Thinking·OS

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Axiom is part of Mathematical logic. Activate to inspect this relation.Mathematical proof depends on Axiom. Activate to inspect this relation.Mathematical proof depends on Mathematical logic. 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.Pythagorean theorem is a Theorem. Activate to inspect this relation.Theorem depends on Axiom. Activate to inspect this relation.Mathematical proofTheoremAxiomMathematical logicPythagorean theorem
Relationship types

15 concepts viewed through this lens. Bridge concepts connect this view to Algebra, Algorithms, Artificial Intelligence, Biochemistry….

Legend
  • Focused concept
  • Connected concept
  • Bridge concept (just outside the lens)
  • 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
5 concepts7 relationships3 disciplines2 relation families

Mathematical proof

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At a glance

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion.

Disciplines
Mathematics · Logic
Role in the graph
Connector
Relationships
3 · 2 relation families
Mental models
1

What am I looking at?

In this lens (15)

Bridge concepts (32)

Just outside the lens — they connect it to other context.

  • Turing machine3
    Computational Complexity, Computer Science, Theory of Computation · connects to Algorithm, Computability theory, Lambda calculus
  • Computational complexity theory2
    Algorithms, Computer Science · connects to Algorithm, Computability theory
  • Cardinal Number1
    Set Theory · connects to Axiom of choice
  • Closure1
    Programming Languages · connects to Lambda calculus
  • Computational biology1
    Biology, Computational Biology · connects to Algorithm

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.
  • Mathematical proof is a bridge concept — viewed here through Logic, 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.