Law of large numbers in the context of "Law (mathematics)"

Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event.

Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion).Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability theory describing such behaviour are the law of large numbers and the central limit theorem.

Asteroid impact avoidance encompasses the methods by which near-Earth objects (NEO) on a potential collision course with Earth could be diverted, preventing destructive impact events. An impact by a sufficiently large asteroid or other NEOs would cause, depending on its impact location, massive tsunamis or multiple firestorms, and an impact winter caused by the sunlight-blocking effect of large quantities of pulverized rock dust and other debris placed into the stratosphere. A collision 66 million years ago between the Earth and an object approximately 10 kilometers (6 miles) wide is thought to have produced the Chicxulub crater and triggered the Cretaceous–Paleogene extinction event that is understood by the scientific community to have caused the extinction of all non-avian dinosaurs.

While the chances of a major collision are low in the near term, it is a near-certainty that one will happen eventually unless defensive measures are taken. Astronomical events—such as the Shoemaker-Levy 9 impacts on Jupiter and the 2013 Chelyabinsk meteor, along with the growing number of near-Earth objects discovered and catalogued on the Sentry Risk Table—have drawn renewed attention to such threats. The popularity of the 2021 movie Don't Look Up helped to raise awareness of the possibility of avoiding NEOs. Awareness of the threat has grown rapidly during the past few decades, but much more needs to be accomplished before the human population can feel adequately protected from a potentially catastrophic asteroid impact.

Jacob Bernoulli (also known as James in English or Jacques in French; 6 January 1655 [O.S. 27 December 1654] – 16 August 1705) was a Swiss mathematician. He sided with Gottfried Wilhelm Leibniz during the Leibniz–Newton calculus controversy and was an early proponent of Leibnizian calculus, to which he made numerous contributions. A member of the Bernoulli family, he, along with his brother Johann, was one of the founders of the calculus of variations. He also discovered the fundamental mathematical constant e. However, his most important contribution was in the field of probability, where he derived the first version of the law of large numbers in his work Ars Conjectandi.

Andrey Andreyevich Markov (14 June [O.S. 2 June] 1856 – 20 July 1922) was a Russian mathematician celebrated for his pioneering work in stochastic processes. He extended foundational results—such as the law of large numbers and the central limit theorem—to sequences of dependent random variables, laying the groundwork for what would become known as Markov chains. To illustrate his methods, he analyzed the distribution of vowels and consonants in Alexander Pushkin's Eugene Onegin, treating letters purely as abstract categories and stripping away any poetic or semantic content.

He was also a strong chess player.