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The Basel problem is a problem in mathematical analysis with relevance to number theory, first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. Since the problem had withstood the attacks of the leading mathematicians of the day, Euler's solution brought him immediate fame when he was twenty-eight. Euler generalised the problem considerably, and his ideas were taken up years later by Bernhard Riemann in his seminal 1859 paper "On the Number of Primes Less Than a Given Magnitude", in which he defined his zeta function and proved its basic properties. The problem is named after Basel, hometown of Euler as well as of the Bernoulli family who unsuccessfully attacked the problem.

The Basel problem asks for the precise summation of the reciprocals of the squares of the natural numbers, i.e. the precise sum of the infinite series:

${\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n^{2}}}={\frac {1}{1^{2}}}+{\frac {1}{2^{2}}}+{\frac {1}{3^{2}}}+\cdots .}$

The sum of the series is approximately equal to 1.644934. The Basel problem asks for the exact sum of this series (in closed form), as well as a proof that this sum is correct. Euler found the exact sum to be π²/6 and announced this discovery in 1735. His arguments were based on manipulations that were not justified at the time, although he was later proven correct, and it was not until 1741 that he was able to produce a truly rigorous proof.

In computing, a fork bomb (also called rabbit virus or wabbit) is a denial-of-service attack wherein a process continually replicates itself to deplete available system resources, slowing down or crashing the system due to resource starvation.

Swarm intelligence (SI) is the collective behavior of decentralized, self-organized systems, natural or artificial. The concept is employed in work on artificial intelligence. The expression was introduced by Gerardo Beni and Jing Wang in 1989, in the context of cellular robotic systems.

SI systems consist typically of a population of simple agents or boids interacting locally with one another and with their environment. The inspiration often comes from nature, especially biological systems. The agents follow very simple rules, and although there is no centralized control structure dictating how individual agents should behave, local, and to a certain degree random, interactions between such agents lead to the emergence of "intelligent" global behavior, unknown to the individual agents. Examples of swarm intelligence in natural systems include ant colonies, bird flocking, hawks hunting, animal herding, bacterial growth, fish schooling and microbial intelligence.

The application of swarm principles to robots is called swarm robotics, while 'swarm intelligence' refers to the more general set of algorithms. 'Swarm prediction' has been used in the context of forecasting problems. Similar approaches to those proposed for swarm robotics are considered for genetically modified organisms in synthetic collective intelligence.

Longcat (2002 – 20 September 2020) was a Japanese domestic cat that became the subject of an Internet meme due to her length. Longcat, whose real name was "Shiroi", was born in 2002. An image depicting her being held with "outstretched paws" became popular on Japanese imageboard Futaba Channel, where it was nicknamed "Nobiko" ("Stretch" in Japanese) some time around 2005 or 2006. She was reportedly 65 centimetres (26 in) "from head to toe".

Subsequently, the meme spread to English-language websites, primarily 4chan's /b/, where it was edited into various images, and even had a song written about it. A backstory was invented for the cat, involving a world-ending battle called "Catnarok" with a nemesis named "Tacgnol" (resembling Longcat with the colors inverted).

The virtual community and message board Subeta, which made available a number of pixel art virtual accessories for user avatars, briefly introduced a "Longcat scarf" in 2007; this prompted "a legion of internet users to attack Subeta", primarily in the form of a DDoS campaign involving "all of the chans", until the Longcat item was removed later in the month. A Pokémon design released in 2019, the "Gigantamax Meowth", was compared by some commentators to Longcat.

In a 2019 interview, Longcat's owner said that the cat was "originally rescued after being discovered on the street in 2002", and at the time was thin with gray hair; as she grew older, she became white and fluffy. The cat was deaf. In 2019, Longcat's owner said that, at the age of 17, the cat no longer "climbed to high places" but was "relaxing and living her life".

In September 2020, after a period of ill health, Longcat was taken to the hospital, and died at the age of 18.

Windy City Heat is a made-for-TV reality film produced by Comedy Central. It first aired on October 12, 2003.

The Northeast blackout of 2003 was a widespread power outage throughout parts of the Northeastern and Midwestern United States, and the Canadian province of Ontario on August 14–28, 2003, beginning just after 4:10 p.m. EDT.

Some power was restored by 11 p.m. Most did not get their power back until two days later. In other areas, it took nearly a week or two for power to be restored. At the time, it was the world's second most widespread blackout in history, after the 1999 Southern Brazil blackout. The outage, which was much more widespread than the Northeast blackout of 1965, affected an estimated 10 million people in southern and central Ontario, and 45 million people in eight U.S. states.

The blackout's proximate cause was a software bug in the alarm system at the control room of FirstEnergy, an Akron, Ohio–based company, which rendered operators unaware of the need to redistribute load after overloaded transmission lines drooped into foliage. What should have been a manageable local blackout cascaded into the collapse of the entire Northeast region.

An esoteric programming language (sometimes shortened to esolang) is a programming language designed to test the boundaries of computer programming language design, as a proof of concept, as software art, as a hacking interface to another language (particularly functional programming or procedural programming languages), or as a joke. The use of esoteric distinguishes these languages from programming languages that working developers use to write software. Usually, an esolang's creators do not intend the language to be used for mainstream programming, although some esoteric features, such as visuospatial syntax, have inspired practical applications in the arts. Such languages are often popular among hackers and hobbyists.

Usability is rarely a goal for esoteric programming language designers—often the design leads to quite the opposite. Their usual aim is to remove or replace conventional language features while still maintaining a language that is Turing-complete, or even one for which the computational class is unknown.

In Western art history, Mise en abyme (French pronunciation: ​[miz ɑ̃n‿abim]; also mise en abîme) is a formal technique of placing a copy of an image within itself, often in a way that suggests an infinitely recurring sequence. In film theory and literary theory, it refers to the technique of inserting a story within a story. The term is derived from heraldry and literally means "placed into abyss". It was first appropriated for modern criticism by the French author André Gide.

A common sense of the phrase is the visual experience of standing between two mirrors, seeing as a result an infinite reproduction of one's image. Another is the Droste effect, in which a picture appears within itself, in a place where a similar picture would realistically be expected to appear. That is named after the 1904 Droste cocoa package, which depicts a woman holding a tray bearing a Droste cocoa package, which bears a smaller version of her image.

A mathematical coincidence is said to occur when two expressions with no direct relationship show a near-equality which has no apparent theoretical explanation.

For example, there is a near-equality close to the round number 1000 between powers of 2 and powers of 10:

${\displaystyle 2^{10}=1024\approx 1000=10^{3}.}$

Some mathematical coincidences are used in engineering when one expression is taken as an approximation of another.