P versus NP
The central open question of whether every problem whose answer is easy to check is also easy to solve.
At a glance
Key signals
20% cross fields · reaches 7 more
- Computer Science
- Mathematics
- Computational Complexity
- Explanation
- Examples
- Misconception
- Sourced relations
- 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.
Enables · leads to
One-way functiondepends onP versus NPEstablished
Easy forward, hard back.
Mechanism: One-way functions can exist only if P ≠ NP — the bedrock assumption of cryptography.
Structural role & consequence
Interpreted from the current atlas graph — what the connections mean, not just how many there are.
20% of its relationships cross field boundaries, reaching 7 other disciplines — unusual in a discipline where most concepts stay within their field.
structural · Structural graph analysis — not a claim of importance, causation or history.
Currently dark in the atlas: no key date stored · 5 of 5 of its relations lack claim-level evidence.
atlas representation · Describes the current Thinking OS representation, not the state of the world.
Structural neighbourhood: 5 → 27 → 100 concepts reachable within 3 hops.
structural · Structural reach — being reachable is not the same as being understood.
cross-field
4 within-field, 1 cross-field
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
- 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.
What builds on this
1 concept build on this directly, 3 in total, across 2 disciplines.
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.
Through this lens it connects to Algorithm and Riemann hypothesis.
Through this lens it connects to Complexity Class NP and Class P.
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?”
Concepts
- Riemann hypothesisNumber Theory
explicitly analogous
- One-way functionCryptography
crosses a discipline boundary
- Connects 5 other ideas across 3 disciplines.
- A cross-disciplinary bridge — its connections reach into 7 other fields.
- Most of its connections are of the “Teaching link” kind.
Derived from the graph’s real structure — observations, not a score.
Sources
- On P versus NP $ \cap $ co-NP for decision trees and read-once branching programs (1999) verified
- The P versus NP Question (2010) verified
- P versus NP (2020) verified
- P versus NP (2020) verified