Thinking·OS

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Explore the knowledge graph

Triangle is a Polygon. Activate to inspect this relation.Mathematical proof depends on Axiom. Activate to inspect this relation.Mathematical proof depends on Theorem. Activate to inspect this relation.Mathematical proof is part of Theorem. Activate to inspect this relation.Angle is part of Triangle. Activate to inspect this relation.Area measures Polygon. Activate to inspect this relation.Volume is analogous to Area. Activate to inspect this relation.Pythagorean theorem is a Theorem. Activate to inspect this relation.Pythagorean theorem applies to Triangle. Activate to inspect this relation.Congruence applies to Triangle. Activate to inspect this relation.Congruence is analogous to Similarity. Activate to inspect this relation.Trigonometry applies to Triangle. Activate to inspect this relation.Trigonometry depends on Sine and cosine. Activate to inspect this relation.Theorem depends on Axiom. Activate to inspect this relation.Mathematical proof depends on Mathematical logic. Activate to inspect this relation.Axiom is part of Mathematical logic. Activate to inspect this relation.TheoremMathematical proofAxiomPythagorean theoremMathematical logicTrianglePolygonTrigonometryAngleCongruenceAreaSine and cosineSimilarityVolume
Relationship types
Legend
  • 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 concepts16 relationships3 disciplines5 relation families

At a glance

In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven.

Disciplines
Mathematics · Logic
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 3 disciplines: Geometry, Logic, Mathematics.
  • Theorem is a bridge concept — viewed here through Logic, Mathematics.
  • The connections here span 5 relation families.
  • Oscillation explains 2 concepts in this view (Geometry, Mathematics).

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.