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MathematicsLogicEstablished

Theorem

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

TheoremMathematical proofAxiomPythagorean theoremMathematical logicTrianglePolygonTrigonometryAngle

At a glance

Type
information
Disciplines 2
MathematicsLogic
Mental models 0
—
Role in the graph
Connector

Key signals

Cross-disciplinary reach
Disciplines
2
  • Mathematics
  • Logic
Evidence & development

Dependencies

What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.

Foundations · builds on

Theoremdepends onAxiomEstablished

Open Axiom →

theorem depends on axiom.

Mechanism: A theorem ultimately depends on axioms: it is a truth derived by pure logic from the starting assumptions a system accepts.

Sources:

Enables · leads to

Mathematical proofdepends onTheoremEstablished

Open Mathematical proof →

mathematical proof depends on theorem.

Mechanism: A proof may build on earlier theorems: already-established results become tools in the chain of reasoning for a new one.

Sources:

System context

Mathematical proofis part ofTheoremEstablished

Open Mathematical proof →

mathematical proof is part of theorem.

Mechanism: A theorem is a statement together with its proof: the proof is the rigorous argument that establishes the theorem as true.

Sources:
Pythagorean theoremis aTheoremEstablished

Open Pythagorean theorem →

Pythagorean theorem is a kind of theorem.

Mechanism: The Pythagorean theorem is a proven result: in a right triangle, the square on the longest side equals the sum of the squares on the other two.

Sources:

Structural role & consequence

Interpreted from the current atlas graph — what the connections mean, not just how many there are.

  • Currently dark in the atlas: no key date stored · 4 of 4 of its relations lack claim-level evidence.

    atlas representation · Describes the current Thinking OS representation, not the state of the world.

  • Builds on 1 foundation (requires / depends-on / derived-from / emerges-from).

    structural · Structural graph analysis — not a claim of importance, causation or history.

  • All 3 of its relationships stay within its own discipline — a field-specific concept in the current atlas.

    structural · Structural graph analysis — not a claim of importance, causation or history.

0%

cross-field
3 within-field, 0 cross-field

0 of 4 relations carry evidence · concept has a verified source

Strengths & constraints

Constraints

  • Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
  • No dated history stored — the atlas records no key date for this concept. atlas representation

Conditions

  • Its dependency reading rests on 1 foundation relation. structural
  • Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural

Dependency radial

What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.

AxiomMathematical proofTheorem◀ builds onenables ▶

What builds on this

1 concept build on this directly, 1 in total, across 2 disciplines.

LogicMathematics

Structural downstream reach along dependency edges — not a claim of historical necessity.

Seen through each discipline

How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.

Mathematics

Through this lens it connects to Axiom, Mathematical proof, Mathematical proof and Pythagorean theorem.

Theorem through the Mathematics lens →

Logic

Through this lens it connects to Axiom, Mathematical proof and Mathematical proof.

Theorem through the Logic lens →

Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.

The scientific picture
  • Connects 3 other ideas across 2 disciplines.
  • Most of its connections are of the “Kind & structure” kind.

Derived from the graph’s real structure — observations, not a score.

Sources