Thinking·OS

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Explore the knowledge graph

Coefficient is a Number. Activate to inspect this relation.Coefficient is part of Polynomial. Activate to inspect this relation.Continuity depends on Limit. Activate to inspect this relation.Continuous function depends on Limit. Activate to inspect this relation.Derivative depends on Continuity. Activate to inspect this relation.Derivative requires Continuity. Activate to inspect this relation.Derivative depends on Limit. Activate to inspect this relation.Differential equation is a Mathematical model. Activate to inspect this relation.Differential equation applies to Mathematical model. Activate to inspect this relation.Differential equation depends on Rate of change. Activate to inspect this relation.Differential equation is a Equation. Activate to inspect this relation.Discretization applies to Differential equation. Activate to inspect this relation.Dynamical System depends on Differential equation. Activate to inspect this relation.Factorization applies to Polynomial. Activate to inspect this relation.Infinity applies to Limit. Activate to inspect this relation.Integral is analogous to Rate of change. Activate to inspect this relation.Integral is a Mathematical expression. Activate to inspect this relation.Limit enables Integral. Activate to inspect this relation.Limit enables Rate of change. Activate to inspect this relation.Linear equation is a Equation. Activate to inspect this relation.Numerical approximation applies to Differential equation. Activate to inspect this relation.Polynomial is a Mathematical expression. Activate to inspect this relation.Rate of change depends on Limit. Activate to inspect this relation.Sequence and series applies to Limit. Activate to inspect this relation.Slope models Rate of change. Activate to inspect this relation.Slope is part of Linear equation. Activate to inspect this relation.Tangent depends on Rate of change. Activate to inspect this relation.Mathematical expressionIntegralPolynomialRate of changeLimitCoefficientFactorizationSlopeDifferential equationTangentContinuityContinuous functionDerivativeSequence and seriesInfinityNumberLinear equationEquationMathematical modelDiscretizationDynamical SystemNumerical approximation
Relationship types

172 concepts viewed through this lens. Bridge concepts connect this view to Acoustics, Actuarial Science, Agriculture, Algorithms….

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
22 concepts27 relationships12 disciplines6 relation families

Mathematical expression

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At a glance

In mathematics, an expression is an arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation.

Disciplines
Mathematics · Algebra
Role in the graph
Connector
Relationships
2 · 1 relation families

What am I looking at?

In this lens (172)

Bridge concepts (186)

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

  • Rate of change5
    Calculus, Economics, Physics · connects to Differential equation, Integral, Limit…
  • Enumerative counting4
    Combinatorics · connects to Combination, Generating function, Permutation…
  • Graph data structure4
    Computer Science, Data Structures · connects to Connectivity, Edge, Shortest path…
  • Machine learning3
    Artificial Intelligence, Computer Science, Machine Learning, Statistics · connects to Algorithm, Pattern, Probability
  • Optimization3
    Business, Economics, Engineering, Mathematical Modelling, Optimization, Systems Engineering · connects to Inequality, Linear programming, Mathematical model

Insights from this view

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

  • This view connects 12 disciplines: Algebra, Arithmetic, Calculus, Differential Equations, Economics, Geometry, Mathematical Analysis, Mathematical Modelling, Mathematics, Numerical Analysis, Physics, Systems Science.
  • Mathematical expression is a bridge concept — viewed here through Algebra, Mathematics.
  • The connections here span 6 relation families.
  • Causality explains 2 concepts in this view (Algebra, Mathematical Modelling, Mathematics, Systems Science).

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.