Number Theory
A discipline is a lens, not an owner — the same idea can be viewed through many.
Concepts viewed through this lens
These numbers describe the current Thinking OS knowledge slice, not the whole field.
Disciplines it bridges to
Each bridge is built by ideas the two fields share, the thinking patterns that recur across both, and a representative relationship that shows how they connect.
Number Theoryconnects toMathematics
Shared concepts
Why this bridge exists
Fundamental theorem of arithmetic depends on Prime number — Primes are the building blocks of integers.
Explore this connection →Number Theoryconnects toArithmetic
Why this bridge exists
Fundamental theorem of arithmetic depends on Prime number — Primes are the building blocks of integers.
Explore this connection →Number Theoryconnects toCryptography
Why this bridge exists
Elliptic-curve cryptography depends on Modular arithmetic — Elliptic-curve cryptography computes over a finite field.
Explore this connection →Number Theoryconnects toComputational Complexity
Why this bridge exists
P versus NP is analogous to Riemann hypothesis — Both are Millennium Problems.
Explore this connection →Number Theoryconnects toComputer Science
Why this bridge exists
P versus NP is analogous to Riemann hypothesis — Both are Millennium Problems.
Explore this connection →
Field shape — representation health
50/100 overall · 7 concepts
The eight dimensions measure Thinking OS coverage of this field, not the quality or importance of the discipline.
What kind of structure is this field?
Interpreted from the current atlas — how this field is represented, not a judgement of the field.
Representation health 50/100 — sparse and incomplete. Strongest: evidence, cross-disciplinary. Thinnest: factual depth, pedagogical.
structural · Measures the current Thinking OS representation, not the quality or importance of the field.
82% of its relations reach into 5 other disciplines — an outward-facing field in the atlas.
structural · Measures the current Thinking OS representation, not the quality or importance of the field.
Its 50 representation-health is below the 54 median of 139 similarly-sized disciplines (comparable by concept count).
structural · Measures the current Thinking OS representation, not the quality or importance of the field.
Current atlas gaps: no dated concepts · no relation-level evidence.
atlas representation · Measures the current Thinking OS representation, not the quality or importance of the field.
43% of its concepts have a single connection (mean internal degree 0.6) — a moderately connected internal structure.
structural · Measures the current Thinking OS representation, not the quality or importance of the field.
How this lens connects
The kinds of relationship that characterise this discipline lens in the current slice.
Coverage matrix
How these concepts distribute across domains and concept families — real counts, not a score.
Ideas that connect this discipline outward
Concepts viewed through this lens that reach disciplines it does not itself carry — concept-level bridges (distinct from the discipline-to-discipline bridges below).
- Riemann hypothesisreachesArithmeticComputational ComplexityComputer Science
- Modular arithmeticreachesCryptography
People represented in this atlas
People tagged with this lens who have a recorded contribution. Not exhaustive, and not a ranking.
- Bryan Birch
1931–present
- Robert Langlands
1936–present
- 7 concepts are viewed through this lens.
- 2 of them bridge into other disciplines.
- The most common kind of connection here is “Teaching link”.
- It is most tightly linked to Mathematics.
Derived from the current graph structure — observations, not a judgement of the field.