Mathematics¶
60 primes originate from Mathematics. 44 more draw from it as a secondary origin.
Primary members (60)¶
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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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 (44)¶
Primes whose canonical origin is elsewhere, but who list Mathematics among their alternate origin domains.
- Abstraction — Focus on core elements.
- Algorithm — Step-by-step problem-solving procedure.
- Balance and Symmetry (In Art/Design)
- Bayesian Updating — Update beliefs with evidence.
- Boundary — Defines system limits.
- Complexity — Measures system intricacy.
- Complexity (Time/Space) — Resource scaling with input size.
- Composition — Arranges components into a cohesive whole.
- Conjugate Variables — Interlinked variable pairs.
- Conservation Laws — Quantities remain constant.
- Controllability — Ability to steer system.
- Deductive Reasoning — General to specific conclusions.
- Degrees of Freedom — Independent parameters.
- Dimensionality Reduction — Reduce variables.
- Discrete vs. Continuous (Quantization) — Step vs continuous evolution.
- Falsifiability — A claim is scientific only if it could in principle be empirically refuted.
- Gauge Invariance / Gauge Symmetry — Equivalent representations.
- Heuristic — Mental shortcuts.
- Infinite Regress — Endless chain of explanation.
- Instability — Amplifies perturbations.
- Intermittency — Irregular bursts.
- Inversion — Reversal of structures.
- Iteration — Repeats steps to refine outcomes.
- Markov Decision Processes (MDPs) — Sequential decision-making under uncertainty.
- Network Flow Models — Optimize flow across networks.
- Noether's Theorem — Symmetry links to conservation.
- Paradox — Contradictory but revealing truth.
- Pareto Effect (80/20 Rule) — 80/20 distribution.
- Pattern (in Design) — Repeated motifs.
- Perspective — Representation of depth.
- Perturbation — Small disturbance.
- Perturbation Theory — A technique for handling an intractable problem by splitting it into an exactly solvable baseline plus a small correction, then expanding the quantities of interest as a power series in that small parameter.
- Phase Space — All possible system states.
- Principle of Least Action — Optimal system paths.
- Proportion and Scale — Relative size relationships.
- Queueing — Organizes tasks into a waiting line based on arrival and service rates.
- Recursion — Breaks processes into self-similar steps.
- Renormalization — Adjust parameters across scales.
- Scale Invariance — Behavior unchanged under scaling.
- State and State Transition — Captures system condition and evolution.
- Superposition — Multiple states coexist.
- Symmetry Breaking — Loss of symmetry creates structure.
- Turbulence — Chaotic multi-scale flow.
- Variation Strategies — Deliberately injecting controlled variation into a system and selecting from the results to explore alternatives, accelerate learning, and gain robustness.