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Mathematics

66 primes originate from Mathematics. 47 more draw from it as a secondary origin.

Primary members (66)

Primes whose canonical origin is Mathematics.

  • Approximation — Good-enough representation.
  • Associativity — Grouping does not affect result.
  • Axiomatic Incompatibility — A small set of individually plausible axioms is provably jointly unsatisfiable, forcing a chosen trade-off.
  • Boundedness — Values remain within limits.
  • Cardinality — Size of sets.
  • Central Limit Theorem — Summing many independent finite-variance contributions yields a Gaussian envelope that forgets the shapes of its parts.
  • Chaos — Unpredictable dynamics.
  • Closure — Ensures operations remain within a set.
  • Coaxiality — Two or more spatial entities are coaxial when their constitutive axes coincide, allowing placement, rotation, and radial offset to be reasoned about relative to one common line.
  • Commutativity — Order of inputs does not affect output.
  • Completeness — No gaps in structure.
  • Constraint — Limits possibilities to guide outcomes.
  • Continuity — Smooth change without jumps.
  • Convergence — Movement toward stable state.
  • Correlation — Systematic co-variation between variables, distinct from causation.
  • Decomposition — Breaking a whole into parts that can be analyzed independently and recombined to reconstitute the whole, making complexity tractable through divide-and-conquer.
  • Dimension — Degrees of freedom in a system.
  • Discreteness — Countable steps.
  • Duality — Complementary perspectives.
  • Equivalence Relation — Groups elements into equivalence classes.
  • Equivariance — A map whose output transforms in step with transformations of its input.
  • Exponentiation — Repeated multiplication scaling.
  • Formalization — Rendering informal practice into explicit, codified, rule-governed form.
  • Fractal Geometry — Self-similar patterns.
  • Function (Mapping) — Relates inputs to outputs.
  • Fuzzy Set — A fuzzy set makes belonging graded by assigning every candidate element a membership degree between zero and one, while retaining crisp sets as the endpoint-valued special case.
  • Game-Theoretic Strategy — Strategic interaction analysis.
  • Gradient — Distribution and change over space/time.
  • Idempotence — Repetition yields same result.
  • Infinity — Unbounded quantity.
  • Invariance — Properties unchanged under transformation.
  • Isomorphism — Structure-preserving mapping.
  • Linearity — Proportional output.
  • Local-to-Global Aggregation — Locally checkable properties promote to a global verdict under an explicit aggregation discipline.
  • Mathematical Induction — Proof method across natural numbers.
  • Minimax Strategy — Choose the action whose worst possible outcome is the best worst possible outcome — minimize the maximum loss an adversarial environment can inflict.
  • Modifiable Areal Unit Problem — Statistics computed on aggregated data change, sometimes reversing sign, when the boundaries used to aggregate are redrawn — the partition is a non-neutral analytical input.
  • Network — Models interactions between components.
  • Nonlinearity — Disproportionate output.
  • Optimization — Finds best solution under constraints.
  • Order — Defines ranking or sequencing relationships.
  • Parrondo's Paradox — Two individually losing strategies, coupled through a shared state with opposite-signed regional effects, can combine into a winning one.
  • Partition Dependence of Aggregates — Any statistic computed on partition-aggregated data is a function of the partition itself, not solely of the underlying data.
  • Periodicity — Regular cycles.
  • Permutation — Reassign every member or position of a collection exactly once, preserving membership while changing arrangement; the resulting bijective self-maps compose, invert, and decompose into cycles.
  • Price of Anarchy — The worst-case ratio between the aggregate cost of selfish equilibrium play and the cost under centralized optimal coordination.
  • Probability — Quantifies uncertainty and likelihoods.
  • Progressive Refinement from Core Model — Incremental refinement.
  • Randomness — Model unpredictability.
  • Realized vs Possible Outcomes — The comparison between what a process actually produces and what it could in principle produce, with the gap as the primary object of analysis.
  • Reciprocal Additivity (Optic Equation) — Relate nonzero inputs to one effective result by requiring the reciprocal of the result to equal the sum of the input reciprocals, so parallel contribution becomes ordinary addition after reciprocal transformation.
  • Recurrence — The property by which a state, event, or value reappears across time or iterations because the present state depends on prior states, distinct from mere repetition by its measurable lag structure.
  • Recursive Attenuating Amplification — A one-shot input recirculating through a leaky operator with sub-unit retention produces a bounded total response of input/(1−k).
  • Refinement — Iteratively improving a candidate solution toward adequacy through repeated cycles of evaluation and adjustment that narrow the gap to a target, rather than deriving the answer in one shot.
  • Relation — Describes associations or dependencies.
  • Representation — Model complex ideas.
  • Scale — Properties change with size.
  • Set and Membership — Groups and categorizes elements.
  • Subadditivity — A combined whole never evaluates above the sum of its separately evaluated parts, so decomposition supplies a guaranteed upper bound.
  • Symmetry — Invariance under transformation.
  • Topology — Studies properties preserved under deformation.
  • Transformation — A rule-governed mapping that restructures an input into a different output, holding certain invariants fixed while altering others.
  • Truncation — Apply a declared boundary to retain an admissible bounded part of an ordered, extended, or over-complete object while discarding the part that lies beyond it.
  • Variance Bounds Selection Response — The rate at which selection shifts a population's mean equals within-population variance times selection intensity, so variance is the fuel selection consumes and must be regenerated.
  • Verifier-Prover Asymmetry — Verifying a candidate solution is qualitatively cheaper than finding one, and the cost-ratio supports a characteristic class of designs that split finding from checking.
  • Well-Foundedness (Well-Ordering) — Prevents infinite descent.

Also draws from Mathematics (47)

Primes whose canonical origin is elsewhere, but who list Mathematics among their alternate origin domains.