| Note | Description | | ----------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------- | | [[notes/Aleatory probability.md\|Aleatory probability]] | Probabilities derived from random processes or games of chance that are inherently unpredictable. | | [[notes/Algebraic functions.md\|Algebraic functions]] | Functions defined by polynomials and rational expressions where the variable is raised to integer powers. | | [[notes/All models are wrong.md\|All models are wrong]] | A reminder that scientific and statistical models are simplifications of reality and contain inaccuracies, yet can still be useful. | | [[notes/Banach-Tarski paradox.md\|Banach-Tarski paradox]] | A geometry theorem stating that a sphere can be split into pieces and reassembled into two identical spheres of the original size. | | [[notes/Birthday paradox.md\|Birthday paradox]] | In a group of just 23 people, there is a ~50% chance that at least two share the same birthday. | | [[notes/Black swan.md\|Black swan]] | An unpredictable, rare event with severe consequences that often appears obvious in hindsight. | | [[notes/Bonferroni correction.md\|Bonferroni correction]] | A statistical adjustment to control the probability of making false discoveries when conducting multiple comparisons. | | [[notes/Butterfly effect.md\|Butterfly effect]] | The sensitive dependence on initial conditions in chaotic systems, where small changes can lead to vastly different outcomes. | | [[notes/Category theory.md\|Category theory]] | A branch of mathematics that studies abstract structures and relationships between them through objects and morphisms. | | [[notes/Composition.md\|Composition]] | Relationships that can be deduced can also be omitted. | | [[notes/Constructor theory.md\|Constructor theory]] | The theory that fundamental laws can be expressed in terms of what physical transformations are possible and impossible. | | [[notes/Credence probability.md\|Credence probability]] | An individual’s subjective degree of belief in the truth of a proposition, often expressed as a probability. | | [[notes/Data dredging.md\|Data dredging]] | The misuse of data analysis to find spurious patterns by performing numerous statistical tests without prior hypotheses. | | [[notes/Domino effect.md\|Domino effect]] | A cumulative chain reaction where one event sets off a sequence of similar events, often used to describe cascading failures. | | [[notes/Double pendulum.md\|Double pendulum]] | A dynamical system of two linked pendulums that exhibits chaotic motion due to sensitivity to initial conditions. | | [[notes/Ergodic theory.md\|Ergodic theory]] | A branch of mathematics that studies the statistical behaviour of dynamical systems over long periods of time. | | [[notes/Ergodicity.md\|Ergodicity]] | A property of a system where time averages and ensemble averages coincide; often contrasted with path‑dependent processes. | | [[notes/Eulerian path.md\|Eulerian path]] | A trail in a graph that visits every edge exactly once. | | [[notes/Feigenbaum constant.md\|Feigenbaum constant]] | A mathematical constant (~4.669) that characterizes the period‑doubling route to chaos in certain dynamical systems. | | [[notes/First-order logic.md\|First-order logic]] | A formal system that allows quantification over individual variables, widely used in mathematics and computer science. | | [[notes/Forking paths problem.md\|Forking paths problem]] | Narrative branching in literature. | | [[notes/Hamiltonian path.md\|Hamiltonian path]] | A path in a graph that visits each vertex exactly once. | | [[notes/Howler.md\|Howler]] | A mathematical fallacy where a correct result is derived by incorrect lines of reasoning. | | [[notes/Inspection paradox.md\|Inspection paradox]] | A probability paradox where sampling tends to overrepresent classes with larger sizes or longer durations. | | [[notes/Intransitivity.md\|Intransitivity]] | The failure of a relation to be transitive, so that if A is related to B and B to C, A may not be related to C. | | [[notes/Kaprekar's constant.md\|Kaprekar's constant]] | The number 6174, which arises as the fixed point of an iterative process of rearranging and subtracting digits in base 10. | | [[notes/Khinchin's constant.md\|Khinchin's constant]] | A mathematical constant (≈2.685) that appears in the geometric mean of the partial quotients of continued fractions. | | [[notes/Klein bottle.md\|Klein bottle]] | A non‑orientable surface with no distinct inside or outside, existing in four-dimensional space. | | [[notes/Langlands program.md\|Langlands program]] | A set of conjectures connecting number theory, representation theory, and geometry, seeking a unified theory of mathematics. | | [[notes/Lipschitz condition.md\|Lipschitz condition]] | The condition that functions change slowly, guaranteeing uniqueness and stability of