Hint: You are looking at the most popular articles. If you are interested in popular topics instead, click here.

The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later. It is constructed by writing the positive integers in a square spiral and specially marking the prime numbers.

Ulam and Gardner emphasized the striking appearance in the spiral of prominent diagonal, horizontal, and vertical lines containing large numbers of primes. Both Ulam and Gardner noted that the existence of such prominent lines is not unexpected, as lines in the spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler's prime-generating polynomial x² − x + 41, are believed to produce a high density of prime numbers. Nevertheless, the Ulam spiral is connected with major unsolved problems in number theory such as Landau's problems. In particular, no quadratic polynomial has ever been proved to generate infinitely many primes, much less to have a high asymptotic density of them, although there is a well-supported conjecture as to what that asymptotic density should be.

In 1932, more than thirty years prior to Ulam's discovery, the herpetologist Laurence Klauber constructed a triangular, non-spiral array containing vertical and diagonal lines exhibiting a similar concentration of prime numbers. Like Ulam, Klauber noted the connection with prime-generating polynomials, such as Euler's.

Bardcore (from the Celtic-origin word “bard” meaning ‘poet’ or ‘storyteller’) or tavernwave is a 2020 internet phenomenon consisting of medievalised remakes of hit pop songs.

This list of the oldest companies in the world includes brands and companies, excluding associations and educational, government, or religious organizations. To be listed, a brand or company name must remain operating, either in whole or in part, since inception. Note however that such claims are often open to question and should be researched further before citing them.

Potoooooooo or variations of Pot-8-Os (1773 – November 1800) was an 18th-century thoroughbred racehorse who won over 30 races and defeated some of the greatest racehorses of the time. He went on to be a sire. He is now best known for the unusual spelling of his name, pronounced 'Potatoes'.

TLA⁺ is a formal specification language developed by Leslie Lamport. It is used to design, model, document, and verify programs, especially concurrent systems and distributed systems. TLA⁺ has been described as exhaustively-testable pseudocode, and its use likened to drawing blueprints for software systems; TLA is an acronym for Temporal Logic of Actions.

For design and documentation, TLA⁺ fulfills the same purpose as informal technical specifications. However, TLA⁺ specifications are written in a formal language of logic and mathematics, and the precision of specifications written in this language is intended to uncover design flaws before system implementation is underway.

Since TLA⁺ specifications are written in a formal language, they are amenable to finite model checking. The model checker finds all possible system behaviours up to some number of execution steps, and examines them for violations of desired invariance properties such as safety and liveness. TLA⁺ specifications use basic set theory to define safety (bad things won't happen) and temporal logic to define liveness (good things eventually happen).

TLA⁺ is also used to write machine-checked proofs of correctness both for algorithms and mathematical theorems. The proofs are written in a declarative, hierarchical style independent of any single theorem prover backend. Both formal and informal structured mathematical proofs can be written in TLA⁺; the language is similar to LaTeX, and tools exist to translate TLA⁺ specifications to LaTeX documents.

TLA⁺ was introduced in 1999, following several decades of research into a verification method for concurrent systems. A toolchain has since developed, including an IDE and distributed model checker. The pseudocode-like language PlusCal was created in 2009; it transpiles to TLA⁺ and is useful for specifying sequential algorithms. TLA⁺² was announced in 2014, expanding language support for proof constructs. The current TLA⁺ reference is The TLA⁺ Hyperbook by Leslie Lamport.

Bullshit Jobs: A Theory is a 2018 book by anthropologist David Graeber that argues the existence and societal harm of meaningless jobs. He contends that over half of societal work is pointless, which becomes psychologically destructive when paired with a work ethic that associates work with self-worth. Graeber describes five types of meaningless jobs, in which workers pretend their role is not as pointless or harmful as they know it to be: flunkies, goons, duct tapers, box tickers, and taskmasters. He argues that the association of labor with virtuous suffering is recent in human history, and proposes universal basic income as a potential solution.

The book is an extension of a popular essay Graeber published in 2013, which was later translated into 12 languages and whose underlying premise became the subject of a YouGov poll. Graeber subsequently solicited hundreds of testimonials of meaningless jobs and revised his case into a book that was published by Simon & Schuster in May 2018.

In mathematics, 0.999... (also written as 0.9, among other ways) denotes the repeating decimal consisting of infinitely many 9s after the decimal point (and one 0 before it). This repeating decimal represents the smallest number no less than every decimal number in the sequence (0.9, 0.99, 0.999, ...). This number is equal to 1. In other words, "0.999..." and "1" represent the same number. There are many ways of showing this equality, from intuitive arguments to mathematically rigorous proofs. The technique used depends on the target audience, background assumptions, historical context, and preferred development of the real numbers, the system within which 0.999... is commonly defined. (In other systems, 0.999... can have the same meaning, a different definition, or be undefined.)

More generally, every nonzero terminating decimal has two equal representations (for example, 8.32 and 8.31999...), which is a property of all base representations. The utilitarian preference for the terminating decimal representation contributes to the misconception that it is the only representation. For this and other reasons—such as rigorous proofs relying on non-elementary techniques, properties, or disciplines—some people can find the equality sufficiently counterintuitive that they question or reject it. This has been the subject of several studies in mathematics education.

The Norwegian butter crisis began in late 2011 with an acute shortage of butter and inflation of its price across markets in Norway. The shortage caused soaring prices and stores' stocks of butter ran out within minutes of deliveries. According to the Danish tabloid B.T., Norway was gripped by smør-panik ("butter panic") as a result of the butter shortage.

The two capacitor paradox or capacitor paradox is a paradox, or counterintuitive thought experiment, in electric circuit theory. The thought experiment is usually described as follows: Two identical capacitors are connected in parallel with an open switch between them. One of the capacitors is charged with a voltage of ${\displaystyle V_{i}}$, the other is uncharged. When the switch is closed, some of the charge ${\displaystyle Q=CV_{i}}$ on the first capacitor flows into the second, reducing the voltage on the first and increasing the voltage on the second. When a steady state is reached and the current goes to zero, the voltage on the two capacitors must be equal since they are connected together. Since they both have the same capacitance ${\displaystyle C}$ the charge will be divided equally between the capacitors so each capacitor will have a charge of ${\displaystyle {Q \over 2}}$ and a voltage of ${\displaystyle V_{f}={Q \over 2C}={V_{i} \over 2}}$. At the beginning of the experiment the total initial energy ${\displaystyle W_{i}}$ in the circuit is the energy stored in the charged capacitor:

${\displaystyle W_{i}={1 \over 2}CV_{i}^{2}}$.

At the end of the experiment the final energy ${\displaystyle W_{f}}$ is equal to the sum of the energy in the two capacitors

${\displaystyle W_{f}={1 \over 2}CV_{f}^{2}+{1 \over 2}CV_{f}^{2}=CV_{f}^{2}=C({V_{i} \over 2})^{2}={1 \over 4}CV_{i}^{2}={1 \over 2}W_{i}}$

Thus the final energy ${\displaystyle W_{f}}$ is equal to half of the initial energy ${\displaystyle W_{i}}$. Where did the other half of the initial energy go?