Domain 02 · Mathematics Codex
Number Systems & Number Theory
From counting marks on the Ishango bone to the Riemann Hypothesis — the complete mathematics of number.
Scope
Natural numbers, integers, rational numbers, real numbers, complex numbers, p-adic numbers, quaternions; prime numbers, divisibility, modular arithmetic, Diophantine equations, elliptic curves, analytic and algebraic number theory.
Number theory asks the oldest and hardest questions in mathematics. What patterns do the primes follow? Can every even number greater than 2 be written as the sum of two primes (Goldbach's conjecture — still unproved)? The field has produced the longest-standing open problems in mathematics and the deepest connections between seemingly unrelated areas.
Entries in this domain
Build status: This domain is in active build. Live entries are marked below. All other entries are planned and pending — see build status for the full picture.
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Natural Number
Live
The counting numbers — the oldest mathematical objects in human history, invented independently by every known civilisation.
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Integer
Pending
The whole numbers — positive, negative, and zero — forming the simplest ring in abstract algebra.
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Prime Number
Pending
A natural number greater than 1 with no divisors other than 1 and itself — the atoms of arithmetic.
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Rational Number
Pending
Any number expressible as a ratio p/q of two integers where q ≠ 0.
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Real Number
Pending
The complete ordered field that fills the number line without gaps — the foundation of calculus.