Abraham De Moivre

Abraham De Moivre (1667-1754) was a French-born mathematician who made significant contributions to analytic geometry, probability theory, and mathematics of annuities. After fleeing religious persecution in France, he spent most of his career in England where he became a prominent member of scientific circles that included Isaac Newton and Edmond Halley. De Moivre is best known for De Moivre's formula, which establishes the relationship between complex numbers and trigonometry, and his work on the normal distribution and probability theory. His book "The Doctrine of Chances" (1718) laid important groundwork for modern probability theory and its applications. His developments in probability included the theory of recurring series, methods of approximating certain sums, and the discovery of the theory of annuities. The normal distribution's mathematical properties were first discovered by De Moivre as a close approximation to the binomial distribution. De Moivre worked as a tutor of mathematics throughout his life, earning a modest living while pursuing his theoretical work. Despite financial hardship, he produced influential mathematical works that would later prove foundational to statistics, probability theory, and actuarial science.

Reader reviews and commentary on De Moivre's works focus primarily on his mathematical texts, especially "The Doctrine of Chances." Academic readers cite the clear presentation of probability concepts and practical examples that made complex ideas accessible to 18th-century audiences. Mathematics historians praise his methodical development of probability theory through gambling problems. Some readers note the challenging nature of the original texts for modern readers due to outdated language and notation. The lack of modern translations or annotated editions makes his works less accessible to non-specialists. No ratings exist on major review platforms like Goodreads or Amazon for De Moivre's original works. His mathematical concepts appear mainly in academic papers and modern textbooks that reference his contributions. Students occasionally review these textbook sections, noting that while the underlying ideas are fundamental, the historical presentation requires additional context to fully grasp. Most reader discussion appears in academic journals and mathematics forums rather than consumer review sites.

De Mensura Sortis (1711) First major work establishing probability theory as a mathematical discipline, focusing on probability in games of chance.

Doctrine of Chances (1718) Comprehensive treatise on probability theory and its applications, introducing methods for calculating probabilities of compound events.

Miscellanea Analytica de Seriebus et Quadraturis (1730) Mathematical work containing the derivation of Stirling's approximation and developments in infinite series.

Annuities upon Lives (1725) Technical analysis of life insurance and annuity calculations, introducing mortality tables and actuarial mathematics.

The Analytic Method of Drawing General Conclusions from Particular Cases (1733) Paper presenting mathematical induction principles and methods for generalizing mathematical patterns.

A Method of Approximating the Sum of the Terms of the Binomial (a+b)n Expanded into a Series (1733) Mathematical paper introducing what became known as the normal distribution approximation to the binomial distribution.

Pierre-Simon Laplace developed probability theory and statistical methods that built upon De Moivre's work. His contributions to mathematical astronomy and the nebular hypothesis connect with De Moivre's interest in applying probability to real-world problems.

Jacob Bernoulli established fundamental concepts in probability theory and wrote "Ars Conjectandi" which influenced De Moivre's approach. His work on infinite series and the law of large numbers shares mathematical foundations with De Moivre's investigations.

Thomas Bayes focused on inverse probability and conditional probability theory, extending concepts De Moivre explored. His theorem became a cornerstone of statistical inference and probability theory.

Leonard Euler worked on infinite series and developed mathematical notation that clarified concepts De Moivre studied. His contributions to mathematical analysis and number theory overlap with De Moivre's mathematical interests.

Joseph Louis Lagrange advanced calculus and analytical mechanics using mathematical techniques similar to De Moivre's methods. His work on differential equations and probability theory connects with De Moivre's mathematical legacy.