothesis applies to Prime number. Activate to inspect this relation.Shor's algorithm applies to Prime number. Activate to inspect this relation.Langlands program applies to Prime number. Activate to inspect this relation.Birch–Swinnerton-Dyer conjecture applies to Prime number. Activate to inspect this relation.Fundamental theorem of arithmetic depends on Divisibility. Activate to inspect this relation.RSA cryptosystem depends on Modular arithmetic. Activate to inspect this relation.Elliptic-curve cryptography depends on Modular arithmetic. Activate to inspect this relation.DivisibilityFundamental theorem of arithmeticIntegerModular arithmeticPrime numberRational numberNatural numberDivisorRSA cryptosystemElliptic-curve cryptographyRiemann hypothesisShor's algorithmLanglands programBirch–Swinnerton-Dyer conjecture
Relationship types
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  • Focused concept
  • Connected concept
  • Arrow points from cause / source to effect / target
  • A line with no arrow is a two-way relationship
  • Node colour marks the concept’s primary discipline
14 concepts15 relationships5 disciplines3 relation families

Divisibility

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At a glance

Divisibility is whether one integer divides another with no remainder, the foundation of number theory.

Disciplines
Number Theory · Mathematics
Role in the graph
Connector
Relationships
3 · 2 relation families

Insights from this view

Structural observations about the concepts shown here — descriptions of this graph, not claims about the world.

  • This view connects 5 disciplines: Arithmetic, Cryptography, Mathematics, Number Theory, Quantum Computing.
  • Divisibility is a bridge concept — viewed here through Mathematics, Number Theory.
  • The connections here span 3 relation families.

Relationships as a list

The focused concept’s relationships. Pick another concept in the graph above to update this list.

Explore through a different lens

A lens is a deterministic projection of the graph. Pick a discipline, thinking pattern or journey to reframe the whole view.

By discipline

ChemistryBiologyPhysicsMathematicsComputer ScienceGeologyMineralogyEconomics

By thinking pattern

Bayesian updatingCause and effectCompoundingConservationConstraintsDefense in depthDiffusion & spreadEmergenceEnergy transformationEntropy & irreversibilityEquilibriumFeedback loopIncentivesInformationLevels & hierarchyModularityNetworksOptimizationOscillationProbabilityRecursion & self-similarityScaleSignal vs noiseSource–pathway–receptorStocks and flowsSymmetry & invarianceThresholds & tipping pointsTrade-offsTriangulationVariation & selectionWaves

By journey

From a Leaf to the ClimateWhy Music Moves UsHow Machines LearnReasoning about a Leaf and the Climate

Concept collections

Concept collections are curated lenses onto the fabric — themed sets of ideas that recur across disciplines. They are not journeys; they are a way to read the graph.

About this view

What this is

Start from one concept and expand outward. The view never shows everything at once — click a node to refocus, filter by relationship type, or switch to an accessible list.

One fabric

3750 concepts and 5051 typed relations form one connected component — no isolated silo.

How to read it

Focus a concept, or apply a lens (discipline, mental model, journey) to see only the threads that matter.