Abraham de Moivre lived a life defined by displacement and intellectual rigor. Born in Vitry, France, on May 26, 1667, he would eventually die in London on November 27, 1754. He was not just a mathematician. He was a pioneer. His work laid the groundwork for analytic trigonometry and, more significantly, modern probability theory.<\/p>\n
His early life was fractured by political and religious turmoil. A French Huguenot, de Moivre faced imprisonment when the Edict of Nantes was revoked in 1685. The revocation targeted Protestants. After a brief stint in jail, he fled to England. The journey changed everything.<\/p>\n
In London, he did not find riches. He found community. He became close friends with Sir Isaac Newton and the astronomer Edmond Halley. This network earned him a seat at the Royal Society of London in 1697. He was later elected to the Berlin and Paris academies. These were high honors. Yet, they did not bring financial stability.<\/p>\n
De Moivre struggled to secure a permanent academic position. He survived as a tutor. He also consulted on gambling and insurance. This practical experience with risk and chance deeply influenced his later work. He understood probability not as abstract theory, but as a tool for understanding real-world uncertainty.<\/p>\n
His first major contribution to the field came from a paper titled “De mensura sortis,” written in 1711. It appeared in Philosophical Transactions<\/em>. He expanded this paper into a book called The Doctrine of Chances<\/em> in 1718.<\/p>\n Probability theory had previous roots. Blaise Pascal and Pierre de Fermat began the conversation with unpublished correspondence in 1654. Christiaan Huygens of Holland published De Ratiociniis in Ludo Aleae<\/em> in 1657. These works focused on dice games. De Moivre took these foundations and expanded them significantly.<\/p>\n One of the most critical concepts in The Doctrine of Chances<\/em> was the definition of statistical independence. De Moivre stated that the probability of a compound event is the product of the probabilities of its components. This rule applies when those events are statistically independent.<\/p>\n This definition remains a cornerstone of probability today. It is how we calculate the likelihood of multiple independent events occurring together.<\/p>\n His book also included many problems related to dice and other games. Some of these problems had appeared in Ars conjectandi<\/em> by Jakob Bernoulli in 1713. Bernoulli\u2019s work was published before de Moivre\u2019s book but after his earlier paper. De Moivre did not merely repeat these problems. He approached them differently.<\/p>\n He derived the principles of probability from the mathematical expectation of events. This was the reverse of current practice. Today, we often start with axioms of probability and derive expectation. De Moivre started with expectation and worked backward to probability.<\/p>\n His second major work was Miscellanea Analytica<\/em> in 1730. This text marked another leap forward. De Moivre was the first to use the probability integral where the integrand is the exponential of a negative quadratic.<\/p>\n This mathematical tool would become essential in later developments of statistics. It allowed for more precise calculations involving normal distributions. While the full implications of this integral would unfold in subsequent centuries, de Moivre<\/p>\n Abraham de Moivre did more than just tinker with numbers. He essentially invented the approximation for factorials that bears James Stirling\u2019s name, despite the misattribution. For large values of n<\/em>, the formula estimates n<\/em>! using the square root of 2\u03c0n<\/em> multiplied by e<\/em> raised to the negative n<\/em> power and n<\/em> to the n<\/em> th power.<\/p>\n This wasn\u2019t just abstract math. In 1733, de Moivre applied this factorial approximation to derive the normal frequency curve. He used it to approximate the binomial law, bridging the gap between discrete counting and continuous probability.<\/p>\n De Moivre was also a pioneer in using complex numbers for trigonometric functions. He developed the identity that now carries his name: (cos x<\/em> + i<\/em> sin x<\/em> )n<\/em> = cos nx<\/em> + i<\/em> sin nx<\/em>.<\/p>\n This formula shifted trigonometry away from pure geometry and into analysis. It allowed mathematicians to treat angles and rotations through algebraic manipulation rather than just geometric construction.<\/p>\n","protected":false},"excerpt":{"rendered":" Abraham de Moivre lived a life defined by displacement and intellectual rigor. Born in Vitry, France, on May 26, 1667, he would eventually die in London on November 27, 1754. He was not just a mathematician. He was a pioneer. His work laid the groundwork for analytic trigonometry and, more significantly, modern probability theory. His […]<\/p>\n","protected":false},"author":1,"featured_media":8100,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":""},"categories":[50],"tags":[],"wpm_language_slugs":{"cs":"jak-abraham-de-moivre-definoval-teorii-pravdepodobnosti-v-18-stoleti","de":"wie-abraham-de-moivre-die-wahrscheinlichkeitstheorie-im-18-jahrhundert","en":"how-abraham-de-moivre-defined-probability-theory-in-the-18th-century","es":"como-abraham-de-moivre-definio-la-teoria-de-la-probabilidad-en-el","fr":"comment-abraham-de-moivre-a-defini-la-theorie-des-probabilites-au","id":"bagaimana-abraham-de-moivre-mendefinisikan-teori-probabilitas-di","it":"come-abraham-de-moivre-defini-la-teoria-della-probabilita-nel-xviii","nl":"hoe-abraham-de-moivre-de-waarschijnlijkheidstheorie-in-de-18e-eeuw","pl":"jak-abraham-de-moivre-zdefiniowal-teorie-prawdopodobienstwa-w-xviii","pt":"como-abraham-de-moivre-definiu-a-teoria-da-probabilidade-no-seculo","ru-ru":"kak-abraham-de-muavr-opredelil-teoriju-verojatnostej-v-xviii-veke","uk-ua":"prihovana-spadschina-de-muavra-v-matematichnomu-analizi-ta"},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.schooler.org.ua\/en\/wp-json\/wp\/v2\/posts\/8101"}],"collection":[{"href":"https:\/\/www.schooler.org.ua\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.schooler.org.ua\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.schooler.org.ua\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.schooler.org.ua\/en\/wp-json\/wp\/v2\/comments?post=8101"}],"version-history":[{"count":0,"href":"https:\/\/www.schooler.org.ua\/en\/wp-json\/wp\/v2\/posts\/8101\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.schooler.org.ua\/en\/wp-json\/wp\/v2\/media\/8100"}],"wp:attachment":[{"href":"https:\/\/www.schooler.org.ua\/en\/wp-json\/wp\/v2\/media?parent=8101"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.schooler.org.ua\/en\/wp-json\/wp\/v2\/categories?post=8101"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.schooler.org.ua\/en\/wp-json\/wp\/v2\/tags?post=8101"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Defining Statistical Independence<\/h3>\n
Analytical Innovations<\/h3>\n
From Geometry to Analysis via Complex Numbers<\/h3>\n