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This is a list of paradoxes, grouped thematically. The grouping is approximate, as paradoxes may fit into more than one category. This list collects only scenarios that have been called a paradox by at least one source and have their own article. Although considered paradoxes, some of these are simply based on fallacious reasoning (falsidical), or an unintuitive solution (veridical). Informally, the term paradox is often used to describe a counter-intuitive result.

However, some of these paradoxes qualify to fit into the mainstream perception of a paradox, which is a self-contradictory result gained even while properly applying accepted ways of reasoning. These paradoxes, often called antinomy, point out genuine problems in our understanding of the ideas of truth and description.

Bead sort, also called gravity sort, is a natural sorting algorithm, developed by Joshua J. Arulanandham, Cristian S. Calude and Michael J. Dinneen in 2002, and published in The Bulletin of the European Association for Theoretical Computer Science. Both digital and analog hardware implementations of bead sort can achieve a sorting time of O(n); however, the implementation of this algorithm tends to be significantly slower in software and can only be used to sort lists of positive integers. Also, it would seem that even in the best case, the algorithm requires O(n²) space.

The hairy ball theorem of algebraic topology (sometimes called the hedgehog theorem in Europe) states that there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres. For the ordinary sphere, or 2‑sphere, if f is a continuous function that assigns a vector in R³ to every point p on a sphere such that f(p) is always tangent to the sphere at p, then there is at least one p such that f(p) = 0. The theorem was first stated by Henri Poincaré in the late 19th century, and first proven in 1912 by Luitzen Egbertus Jan Brouwer.

The theorem has been expressed colloquially as "you can't comb a hairy ball flat without creating a cowlick" or "you can't comb the hair on a coconut".

Raku rules are the regular expression, string matching and general-purpose parsing facility of Raku, and are a core part of the language. Since Perl's pattern-matching constructs have exceeded the capabilities of formal regular expressions for some time, Raku documentation refers to them exclusively as regexes, distancing the term from the formal definition.

Raku provides a superset of Perl 5 features with respect to regexes, folding them into a larger framework called rules, which provide the capabilities of a parsing expression grammar, as well as acting as a closure with respect to their lexical scope. Rules are introduced with the rule keyword, which has a usage quite similar to subroutine definitions. Anonymous rules can be introduced with the regex (or rx) keyword, or simply be used inline as regexes were in Perl 5 via the m (matching) or s (substitution) operators.

A necktie, or simply a tie, is a long piece of cloth, worn, usually by men, for decorative purposes around the neck, resting under the shirt collar and knotted at the throat.

Variants include the ascot, bow, bolo, zipper, cravat, and knit. The modern necktie, ascot, and bow tie are descended from the cravat. Neckties are generally unsized, but may be available in a longer size. In some cultures men and boys wear neckties as part of regular office attire or formal wear. Some women wear them as well but usually not as often as men. Neckties can also be worn as part of a uniform (e.g. military, school, waitstaff), whereas some choose to wear them as everyday clothing attire. Neckties are traditionally worn with the top shirt button fastened, and the tie knot resting between the collar points.

The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object. It works by showing that if one randomly chooses objects from a specified class, the probability that the result is of the prescribed kind is strictly greater than zero. Although the proof uses probability, the final conclusion is determined for certain, without any possible error.

This method has now been applied to other areas of mathematics such as number theory, linear algebra, and real analysis, as well as in computer science (e.g. randomized rounding), and information theory.

Déformation professionnelle (French: [defɔʁmasjɔ̃ pʁɔfɛsjɔnɛl], professional deformation or job conditioning) is a tendency to look at things from the point of view of one's own profession or special expertise, rather than from a broader or humane perspective. It is often translated as "professional deformation", though French déformation can also be translated as "distortion". The implication is that professional training, and its related socialization, often result in a distortion of the way one views the world. Nobel laureate Alexis Carrel observed, "Every specialist, owing to a well-known professional bias, believes that he understands the entire human being, while in reality he only grasps a tiny part of him."

As a term in psychology, it was likely coined by the Belgian sociologist Daniel Warnotte or Russian-American sociologist Pitirim Sorokin.

Smeed's Law, named after R. J. Smeed, who first proposed the relationship in 1949, is a purported empirical rule relating traffic fatalities to traffic congestion as measured by the proxy of motor vehicle registrations and country population. The law proposes that increasing traffic volume (an increase in motor vehicle registrations) leads to an increase in fatalities per capita, but a decrease in fatalities per vehicle.

Smeed also predicted that the average speed of traffic in central London would always be nine miles per hour, because that is the minimum speed that people tolerate. He predicted that any intervention intended to speed traffic would only lead to more people driving at this "tolerable" speed unless there were any other disincentives against doing so.

His hypothesis in relation to road traffic safety has been refuted by several authors, who point out that fatalities per person have decreased in many countries, when the "Law" requires that they should increase as long as the number of vehicles per person continues to rise.