solutions to differential equations. | | [[notes/Logical connectives.md\|Logical connectives]] | Operators such as AND, OR and NOT used in logic to build compound statements. | | [[notes/Lorenz system.md\|Lorenz system]] | A set of three nonlinear differential equations that exhibit chaotic behavior and produce the famous "butterfly" attractor. | | [[notes/Malkus waterwheel.md\|Malkus waterwheel]] | A mechanical device that demonstrates chaotic behaviour in fluid dynamics and time series. | | [[notes/Markov chain.md\|Markov chain]] | A stochastic process where the probability of each state depends only on the previous state, exhibiting the Markov property. | | [[notes/Mean sojourn time.md\|Mean sojourn time]] | The expected time a stochastic process spends in a given state during an interval. | | [[notes/Möbius strip.md\|Möbius strip]] | A surface with only one side and one boundary, formed by joining the ends of a strip of paper after twisting one end 180 degrees. | | [[notes/Monty Hall problem.md\|Monty Hall problem]] | A game show's probability puzzle that resists intuition. | | [[notes/Multiplication.md\|Multiplication]] | The arithmetic operation of scaling one number by another, one of the four basic operations. | | [[notes/Navier–Stokes equations.md\|Navier–Stokes equations]] | Fundamental partial differential equations that describe the motion of viscous fluid substances like liquids and gases. | | [[notes/Nine Zulu Queens Ruled China.md\|Nine Zulu Queens Ruled China]] | A mnemonic for the nesting of number sets. | | [[notes/Nonlinear system.md\|Nonlinear system]] | A system in which outputs are not directly proportional to inputs and small changes can produce large effects. | | [[notes/Order statistics.md\|Order statistics]] | Statistics derived from the ordered values of a sample, such as the minimum, maximum or median. | | [[notes/Pascal's wager.md\|Pascal's wager]] | A life-defining gamble regarding the belief in the existence of God. | | [[notes/Poincaré map.md\|Poincaré map]] | A method for reducing the dimensionality of a dynamical system. | | [[notes/Poincaré recurrence theorem.md\|Poincaré recurrence theorem]] | A theorem stating that certain systems will, after a sufficiently long time, return arbitrarily close to their initial state. | | [[notes/Probabilistic forecasting.md\|Probabilistic forecasting]] | Predicting future events by assigning probabilities to different outcomes based on data and models. | | [[notes/Proof that 1 = 2.md\|Proof that 1 = 2]] | A classic mathematical example of a falsidical paradox. | | [[notes/Propositional logic.md\|Propositional logic]] | A branch of logic dealing with propositions and their connectives, without internal structure. | | [[notes/Ramanujan summation.md\|Ramanujan summation]] | A method of assigning finite values to divergent series using analytic continuation and regularization techniques. | | [[notes/Reversion to the mean.md\|Reversion to the mean]] | The statistical phenomenon where extreme observations are likely to be followed by more average ones. | | [[notes/Riemann hypothesis.md\|Riemann hypothesis]] | The nontrivial zeros of the Riemann zeta function all lie on the critical line with real part 1/2. | | [[notes/Self-organized criticality.md\|Self-organized criticality]] | A property of dynamical systems that naturally evolve to a critical state where minor events can trigger large responses. | | [[notes/Serendipity.md\|Serendipity]] | The occurrence of beneficial discoveries by chance or accident while seeking something else. | | [[notes/Sierpiński triangle.md\|Sierpiński triangle]] | A fractal composed of an equilateral triangle subdivided recursively into smaller triangles, exhibiting self‑similarity. | | [[notes/Simpson’s paradox.md\|Simpson’s paradox]] | The counter-intuitive disappearance or reversal of a group-level statistical trend once the data are combined. | | [[notes/Smale’s horseshoe.md\|Smale’s horseshoe]] | A mathematical mapping demonstrating chaos, stretching and folding a region like a horseshoe. | | [[notes/The other butterfly effect.md\|The other butterfly effect]] | A variant of the butterfly effect emphasizing that small positive actions can also lead to significant beneficial outcomes. | | [[notes/Three prisoners problem.md\|Three prisoners problem]] | A game theory puzzle that resists intuition. | | [[notes/Transitivity.md\|Transitivity]] | A mathematical property where if A is related to B and B to C, then A is related to C; important in ordering relations. | | [[notes/Twin prime conjecture.md\|Twin prime conjecture]] | The hypothesis that there are infinitely many pairs of prime numbers that differ by two. | | [[notes/White Earth climate.md\|White Earth climate]] | A hypothetical climate state where the Earth becomes entirely ice-covered, reflecting most sunlight and remaining cold. |