Jean-Baptiste le Rond d'Alembert (; ; 16 November 1717 – 29 October 1783) was a French mathematician,

mechanician A mechanician is an engineer or a scientist working in the field of mechanics, or in a related or sub-field: engineering or computational mechanics, applied mechanics, geomechanics, biomechanics, and mechanics of materials. Names other than mechan ...

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate ca ...

, philosopher, and

music theorist Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the " rudiments", that are needed to understand music notation (k ...

. Until 1759 he was, together with

Denis Diderot Denis Diderot (; ; 5 October 171331 July 1784) was a French philosopher, art critic, and writer, best known for serving as co-founder, chief editor, and contributor to the ''Encyclopédie'' along with Jean le Rond d'Alembert. He was a promine ...

, a co-editor of the ''

Encyclopédie ''Encyclopédie, ou dictionnaire raisonné des sciences, des arts et des métiers'' (English: ''Encyclopedia, or a Systematic Dictionary of the Sciences, Arts, and Crafts''), better known as ''Encyclopédie'', was a general encyclopedia publis ...

''.

D'Alembert's formula In mathematics, and specifically partial differential equations (PDEs), d'Alembert's formula is the general solution to the one-dimensional wave equation u_(x,t) = c^2 u_(x,t) (where subscript indices indicate partial differentiation, using the d' ...

for obtaining solutions to the

wave equation The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and s ...

is named after him. The wave equation is sometimes referred to as

d'Alembert's equation In mathematics, d'Alembert's equation is a first order nonlinear ordinary differential equation, named after the French mathematician Jean le Rond d'Alembert Jean-Baptiste le Rond d'Alembert (; ; 16 November 1717 – 29 October 1783) was a F ...

, and the

fundamental theorem of algebra The fundamental theorem of algebra, also known as d'Alembert's theorem, or the d'Alembert–Gauss theorem, states that every non- constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomia ...

is named after d'Alembert in French.

Early years

Born in Paris, d'Alembert was the

natural son Legitimacy, in traditional Western common law, is the status of a child born to parents who are legally married to each other, and of a child conceived before the parents obtain a legal divorce. Conversely, ''illegitimacy'', also known as '' ...

of the writer

Claudine Guérin de Tencin Claudine Alexandrine Guérin de Tencin, Baroness of Saint-Martin-de-Ré (27 April 1682 – 4 December 1749) was a French salonist and author. She was the mother of Jean le Rond d'Alembert, who later became a prominent mathematician, ''philosophe' ...

and the chevalier Louis-Camus Destouches, an

artillery Artillery is a class of heavy military ranged weapons that launch munitions far beyond the range and power of infantry firearms. Early artillery development focused on the ability to breach defensive walls and fortifications during sieg ...

officer. Destouches was abroad at the time of d'Alembert's birth. Days after birth his mother left him on the steps of the church. According to custom, he was named after the

patron saint A patron saint, patroness saint, patron hallow or heavenly protector is a saint who in Catholic Church, Catholicism, Anglicanism, or Eastern Orthodoxy is regarded as the heavenly advocacy, advocate of a nation, place, craft, activity, class, ...

of the church. D'Alembert was placed in an

orphanage An orphanage is a residential institution, total institution or group home, devoted to the care of orphans and children who, for various reasons, cannot be cared for by their biological families. The parents may be deceased, absent, or abu ...

for

foundling Foundling may refer to: * An abandoned child, see child abandonment * Foundling hospital, an institution where abandoned children were cared for ** Foundling Hospital, Dublin, founded 1704 ** Foundling Hospital, Cork, founded 1737 ** Foundling Hos ...

children, but his father found him and placed him with the wife of a

glazier A glazier is a tradesman responsible for cutting, installing, and removing glass (and materials used as substitutes for glass, such as some plastics).Elizabeth H. Oakes, ''Ferguson Career Resource Guide to Apprenticeship Programs'' ( Infobase ...

, Madame Rousseau, with whom he lived for nearly 50 years. She gave him little encouragement. When he told her of some discovery he had made or something he had written she generally replied, Destouches secretly paid for the education of Jean le Rond, but did not want his paternity officially recognised.

Studies and adult life

D'Alembert first attended a private school. The chevalier Destouches left d'Alembert an

annuity In investment, an annuity is a series of payments made at equal intervals.Kellison, Stephen G. (1970). ''The Theory of Interest''. Homewood, Illinois: Richard D. Irwin, Inc. p. 45 Examples of annuities are regular deposits to a savings account, m ...

of 1200

livres The (; ; abbreviation: ₶.) was one of numerous currencies used in medieval France, and a unit of account (i.e., a monetary unit used in accounting) used in Early Modern France. The 1262 monetary reform established the as 20 , or 80.88 ...

on his death in 1726. Under the influence of the Destouches family, at the age of 12 d'Alembert entered the

Jansenist Jansenism was an early modern theological movement within Catholicism, primarily active in the Kingdom of France, that emphasized original sin, human depravity, the necessity of divine grace, and predestination. It was declared a heresy by t ...

Collège des Quatre-Nations The Collège des Quatre-Nations ("College of the Four Nations"), also known as the Collège Mazarin after its founder, was one of the colleges of the historic University of Paris. It was founded through a bequest by the Cardinal Mazarin. At his d ...

(the institution was also known under the name "Collège Mazarin"). Here he studied philosophy, law, and the arts, graduating as '' baccalauréat en arts'' in 1735. In his later life, d'Alembert scorned the Cartesian principles he had been taught by the

Jansenists Jansenism was an early modern theological movement within Catholicism, primarily active in the Kingdom of France, that emphasized original sin, human depravity, the necessity of divine grace, and predestination. It was declared a heresy by th ...

: "physical promotion, innate ideas and the vortices". The Jansenists steered d'Alembert toward an

ecclesiastical {{Short pages monitor