Mathematical proof
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion.
At a glance
Key signals
0% cross fields · reaches 0 more
- Mathematics
- Logic
- Explanation
- Examples
- Misconception
- Sourced relations 4
- Attribution
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
Mathematical proofdepends onAxiomEstablished
mathematical proof depends on axiom.
Mechanism: A proof rests on axioms: it derives a new truth by chaining logical steps from statements accepted without proof.
- Wikidata verifiedmoderate evidence
Mathematical proofdepends onMathematical logicEstablished
mathematical proof depends on mathematical logic.
Mechanism: A proof is a chain of logically valid steps from accepted axioms to a theorem — certainty earned by reasoning.
- Wikipedia (English & German editions) verifiedmoderate evidence
Mathematical proofdepends onTheoremEstablished
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.
- Wikidata verifiedmoderate evidence
System context
Mathematical proofis part ofTheoremEstablished
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.
- Wikidata verifiedmoderate evidence
Structural role & consequence
Interpreted from the current atlas graph — what the connections mean, not just how many there are.
Builds on 3 foundations (requires / depends-on / derived-from / emerges-from).
structural · Structural graph analysis — not a claim of importance, causation or history.
Currently dark in the atlas: 4 of 4 of its relations lack claim-level evidence.
atlas representation · Describes the current Thinking OS representation, not the state of the world.
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.
cross-field
3 within-field, 0 cross-field
Strengths & constraints
Constraints
- Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
Conditions
- Its dependency reading rests on 3 foundation relations. 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.
Seen through each discipline
How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.
Through this lens it connects to Axiom, Theorem, Theorem and Mathematical logic.
Through this lens it connects to Axiom, Theorem, Theorem and Mathematical logic.
Key dates
- c. 300 BCEFormalizationEuclid's Elements establishes the axiomatic-deductive proof. — MacTutor History of Mathematics Archive
Related ideas to explore
Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.
This idea also appears in…
The same structure shows up in other disciplines. These are real recurrences drawn from the graph — a starting point for asking “what carries over, and what changes?”
Cause and effect33 disciplines · 31 concepts
Concepts
shares a mental model
shares a mental model
shares a mental model
shares a mental model
shares a mental model
shares a mental model
Mental models at work here
- Connects 3 other ideas across 2 disciplines.
- Most of its connections are of the “Dependency” kind.
- It exercises 1 reusable thinking pattern.
Derived from the graph’s real structure — observations, not a score.
Sources
- Wikipedia (English & German editions) verifiedmoderate evidence
- Wikidata verifiedmoderate evidence
- Mathematical Logic (2025) verified
- Mathematical proof verified
- Proof, Mathematical Problem-Solving, and Explanation in Mathematics Teaching (2009) verified