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 m ...

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 cau ...

, philosopher, and

music theorist Music theory is the study of theoretical frameworks for understanding 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 ...

. 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 along with Jean le Rond d'Alembert. He was a prominent figure during th ...

, a co-editor of the ''

Encyclopédie , better known as ''Encyclopédie'' (), was a general encyclopedia published in France between 1751 and 1772, with later supplements, revised editions, and translations. It had many writers, known as the Encyclopédistes. It was edited by Denis ...

''.

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_-c^2u_=0,\, u(x,0)=g(x),\, u_t(x,0)=h(x), for -\infty < x<\infty,\,\, t>0 It ...

for obtaining solutions to the

wave equation The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light ...

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

d'Alembert's equation In mathematics, d'Alembert's equation, sometimes also known as Lagrange'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 ( ...

, and the

fundamental theorem of algebra The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant polynomial, constant single-variable polynomial with Complex number, complex coefficients has at least one comp ...

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 marriage, married to each other, and of a child Fertilisation, conceived before the parents obtain a legal divorce. Conversely, ''illegitim ...

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 Salon (gathering), salonist and author. She was the mother of Jean le Rond d'Alembert, who later became a prominent mathemat ...

and the chevalier Louis-Camus Destouches, an

artillery Artillery consists of ranged weapons that launch Ammunition, munitions far beyond the range and power of infantry firearms. Early artillery development focused on the ability to breach defensive walls and fortifications during sieges, and l ...

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 Catholicism, Anglicanism, Eastern Orthodoxy or Oriental Orthodoxy is regarded as the heavenly advocate of a nation, place, craft, activity, class, clan, fa ...

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 by their biological families. The parents may be deceased, absent, or abusi ...

for

foundling Foundling or The Foundling may refer to: Places * Foundling hospital, an institution where abandoned children were cared for ** Foundling Hospital, Dublin, founded 1704 ** Foundling Hospital, Cork, founded 1737 ** Foundling Hospital, founded 17 ...

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

glazier A glazier is a tradesperson 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'' ( Infoba ...

, 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 Paternity may refer to: *Father, the male parent of a (human) child *Paternity (law), fatherhood as a matter of law * ''Paternity'' (film), a 1981 comedy film starring Burt Reynolds * "Paternity" (''House''), a 2004 episode of the television seri ...

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 based on a contract with a lump sum of money. Insurance companies are common annuity providers and are used by clients for things like retirement or death benefits. Examples ...

of 1,200

livres Livre may refer to: Currency * French livre, one of a number of obsolete units of currency of France * Livre tournois, one particular obsolete unit of currency of France * Livre parisis, another particular obsolete unit of currency of France * F ...

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

Jansenist Jansenism was a 17th- and 18th-century theological movement within Roman Catholicism, primarily active in France, which arose as an attempt to reconcile the theological concepts of free will and divine grace in response to certain development ...

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 ...

(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 a 17th- and 18th-century theological movement within Roman Catholicism, primarily active in France, which arose as an attempt to reconcile the theological concepts of free will and divine grace in response to certain development ...

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

ecclesiastical {{Short pages monitor